• WK seminar

In massively collaborative projects such as scientific or community databases, users often need to agree or disagree on the content of individual data items. On the other hand, trust relationships often exist between users, allowing them to accept or reject other users' beliefs by default. As those trust relationships become complex, however, it becomes difficult to define and compute a consistent snapshot of the conflicting information. Previous solutions to a related problem, the update reconciliation problem, are dependent on the order in which the updates are processed and, therefore, do not guarantee a globally consistent snapshot. This paper proposes the first principled solution to the automatic conflict resolution problem in a community database. Our semantics is based on the certain tuples of all stable models of a logic program. While evaluating stable models in general is well known to be hard, even for very simple logic programs, we show that the conflict resolution problem admits a PTIME solution. To the best of our knowledge, ours is the first PTIME algorithm that allows conflict resolution in a principled way. We further discuss extensions to negative beliefs and prove that some of these extensions are hard. This work is done in the context of the BeliefDB project at the University of Washington, which focuses on the efficient management of conflicts in community databases. PROJECT WEB PAGE http://db.cs.washington.edu/beliefDB/

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

• Event: "Enjeux de Modélisation et Analyse Liés aux Problèmes de Surfaces Rugueuses et de Défauts" (2010)

We consider a model describing an experimental setting, in which locusts run in a ring-shaped arena. With intermediate spatial density of the individuals, coherent motion is observed, interrupted by sudden changes of direction ("switching"). Contrary to the known model of Czirok and Vicsek, our model assumes runs of the individuals in either positive or negative direction of the 1D arena with the same speed, that are subject to random switches. As supported by experimental evidence, the individual switching frequency increases in response to a local or global loss of group alignment, which constitutes a mechanism to increase the coherence of the group. We show that our individual based model, although phenomenologically very simple, exhibits nontrivial dynamics with a "phase change" behaviour, and, in particular, recovers the observed group directional switching. Passing to the corresponding Fokker-Planck equation, we are able to give estimates of the expected switching times in terms of number of individuals and values of the model coefficients. Then we pass to the kinetic description, recovering a system of two kinetic equations with nonlocal and nonlinear right hand sides, which is valid when the number of individuals tends to infinity. We perform a mathematical analysis of the system, show some numerical results and point out several interesting open problems.

• WK seminar

Database transformations provide a unifying view for queries and updates, the two fundamental types of computations in any databases capturing the capability to retrieve and update data. The integration of queries and updates has always been a research challenge in database theory. The emerging new application areas such as web-based systems and service-oriented architectures have further increased the importance of this problem. Recently, it was shown that non-deterministic database transformations can be captured exactly by a variant of Abstract State Machines (ASMs), the so-called Database Abstract State Machines (DB-ASMs). In this talk I will present a logic for DB-ASMs. in spite of bounded non-determinism permitted by DB-ASMs, the logic for DB-ASMs is proven to be sound and complete when the logic of meat-finite states is parameterised by the first-order logic. This is due to the finiteness condition stipulated on the database part of a state of database transformations, which thereby leads to the finiteness of update sets and multisets in one-step transitions. We can then formalise non-determinism of DB-ASMs by utilising a modal operator [] for an update set of multiset generated by a DB-ASM rule. The logic for DB-ASMs lies down a solid foundation for developing verification techniques to study the properties of database transformations in various data-intensive applications.

• Thematic program: Databases and Ontologies in Advanced Information Systems (DATA-09-Prolongation) (2009 Prolongation into 2010)

• Thematic program: Quantum many-body systems and NLS approximations: experiments and simulations (QUANTUM-09-Prolongation) (2009 Prolongation into 2010)

Motivated by the Helmholtz EVP within the random laser theory, we focus on the numerical computation of an interior Helmholtz BVP. Using the Galerkin discretization we discuss an abstract convergence analysis with explicit dependence on the wave number. It is based on the approximation of a suitable adjoint problem and thus rests on the regularity analysis of the dual solution operator. We first will present stability results in the context of classical point wise polynomial approximation. Then we indicate better convergence by a refined regularity theory and illustrate these results with numerical computations in Ngsolve.

• WK student seminar

Steady three-dimensional transonic flows through channels so narrow that the classical boundary layer approach fails are considered. Under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes two dimensional to the leading order. The resulting interaction problem is formulated by means of asymptotic analysis for large Reynolds numbers.

• WK student seminar

We consider a flexible, piezoelectric beam fixed at one and and with a tip mass on the other. Boundary control has been applied to asymptotically stabilize the beam´s deflection. However, system does not exponentially converge to zero state and as a proof, spectral analysis of the system operator is offered. Finally, a hybrid symbolic-numerical simulation method is performed for a better understanding of system´s dinamical behavior.

• WK student seminar

Modern nanoscale semiconductor devices require a modeling not only by the particle and current density, but also by the energy and energy current density, and even higher order effects. In this way electron temperature effects are accounted for, which can lead to a significant heating of the devices, since the electron temperature can reach several thousand degrees. Numerical simulations suggest that a boundary layer occurs in the electron temperature. Yamnahaki introduced a correction to the drift diffusion equations boundary conditions in 1992, which can be derived by the introduction of a boundary layer. We will present now progress on the derivation of higher order boundary conditions for the energy-transport equations and discuss alternatives.

• WK student seminar

We consider the Kusuoka-Lyons-Victoir method of cubature on Wiener space. We analyse the basic assumptions. We discuss possibilities of its application to stochastic partial differential equations and stochastic differential equations whose coefficients do not satisfy the usual global Lipschitz conditions.

• WK student seminar

We consider the reduced model proposed by DeSimone, Kohn, Müller, Otto, and Schäfer in 2001. It is valid for sufficiently large and thin ferromagnetic samples. The solution describes the stationary magnetization in presence of an applied exterior field. We analyze the model problem and give a precise and appropriate functional analytic framework. Existence and uniqueness of a minimizer $m^*$ in our functional setting is proven. Based on some regularity results from DeSimone, Kohn, Müller, and Otto 2002, we propose a numerical discretization strategy by use of lowest-order Raviart-Thomas finite elements. Numerical examples conclude the talk.

• WK student seminar

In this talk we present preliminary results on the Faraday instability simulation using a two-fluid approach.

• Event: "Numerical models and methods for compressible and two-phase flow" (2010)

We study how the Reynolds approximation is perturbed by a non-regular roughnes of the boundary. We explicit the critical values of abrupt changes in the profile. The lubrification approximation is mathematically justified through a variant of the noton of twoscale convergence.

• Event: "Numerical models and methods for compressible and two-phase flow" (2010)

We study numerically an instability mechanism for the formation of shear bands at high strain-rate deformations of metals. We use a reformulation of the problem that exploits scaling properties of the model, in conjunction with adaptive nite element methods of any order in the spatial discretization and implicit Runge-Kutta methods with variable step in time. The numerical schemes are of implicit-explicit type and provide adequate resolution of shear bands up to full development. We nd that already from the initial stages, shear band formation is associated with collapse of stress diusion across the band and that process intensi es as the band fully forms. For fully developed bands, heat conduction plays an important role in the subsequent evolution by causing a delay or even stopping the development of the band.

• Event: "Numerical models and methods for compressible and two-phase flow" (2010)

Thin fluid films can have surprising behavior depending on the boundary conditions enforced, the energy input and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime.

• Event: "Numerical models and methods for compressible and two-phase flow" (2010)

The evolution of large amplitude internal solitary waves propagating towards the shore is studied. The mathematical model describing solitary waves interaction and decaying has been derived. It is a variant of the Choi-Camassa equations for two-layer and three-layer flows. The exact solution representing the waves of permanent form for sharp interfaces is found. It is shown by the comparison between experimental data and numerical results that the rate of wave decay before and after interaction of solitary waves moving in opposite directions can be predicted by the model to a high accuracy.

• Event: "Numerical models and methods for compressible and two-phase flow" (2010)

In the first part of our talk, we present experimental observations concerning the flow of a densely packed grain collection down a two-dimensional inclined channel. These results oppose the the predictions of the kinetic theory. We evidence that that continuous paths of transient contacts are effective for transporting momentum and energy through the bulk, so that the binary collision hypothesis (which is at the basis of the kinetic theories) is inadequate to describe dense flows. We propose an alternative model, which succeeds in accounting for the observed velocity profiles, and for the and the paradoxical nonzero shear rate in the vicinity of the free surface. In the second part, we emphasize some remarkable features exhibited by dry grain avalanches in laboratory experiments. According to the slope angle, the rear front propagates either upwards or downwards, with velocity approximately equal to the depth averaged velocity of the avalanche. As a counterpart, in both regimes, the velocity magnitude of the head front remains of the order of twice the depth averaged avalanche velocity. We suggest simple elementary mechanisms capable of accounting for these observations. We propose then an analytical modelling aimed at describing the combined processes governing the avalanche expansion. The two solutions that we obtain for the growth regimes and for the avalanche shapes resemble very closely the observations made in the laboratory and in the field.

• Event: "Numerical models and methods for compressible and two-phase flow" (2010)

This work is aimed to quantify the efficiency of DNA-DNA binding and signal-to-noise ratio in field-effect biosensors. For that we link together a time-dependent model for molecule motion in the analyte and a stochastic approach, which describes the chemical reaction at the functionalised surface.

• WK student seminar

To simulate big structures it is often necessary to parallelize algorithms. One way to do that is to use a domain decomposition method. In this talk, an overview on some domain decomposition methods will be given and the used domain decomposition method for parallelizing the BioFET algorithm will be shown.

• WK student seminar

Some new results on convergence to steady states in simple open quantum system are presented. We discuss how the entropy method can be applied to get convergence estimates, and if the resulting estimates are sharp.

• WK student seminar

We sketch the ideas to derive an efficient and accurate numerical integrator for the solution of linear, highly oscillatory ordinary differential equations. Standard methods (like Runge-Kutta schemes) would require to resolve the oscillations of the solution in order to yield good approximations. Our new difference scheme can deal with much coarser stepsizes. We use an analytic WKB-transformation to filter out the dominant oscillations. The resulting ODE is much smoother and hence can be discretized on a much coarser grid. Additionally advanced numerical methods are used to approximate the occurring highly oscillatory integrals. The error estimates for the resulting scheme are confirmed by numerical tests and show asymptotic correctness.

• WK student seminar

The problem to assign papers to referees gained a considerable interest in the recent years, especially in the scope of conference management systems. These systems need to achieve a fair and balanced distribution of papers among referees, where the conditions of fairness and balance may be defined in several ways. We present two algorithms to distribute a possibly large number of papers among a smaller number of referees, each paper requiring k reports. The first one is an approximation algorithm, using an iteration of weighted maximum matching in bipartite graphs. The second one is an exact algorithm based on b-matching. The optimality criterion for the assignment is not based on a local view of each referee, but on a global performance of the whole k-assignment satisfying a fairness criterion. We introduce an objective function for the k-assignment problem ensuring a specific notion of fairness when it is maximized. We show how a few precisely defined fairness criteria can be achieved that way. This includes a particularly notable extension of rank-maximality, a notion ntroduced by Irving et al. Our second algorithm computes in polynomial time optimal k-assignments with respect to the aforementioned fairness function.

• Thematic program: Databases and Ontologies in Advanced Information Systems (DATA-09-Prolongation) (2009 Prolongation into 2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

• Thematic program: Gyrokinetics for ITER (ITER-09) (2009)
• Event: "Gyrokinetics for ITER" (2010)

Lesson 4: Soving systems of Hamilton-Jacobi equations

Lesson 3: Intergenerational equity, time inconsistency and equilibrium strategies

Lesson 2: Solving the Hamilton-Jacobi equation

Lesson 1: The Ramsey growth model in economic theory

Abstract: Periodic irrotational traveling water waves are known to be smooth, with exception of the largest possible wave which has a corner at the wave crest (the lateral tangents being at an angle of 2\pi/3). Is the regularity of waves of small and moderate amplitude destroyed by vorticity? This is joint work with J. Escher.

• Event: 10. Pauli Kolloquium (2010)

Abstract: I show that first order symmetric hyperbolic systems in three space and one time variable always have multiple characteristics if the order n of the system is congruent 2 mod 4, n = 2, 6, 10, etc. The proof has a topological flavour and leads to an interesting algebraic problem.

• Event: 10. Pauli Kolloquium (2010)

We consider Composite Piezoelectric Cantilever and in order to stabilize this system, passivity based feedback control has been applied. The asymptotic stability of the closed-loop error system is proven using semigroup theory and LaSalle´s invariance principle. Moreover, we discuss exponential stability and show that the system is not exponentially stable.

• WK student seminar

We will start with a short introduction to a new model for mulitmode lasing systems. Within this approach the key simulation reduces to a full space Helmholtz EVP. Then we will discuss the numerical computation exploiting the FEM-Code of Joachim Schöberl. Finally we give an outlook on further collabortations with physisists from the institut of theoretical physics at the Vienna University of Technology.

• WK student seminar

In this work, we investigate the dynamics of a modified Keller-Segel type model. On the contrary to the classical configuration, the chemical production term is located on the boundary. In the one-dimensional case and in a particular case in dimension two, we prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass and they blow-up in finite time above the critical mass. Furthermore, in the one-dimensional case, using entropy techniques, we provide quantitative convergence results for the subcritical case. This work is completed with a more realistic model (still one-dimensional) for modeling purpose. In this new setting, the chemical is supplied by a quantity which evolves by exchanging particles at the boundary.
Finally some results are given for the two-dimensional case and we also provide some links with cell polarisation that is an essential step for many biological processes and that is involved for instance in cell migration, division, or morphogenesis.

• Thematic program: Cell movement and cell transport (CELL-09) (2009)
• WK seminar

Steady transonic flows through channels so narrow that the classical boundary layer approach fails are considered. The resulting viscous inviscid interaction problem for weakly three dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes two-dimensional in the leading order approximation. The behavior of the flow upstream of a surface mounted three-dimensional obstacle will be demonstrated.

• WK student seminar

First, we will give an introduction to fast-slow systems. The geometric viewpoint of the theory will be emphasized. Then we discuss the three-dimensional FitzHugh-Nagumo (FHN) equation and its bifurcations. The singular limit bifurcation diagram of the FHN equation will be derived. We shall also look at mixed-mode oscillations (MMOs) in the FHN equation and outline the role of MMOs in chemistry, neuroscience and physics.

• WK seminar

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. As such, our results suggest that any satisfactory equilibrium-based asset pricing model must be able to generate both large and time-varying compensations for fears of disasters. Our empirical investigations are essentially model-free, involving new extreme value theory approximations based on ``medium'' size jumps in high-frequency intraday prices for estimating the expected values of the tails under the statistical probability measure, and short maturity out-of-the money options and new model-free implied variation measures for estimating the corresponding risk neutral expectations.

• Event: Working Group "The interplay between Financial and Insurance Mathematics, Statistics and Econometrics" (2010)

In the context of high frequency data, like financial data, many questions have been solved in the recent years. But of course there are still many open problems, and we will review a few of those. This review will include specific problems like the estimation of the volatility when there are high activity jumps, and more general questions like the choice of appropriate models.

• Event: Working Group "The interplay between Financial and Insurance Mathematics, Statistics and Econometrics" (2010)

We describe a new approach to scenario generation in risk management, which combines serveral well- known approaches from the literature. teh approach is based on the calibration of underlying stochastic differential equation to a given time series and is flexible towards thhe inclusion of extreme events, business time versus trading time, etc. Serveral implementations are presented,

• Thematic program: The interplay between Financial and Insurance Mathematics, Statistics and Econometrics (FINANCE-09) (2009)

The price of anarchy, the most popular measure of the inefficiency of selfish behavior, assumes that players successfully reach some Nash equilibrium. We prove that for most of the classes of games in which the price of anarchy has been studied, results are "intrinsically robust" in the following sense: an upper bound on the worst-case price of anarchy for pure Nash equilibria *necessarily* implies the exact same worst-case upper bound for a much larger sets of outcomes, including mixed Nash equilibria, correlated equilibria, and sequences of outcomes generated by natural experimentation strategies (such as successive best responses or simultaneous regret-minimization). Byproducts of our work include several new results for the inefficiency of equilibria in congestion games.

• Event: 9. Pauli Kolloquium (2009)

We consider the problem of optimal risk sharing between two agents with quasi convex risk measures. Quasi Convex and cash sub additive risk measures take into account the time value of money and reflect that diversification should not increase risk.

• WK student seminar

The information contained in the market in terms of option prices is commonly transfered into terms of implied volatilities, or when the underlying is assumed to follow a continuous stochastic process, equivalently into terms of Local volatilities. In this talk we will present a different code book, based on the assumption that the underlying follows a Jump process with possibly infinitely many jumps in every interval, more specific a L\'{e}v process. Thereafter we present a possible extension to a dynamic L\'{e}vy model, the "tangent L\'{e}vy model" due to Carmona and Nadtochiy (2009).

• WK student seminar

The modelling of biosensors (field-effect devices with biofunctionalized surface layers) becomes complicated due to the fact that they comprise a biomolecular and a nanoelectronic part with different length scale, namely the microscopic scale of the biomolecules and the macroscopic scale of the sensor area. Both parts will be surveyed separately. Another crucial aspect of the modelling is the calculation of charge distribution in biofunctionalized surface layers. The atomistic model, that includes the effects of hydrogen and analyte ions, surface charges, and partial charges of biomolecules with a given potential difference (or voltage) between the charged surfaces, will be detailed. The self-consistent loop between micro- and macroscopic simulations that provides the basis for the quantitative description of BioFETs and their predictive simulation will also be presented.

• WK student seminar

This talk gives an overview on the equations and numerical methods used for the macroscopic part of our BioFET model.

• WK student seminar

This talk gives a brief overview of Computer Science Logic and related areas in Vienna in general, and some ongoing research activities at the Knowledge Based Systems Group of the Vienna University of Technology in particular.

• Event: 8th "Pauli Colloquium" (2009)

The talk consists of two parts. First we will give an introduction to web search engines, describing their main components and data structures. Then we will discuss the way web search engines make (most of their) money, namely their auction-based advertisement system.

• Event: 8th "Pauli Colloquium" (2009)

We consider a nonlinear heat equation with a gradient term. We construct a blow-up solution for this equation with a prescribed blow-up profile. For that, we translate the question in selfsimilar variables and reduce the problem to a finite dimensional one. We then solve the finite dimensional problem using index theory.

• WK student seminar

With the help of specially fitted approximations of three dimensional pictures of lamellipodia we extract the positions of actin filaments in it.

• WK student seminar

We present new results on the generalized Proudman-Johnson equation and the Hunter-Saxton system. In the first part, we derive the Proudman-Johnson equation and put it in context with the Hunter-Saxton equation modeling liquid crystals and the famous Burgers equation. Then we give a blow-up criterion and show that geometric properties of certain initial data are preserved in time. In the second part, we prove local existence for the periodic Hunter-Saxton system, which is the short-wave limit of the Camassa-Holm system (a model for shallow water waves). Finally, we show that there are solutions which blow up in finite time, as well as solutions existing globally.

• WK seminar

We present recent results on the time evolution of finite dimensional open quantum systems in Lindblad form. Existence of steady states and convergence results will be discussed, along with a detailed picture of the processes taking place.

• WK student seminar

• WK student seminar

We consider the deterministic and stochastic Navier-Stokes equations. We give some recent results, and discuss possible applications to turbulence modelling.

• WK student seminar

The full minimization problem in micromagnetics due to Landau and Lifschitz is, from a numerical point of view, very complex. In [DeSimone, Kohn, Müller, Otto, Schäfer 2001] a reduced model in thin-film micromagnetics has been proposed and analyzed with focus on a distributional point of view. The functional analytic framework presented in [Ferraz-Leite, Melenk, Praetorius 2009] seems to be more suitable for numerical analysis. We introduce a conforming finite element discretization of our energy space and propose a penalization strategy to control the side constraint. Numerical examples show, that the penalization strategy is superior to an interior point method as proposed in [Drwenski 2008] with respect to computational effort.

• WK student seminar

We deal with a new class of equations arising in the modelling of biofilms.Based on the experimental observations we will derive these equations.The peculiarity of these equations is that they comprise two kinds of degeneracy:porous medium as well as fast diffusion.Long time dynamics based on the global attractors of such equations as well as biological interpetations are discussed. Some open problems will be discussed.

• Thematic program: Cell movement and cell transport (CELL-09) (2009)

Nowadays, there exist different mathematical formulations to study the dynamics of fully nonlinear free-surface waves. On the other hand, there have been a growing interest in understanding the wind effects on different nonlinear surface waves phenomena, like Benjamin-Feir instability and the formation of extreme "freak" waves. As we shall see, no definitive conlusions about the wind effects in fully nonlinear simulations have been reached, owing to the complexity of the wind-waves interactions problem. In this study, we use a Higher Order Spectral (HOS) method to simulate numerically the nonlinear evolution of gravity waves in the presence of a turbulent airflow above the waves. After a description of the physics involved in the problem of wind-waves interactions, we present various approaches to introduce aerodynamic drag forces in DNS of surgace gravity waves. It will be assumed that the wave motions are "weakly viscous". Thus, we can use a quasi-potential approximation to incorporate weak dissipation effects in our fully nonlinear simulations. Although the coupling of the wave with the airflow, via the pressure surface field, is usually based on the linear approach for the wind-wave interaction problem, we will present methods to go beyong the linear theory of wind-wave interactions. These models of wind effects are such that nonlinearity in the waves can affect the forcing during the course of the evolution.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

After recalling briefly its derivation from the two-layer system with a rigid lid, we present theoretical and numerical results on a model for large amplitude internal waves which in some sense extends to internal waves the classical Saint-Venant ("Shallow water") system for surface waves. This model turns out to be nonlocal in two horizontal dimensions due to the rigid lid assumption.
This is based on a joint work with Philippe Guyenne and David Lannes.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

Deep-water capillary-gravity waves on the surface of a three-dimensional fluid exhibit a very interesting range of behavior - including lump or wave-packet solitary waves - and are also numerically challenging. We shall describe some of the models we have put forth and the numerical methods used to compute solutions. We present computations of the dynamics of waves showing interesting inelastic solitary wave collisions and, in some models, computations pointing to a wave-breaking singularity.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

The Partial Differential Equations (PDE) which naturally arise in Fluid Mechanics problems admit transformations conserving the whole set of solutions. They form the so-called symmetry group of the PDE. Usually, this group contains some important physical properties of the system expressed in the language of symmetries. It appears natural to expect numerical methods to preserve at least some of symmetry transformations of the continuous system. In this talk, we present various approaches for the construction of such invariant schemes. Some comparisons are made and good performance of invariant schemes is highlighted.
This is a joint work with A. Hamdouni.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

We present a class of relaxation schemes for the shallow water equations. These schemes are based on classical relaxation models for conservation laws. We consider finite volume as well as finite element spatial discretizations combined with TVD Runge-Kutta time stepping mechanisms. Numerical results are presented for several benchmark test problems.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

For the simulation of fully nonlinear surface gravity waves, a fast, accurate and robust numerical scheme is presented. The method is based on a boundary integral formulation,rewritten in a convenient form, together with a pseudo-spectral spatial scheme and a high-order temporal one. Various applications are presented.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

We apply and analyse some finite volume schemes to several Boussinesq type systems of water wave theory. A comparison with other numerical methods such as pseudo-spectral, standard Galerkin and discontinuous Galerkin is made. Special attention is given to the run-up of long waves on a plane beach. Various algorithms are considered. Validation by experimental data is presented for the head-on collision of solitary waves, wet dam break problem and the run-up of non-breaking and breaking solitary waves on a plane beach.
This is a joint work with D. Dutykh and Th. Katsaounis.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

Abstract: The problems of wave impact, wave breaking and other violent phenomena necessitate taking into account the compressibility of the air-water mixture. To meet these practical needs, F. Dias, D. Dutykh and J.-M. Ghidaglia proposed recently a simple single velocity, single energy two-phase model [Dias et al., 2009]. Properties and performance of this so-called four-equations model have already been discussed in the literature.
However, this model [Dias et al., 2009] was presented as it is without any derivation or justification procedure. The main goal of this communication is to fill in this gap. Namely, we derive the four-equations model from the complete six-equations two-phase system [Ishii, 1975, Ghidaglia et al., 2001, Rovarch, 2006] as a result of a special velocity and energy relaxation procedure. Mathematically this goal is achieved with the Chapman-Enskog type asymptotic expansion. Finally, the incompressible limit is discussed and some numerical results on compressible lock-exchange type flows are presented.
This is a joint work with Y. Meyapin and D. Dutykh.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

Thin fluid films can have surprising behaviors depending on the boundary conditions enforced, the energy input, and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

In the mountain regions snow avalanches represent a major natural hazard for both life and property. In the present study we focus mainly on two aspects of the avalanche simulation problem. Namely, the first part of the talk is devoted to some two-fluid models of a powder-snow avalanche. After a brief review of existing approaches we present a model which has a property to be consistent in the kinetic energy. Numerical results on an avalanche flow around an obstacle are presented.
In the second part, we investigate the obstacle deformation process under an avalanche impact. We use a weak fluid-structure interaction approach which is valid in the case of infinitesimal deformations. It is often the case in many practical situations when the loading process does not lead to drastic consequences. We present several numerical simulations which allow to determine the stress distribution inside the obstacle. This information is crucial for material damage estimation. Presented techniques and results have potentially important applications in vulnerability assessment of protecting structures.
This is a joint work with D. Dutykh and D. Bresch

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

We consider a family of systems of Boussinesq type due to Bona, Chen and Saut approximating the Euler equations of surface water wave theory, and modeling two-way nonlinear dispersive long wave propagation. We review recent progress on the theory of well-posedness of initial- and initial-boundary-value problems for these systems in two space dimensions. We approximate the systems by fully discrete numerical schemes using Galerkin - finite element methods for the spatial discretization, and analyze the stability and convergence of these schemes. The numerical methods are used as exploratory tools in a series of numerical experiments simulating various complex two-dimensional flows. We also study, by numerical means, interactions of solitary-wave solutions of these systems in one space dimension, including head-on and overtaking collisions, and interactions of solitary waves with the boundaries.

• Event: "Numerical methods for complex fluid flows - Effective algorithms and physical modeling" (2009)

Probabilistic databases arise naturally in many data management scenarios, such as Web information extraction, data cleaning, data integration, sensor data management, and scientific databases. In this talk I present MayBMS, a state-of-the-art database management system for efficiently managing and processing large collections of probabilistic data. MayBMS is based on a clean yet expressive query language that captures many important use cases of probabilistic databases, including hypothetical query processing, managing evidence, and Bayesian inference. MayBMS employs a succinct representation system for probabilistic databases called U-relations, which unifies various approaches to representing uncertain data, such as c-tables and vertical decomposition. MayBMS follows a principled approach to leveraging the strengths of previous database research for achieving scalability. The talk covers the design of the query language, storage structures, as well as query evaluation and optimization techniques.

• Thematic program: Databases and Ontologies in Advanced Information Systems (DATA-09) (2009)

We present some results concerning existence, uniqueness and asymptotic behavior for a class of second order difference equations associated to maximal monotone operators in Hilbert spaces. Different boundary conditions are associated. In the subdifferential case, the problem is equivalent with a minimization problem. Continuous dependence on data of the solution is also analyzed.

• WK seminar

In this talk, we consider the three-dimensional exterior problem for stationary Navier-Stokes equations. The model describes the flow past an obstacle of a viscous and incompressible fluid. Since the flow domain is unbounded, we choose to set the problem in weighted Sobolev spaces in order to describe the behavior at infinity of the solutions. In addition, to take into account the better decay properties of the solutions outside the wake region, that appears behind the obstacle during the flow, we also consider anisotropically weighted spaces. An important tool for the investigation of the problem is the study of a linearized problem : the stationary Oseen equations

• Thematic program: Cell movement and cell transport (CELL-09) (2009)

In this talk, we consider damped wave equations with nonlinear convection term and investigate on the asymptotic stability of corresponding nonlinear waves.
More precisely, we treat stationary waves and traveling waves for our problems, and derive the stability and the corresponding convergence rate under smallness condition on the initial perturbation.
Our results are based on a weighted energy method and we shall introduce our method in detail.

• WK seminar

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

Entanglement-based technologies, such as quantum information processing, quantum simulations, and quantum-enhanced metrology, have the potential to revolutionize our way of computing and measuring and help to clarify the puzzling concept of entanglement itself. Ultracold atoms on atom chips are an attractive system for their implementation, as they provide control over quantum systems in a compact, robust, and scalable setup. An enabling technology in this system is a potential depending on the internal atomic state.
Coherent dynamics in such a potential combined with collisional interactions allows entanglement generation both for individual atoms and ensembles. Here we report experiments in which we demonstrate coherent dynamics of Bose-condensed atoms in such a potential, generated in a novel way with microwave near-fields on an atom chip.
We entangle atomic internal and motional states in a controlled and reversible way, realizing a trapped-atom interferometer with internal-state labeling. Furthermore, our system provides control over collisions in mesoscopic condensates with well-defined atom number, paving the way for on-chip generation of many-particle entanglement and quantum-enhanced metrology with spin-squeezed states.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

I will briefly review the physics of antiferromagnetic spinor condensates beyond mean field and its analogies with a three-well system. In the second part of the talk I will present our approach to adiabatically engineer correlated states in such systems and how we plan to implement it experimentally.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

We implement a double-well on an atom chip that combines compactness, fast cycle times, and flexible trap geometries. While we currently use only one double-well, our two-layer chip design creates smooth static magnetic multi-well 3D potentials in linear and topologically connected geometries. Atoms are detected by absorption imaging, with an equivalent noise of 1 atom RMS per pixel. Our chip and imaging system are compatible with small and micro BECs ranging from tens to thousands of 87Rb atoms.
We directly measure the atom number statistics of a BEC in double-well and its dependence on the splitting dynamics, atom loss and atom number.
We report -3.5dB of number squeezing. We also investigated number squeezing dependence with temperature and the transition to thermal gases.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

We study a system composed of one electron and two doubly charged ions which are held in a Penning trap. There exist electronically highly excited states in which the electron is delocalized among the two ions forming a giant molecule of several micrometer size. At energies close to the top of the Coulomb barrier these molecular states can be regarded as superpositions of Rydberg states of individual ions. We illuminate the possibility for observing coherent charge transfer between the ions caused by laser induced tunneling between the two Coulomb wells.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

We present a theory of measurement-induced interference for weakly interacting Bose-Einstein condensed (BEC) gases.
We show that the many-body state resulting from evolution from an initial fragmented (Fock) state can be approximated as a superposition of Gross-Pitaevskii (GP) states; the measurement breaks the initial U(1) phase symmetry, producing a distribution pattern corresponding to only one of the GP solutions. Analytically solvable models, such as two-mode on-chip adiabatic recombination and soliton generation in quasi one-dimensional condensates, will be briefly commented upon.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

The mystery of the apparent relative phase between independent condensates [1] is explained by the bosonic Quantum de Finetti Theorem [2].
[1] Observation of interference between two Bose condensates, Science 275: 637 - 641 (1997) [2] Locally normal symmetric states and an analogue of de Finetti’s theorem, Z. fuer Wahrscheinlichkeit und verw. Geb. 33: 343 – 351 (1976)

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

One-dimensional (1D) strongly interacting quantum systems show surprising many-body effects as quantum fluctuations and correlations are enhanced by the confinement. I report on the realization of a highly-correlated, excited many-body state with strong attractive interactions. This novel state of matter in 1D geometry is known as the super-Tonks-Girardeau gas (sTG) and was predicted in [1]. Counter-intuitively, although bosons strongly attract each other in this phase, they behave similar to repulsively interacting fermions, showing an effective long range interaction.
We load a Bose-Einstein condensate of cesium atoms into an array of tube-like 1D traps generated by a 2D optical lattice, and control the interaction strength by means of magnetic Feshbach resonances. When the 3D scattering length is increased towards and beyond the length scale set by the tight transversal confinement, a confinement-induced resonance [2] is observed, that allows us to tune the effective 1D-interaction parameter to large positive and large negative values. We realize the crossover all the way from a non-interacting gas, via the 1D mean-field and Tonks-Girardeau regime, to the sTG gas. Despite the fact that the interaction is strongly attractive, we find the sTG gas to be surprisingly stable.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

We present the results of our numerical simulations of the transient (time-dependent) and steady-state distribution of the relative phase of two coherently-split 1D atomic quasicondensates. We demonstrate the way to determine both the temperature and tunnel-coupling energy of two condensates from measurements of the relative phase autocorrelation function and the phase-contrast distribution in the steady-state limit. The evolution of the relative phase from its initial to final distribution and the underlying dephasing mechanism are discussed with regard to the numerically obtained scaling properties of the typical time of the subexponential decay of the phase coherence.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long range order can be experimentally probed in principle using an interference measurement.
The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting 1D fluid. We also evaluate the particle density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction of the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

"We propose a new approach to dynamic decoherence control of many-body systems, focusing on finite-temperature Bose-Einstein Condensates (BEC) in a double-well potential. Due to the many-body interactions the standard “echo” control method becomes less effective. The proposed approach takes advantage of the interaction-induced change of the spectrum, to obtain the optimal rate of pi-flips of the relative phase between maximally distinguishable collective states. This method is particularly useful for probing and diagnosing the many-body decoherence dynamics."

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

• Event: Workshop "Bosonic Josephson junctions and tunnel-coupled systems" (2009)

To compute a numerical approximation of a special class of highly oscillatory linear ODEs in an efficient way we use a WKB based transformation to seperate the slow and fast oscillations of the system. In this talk we present a WKB ansatz for a vector valued ODE and sketch the idea how to construct the mentioned transformation based on the WKB approximation. The gained equivalent system is approximated via a truncated series (picard iteration). The derived numerical scheme yields an error estimate which is reciprocal to sqare of the "frequence" of the solution and hence yielding better and better error bounds as the system becomes more and more oscillatory.

• WK student seminar

In this talk we will present the idea of a quantum entropy method as a tool to study long-time behaviour of open quantum systems. We start with a synopsis of the classic entropy method and open quantum systems. The focus is then on a quantum entropy method, and we present some recent results on convergence rates towards a (not necessarily unique) steady state.

• WK student seminar

This talk is concerned the competition between aggregation(high concentration or blow-up in finite time) and diffusion(global existence) phenomena in the Keller Segel model for chemotaxis. It is well known that this competition depends strongly on the dimension of the space. We present some panoramic results of global existence and blow-up for the parabolic-elliptic variant of this model, then we end up by proving some concentration results for the parabolic parabolic variant.

• WK student seminar

From the Boltzmann equation A. Yamnahakki (Mathematical Models and Methods in applied Sciences, Vol. 5, No. 4 (1995), 429) derived by an asymptotic analysis Robin boundary conditions for the drift-diffusion model. In this talk we will present progess on the derivation of higher order boundary conditions for the energy-transport model from the Boltzmann equation.

• WK student seminar

Protein-protein interactions are often performed by helix-helix recognition in cell membranes. They are crucial for signal transduction, cell's growth/apoptosis as well as for organization of protein topology and final folding (only about 150 spatial structures of membrane proteins are known). It is started to be possible to explore the helix-helix interactions in membrane theoretically In Silico - Monte Carlo simulations with implicit membrane representation successfully predict alpha-helical dimers (transmembrane region) – glycophorin A, pro-apoptotic factor BNIP3 and Ephrin receptor 1 from the family of Receptor Tyrosine Kinases (RTKs) with a good agreement of NMR and mutagenesis data, coming later. There is a promising perspective for structural-based design of TM peptides with inhibition effect on badly down regulated onco-receptors in plasma membrane. Also, the role of helix-helix interactions in translocation/stabilization into lipid bilayer of TM helices is getting feasible (Lactose Permease protein is taken). In silico Monte Carlo experiment and In vitro translation in the presence of dog pancreas rough microsomes have shown that it is achievable for helices with charged residues in TM region to be inserted into lipid bilayer together, in pairs, while the single helices do not insert. Moreover, the pair-helices insertion into hydrophobic surrounding is accomplished only in a case of native-like packing between helices.

• Thematic program: Cell movement and cell transport (CELL-09) (2009)
• WK seminar

The circulatory system is highly integrated and modeling its various functions is an incredibly challenging problem, which requires addressing many fundamental issues, both from the mathematical and computational viewpoints. In this talk we introduce some non-Newtonian mathematical models of the cardiovascular system and comment on their mathematical properties and significance to yield realistic and accurate numerical results. The geometrical multiscale approach, consisting in coupling a hierarchy of models with different levels of complexity and detail will be discussed, and some numerical simulations illustrating its effectiveness will be presented.

• Thematic program: Cell movement and cell transport (CELL-09) (2009)
• WK seminar

We consider the problem of determining doping profile in semiconductors from standard voltage boundary measurements. We derive a dual inverse problem, obtain its asymptotic simplification (for large contrast of conductivities), and prove first uniqueness results in the important unipolar case.

• WK seminar

We consider the reduced model proposed by DeSimone, Kohn, Müller, Otto and Schäfer 2001 which is valid for sufficiently large and thin ferromagnetic samples. We analyze the model problem and recall the appropriate functional analytic framework. Existence and uniqueness of a minimizer in our functional setting is proven. Furthermore, we state the Euler-Lagrange equation and propose a conforming discretization scheme to solve the resulting system of equations.

• WK student seminar

A presentation of the concept of local volatility and different approaches of calibration of the local volatility model to market prices. Focus lies on parametric approaches, in particular a log-normal mixture density model, (Brigo, Mercurio 2002), that is fitted to the implied volatility surface according to Heston.

• WK student seminar

We consider the problem of optimal consumption and terminal wealth in an Ornstein-Uhlenbeck market. We will find the optimal rate of consumption under exponential utility and discuss the behaviour under other utility functions.

• WK student seminar

We present an a priori analysis of the $hp$-approximation for the primal-dual formulation of frictional contact in linear elasticity. We employ a novel $hp$-mortar projection operator, which is uniformly stable in the mesh width and has a bound growing slowly in the polynomial degree. Next, we generalise the residual error indicator to the present context. Numerical results show that an $hp$-adaptive strategy leads to exponential convergence.

• WK student seminar

• Event: Minicourse on "Ultracold bosons" (2009)

• Event: Minicourse on "Ultracold bosons" (2009)

• Event: Minicourse on "Ultracold bosons" (2009)

Charged boundaries between a solid phase functionalized with biomolecules and an electrolyte are important in biophysics and in biotechnology. Here we present a Metropolis Monte Carlo algorithm for the constant-voltage ensemble that includes the effects of both the biomolecules and the electrical double layer at the interface and that provides the simulation capability to study the electrostatics of the surface layer. The resulting concentration profiles show a three-layer structure and non-trivial interaction between the electric double layer and the counter-ions.

• WK student seminar

In this talk we first describe what a financial derivative is and how the modern theory of stochastic processes allows to derive the fair value of it. Then we describe the shortcomings of the celebrated Black-Scholes model. We provide a short introduction to Lévy processes, a class of stochastic processes that allows to overcome several of the limitations of the Black-Scholes model. Finally we describe how one can derive the price of a derivative using either Fourier transform methods or partial integro-differential equations (PIDEs).

• WK seminar

Transonic flows through channels so narrow that the classical boundary layer approach fails are considered. As a consequence the properties of the inviscid core and the viscosity dominated boundary layer region can no longer be determined in subsequent steps but have to be calculated simultaneously. The resulting viscous inviscid interaction problem for weak three dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layer becomes planar in the leading order approximation. Representative solutions for subsonic as well as for supersonic flows disturbed by three dimensional surface mounted obstacles will be presented.

• WK student seminar

Energy solutions of rate-independent evolution problems, as recently proposed by A. Mielke and his collaborators, can be obtained by solving a recursive minimization scheme which involves a functional governing the evolution perturbed by a suitable dissipation term. Rate-independence is guaranteed by the 1-homogeneity of the dissipation, which therefore has a linear growth and provides just a BV estimate for the time-dependence of the approximating solutions. Thus jumps can typically occur during the evolution, at least when the functional is not convex. These jumps can be characterized by a global stability condition which reflects the global character of each minimization step of the approximation scheme. In order to obtain a localized condition (which should also be easier to solve numerically), various viscosity-type corrections have been proposed. The simplest ones consist to add a (asymptotically small) quadratic perturbation to the dissipation term. In this talk we discuss some characterizations of the limit solutions obtained by this kind of viscosity approximation schemes, their link with the variational theory of Gradient Flows and with the original energy formulation. (Joint work in collaboration with A. Mielke and R. Rossi)

• WK seminar

• Thematic program: Motility: from the molecular to the population scale (2008)
• WK seminar

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• Event: Workshop "Quantum Control" (2009)

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• Event: Workshop "Quantum Control" (2009)

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• Event: Workshop "Quantum Control" (2009)

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• Event: Workshop "Quantum Control" (2009)

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• Event: Workshop "Quantum Control" (2009)

• Event: Workshop "Quantum Control" (2009)

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• Event: Workshop "Quantum Control" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

Efficiently processing queries against very large graphs is an important research topic largely driven by emerging real world applications, as diverse as XML databases, GIS, web mining, social network analysis, ontologies, and bioinformatics. In particular, graph reachability has attracted a lot of research attention as reachability queries are not only common on graph databases, but they also serve as fundamental operations for many other graph queries. The main challenge of answering reachability queries in howw to build efficient indices over the graphs in order to achieve the best space/time performance. Many approaches have been proposed for building indices on these graphs. However, due to the large number of vertices in many real world graphs, the computational cost and (index) size of the indices using existing methods would prove too expensive to be practical. In this talk, we introduce our ongoing work on a novel index structure based on the treewidth of the underlying graph. We show that the size off the index for the underlying graph remains linear and the reachability query can be solved in $O(log n)$ where $n$ is the number of vertices in the graph. We demonstrate empirically the effectiveness of our approach.

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

• Event: Workshop "Gyrokinetic Plasma Turbulence" (2009)

The authors report on a new higher-order weak approxmation scheme for SDEs and concrete algorithms based on the scheme. The ODE-valued random variables whose averages approximate the given SDE are constructed by using the notion of free Lie algebra. It is proved that the classical Runge--Kutta method for ODEs is directly applicable to the drawn ODE from the random variable.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

The fast Fourier transform (FFT) technique is now a standard tool for the numerical calculation of prices of derivative securities. Unfortunately, in many important situations, such as the pricing of contingent claims of European type near expiry, and the pricing of barrier options close to the barrier, the standard implementation of this technique leads to serious systematic errors. We propose a new, fast and efficient, variant of the FFT technique, which is free of these problems, and is as easy to implement as the most common version of FFT. We apply this techniques to computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a L\'evy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the results obtained using other (sometimes fundamentally different) approaches that exist in the literature. However, our method is computationally much faster (often, dozens of times faster). Moreover, our technique has the advantage that its application does not entail a detailed analysis of the underlying L\'evy process: one only needs an explicit analytic formula for the characteristic exponent of the process. Thus our algorithm is very easy to implement in practice. Finally, our method yields accurate results for a wide range of values of the spot price, including those that are very close to the barrier, regardless of whether the maturity period of the option is long or short. Joint work with Mitya Boyarchenko. Ahikiko Takahashi "An Asymptotic Expansion Approach in Finance" Abstract: This presentation reviews an asymptotic expansion approach to numerical problems for pricing and hedging derivatives. As examples, plain-vanilla and average options under stochastic volatility models are presented. Olivier Scaillet "Pricing american options under stochastic volatility and stochastic interest rates" Abstract: We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters,this method can accurately price options with time- to-maturity up to several years.The main advantage"of our approach over existing methods lies in its straightforward application to models with stochastic volatility and stochastic interest"rates. We exploit this advantage by providing an analysis of the impact of volatility mean-reversion, volatility of volatility,and correlations on the American put price.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

We discuss market completeness for diffusion-driven factor models beyond the classic requirement that the volatility matrix of traded instruments is invertible. We show that the market generated by a finite-dimensional diffusion model is complete as soon as the coefficients of the SDE are d(x) dP almost surely C1 with locally Lipschitz derivatives. As a consequence, when factor models are considered as diffusions in Hilbert spaces, then any such factor model which admists a finite dimensional representation creates a (locally) complete market. (the limit of locality is given by the existence of the FDR). This is illustrated on the example of Variance Swap Curve Market Models.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

We discuss simple and universal formulae that give quantitative links between tail behaviour and moment explosions of the underlying on one hand, and growth of the volatility smile on the other hand. Practical relevance comes from model calibration and smile extrapolation from market data. Sometimes heat-kernel estimates, or formal applications thereof, can be used although it appears that the existing theory does not fully provide what is needed.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

This presentation reviews an asymptotic expansion approach to numerical problems for pricing and hedging derivatives. As examples, plain-vanilla and average options under stochastic volatility models are presented.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters,this method can accurately price options with time- to-maturity up to several years.The main advantage"of our approach over existing methods lies in its straightforward application to models with stochastic volatility and stochastic interest"rates. We exploit this advantage by providing an analysis of the impact of volatility mean-reversion, volatility of volatility,and correlations on the American put price.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

We translate in semi-group theory a lot of tools of stochastic analysis. If the formula come from the stochastic analysis, they are simpler to check by the theory of P.D.E. as well for instance the Girsanov formula or the Wong-Zakai approximation of a diffusion, as well as Malliavin's theorem on hypoellipticity and various applications to heat-kernels.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

Using the short-time expansion of the heat kernel associated with the logarithm of the stock price in a local volatility model, we will calculate the neary-expiry first order deviation of the implied volatility from the harmonic mean of the local volatility. The general method can be used to obtain more precise asymptotic behavior of the implied volatility. One prominent feature of the first order deviation is that it is relatively stable with respect to the local volatility in the sense that it depends only on the certain integrated deviations of the local volatility from its harmonic average, a property not shared by higher order deviations. A similar theory can be developed for certain stochastic volatility models.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

We study the asymptotic behavior of various distribution densities arising in analytically tractable stochastic volatility models. The main emphasis in this work is on the uncorrelated Hull-White, Stein-Stein, and Heston models. We obtain sharp asymptotic formulas with error estimates for the distribution density of the stock price and the distribution density of a time average of the volatility process. Applications are given to the problem of characterizing the asymptotic behavior of the implied volatility in stochastic volatility models. This is a joint work with E. M. Stein (Princeton University).

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

Implied volatility skew for models with fast mean-reverting stochastic volatility is well understood using singular perturbation methods (Fouque-Papanicolaou-Sircar, CUP 2000). Here, we study the Heston stochastic volatility model in the regime where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. We derive a large deviation principle and compute the rate function by a precise study of the moment generating function and its asymptotic. We then obtain asymptotic prices for Out-of-The-Money call and put options, and their corresponding implied volatilities. Joint work with Jin Feng and Martin Forde.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

Quadratic Wiener functionals , Van Vleck formula, and the KdV equation In this talk,we will give a survey based on a joint work with S. Taniguchi. First of all ,we recal known formulae obtained by R.H.Cameron-M.T.Martin and P.Levy. These are the analogues to the Van Vleck formula for fundamental solutions of Schrodinger equations in cases of potentials associated with harmonic oscillator and uniform magnetic field respectively. Next we will give a framework by which we can systematically discuss these analogues. Finally within the above framework ,we discuss topics related to soliton solutions of the KdV equation in terms of stochastic analysis.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

In the presentation, we give an asymptotic expansion of probability density for a component of general diffusion models. Our approach is based on infinite dimensional analysis on the Malliavin calculus and Kusuoka-Stroock's asymptotic expansion theory for general Wiener functionals. The initial term of the expansion is given by the `energy of path' and we calculate the energy by solving Hamilton equation. We apply our approach to asymptotic expansion of implied volatilities and obtain generalized SABR formula.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

This talk considers some properties of the implied volatility surface for large times to maturity. In particular, the implied volatility smile flattens at long maturities in a rather precise manner. The long implied volatility is almost surely non-decreasing as a function of calendar time, in analogy with the Dybvig-Ingersoll-Ross theorem on long interest rates. An asymptotic formula for the level and slope of the long implied volatility smile is given and is illustrated by examples.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

The first part of the talk will be concerned with moment explosions in stochastic volatility models. A moment explosion is said to occur, if a moment of the price process of some given order exists up to some finite time (the explosion time) and becomes infinite from there on. Through the results of Lee and Benaim & Friz, the moment explosion times are intimately connected to the asymptotic shape of the implied volatility surface. I will present the results of Andersen & Piterbarg and Lions & Musiela on moment explosions in SABR-type stochastic volatility models, and my own results on moment explosions in affine stochastic volatility models. In the second part of the talk I will present results on the long-term behavior of affine stochastic volatility models, which also have applications to the asymptotics of the volatility surface.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

In this talk, we illustrate the use of sophisticated mathematical tools ranging from differential geometry to Hopf algebra to solve concrete problems in financial engineering: -Heat kernel on Riemannian manifold and calibration of Libor market models -Gaussian estimates of Schr"{o}dinger equation and Implied volatility asymptotics. -Hopf algebra and Monte-Carlo pricing.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

Smile risk is most commonly modeled using a stochastic volatility model. We show that matching these models to market data yields vol-of-vols that decay in a power law with time to expiry. This motivates our development of a new model, based on Levy processes, which agrees with the available market data. Asymptotic methods are used to analyze the new model, obtaining effective Black volatilities for options under the new model.

• Event: Workshop "Small time asymptotics, perturbation theory and heat kernel methods in mathematical finance" (2009)

A presentation of one of the most common Stochastic volatility models, some shortfalls when implementing it and its implied volatility surface.

• WK student seminar

• WK student seminar

In order to establish a theoretical foundation for database transformations, a universal computation model as an umbrella for queries and updates is needed. As updates are fundamentally distinct from queries in many respects, computation models for queries cannot be simply extended to database transformations. This motivates the question whether Abstract State Machines (ASMs) can be used to characterize database transformations in general. In the talk I will start examining the differences between database transformations and algorithms, which give rise to the formalization of of five postulates for database transformations. Then a variant of ASMs called Abstract Database Transformations Machines (ASTMs) is developed, and I will sketch the proof that ADTMs capture database transformations, i.e. the main result is that every database transformation stipulated by the postulates can be behaviorally simulated by an ADTM.

• Thematic program: Foundations of Knowledge and Information Handling (2007)

We will investigate the Stop-Loss Start-Gain Strategy, the paradox it involves and how it can be solved.

• WK student seminar

We will derive and study the Proudman-Johnson equation and the CLM equation, both of which can be considered models for three-dimensional vortex dynamics, and their generalizations. In particular, we will present new proofs and criteria for global existence in time or the creation of finite-time singularities.

• WK student seminar

In this paper we introduce a modular framework for abstract argumentation where the argumentation context, that is information about preferences among arguments, values, validity, reasoning mode (skeptical vs. credulous) and even the chosen semantics can be explicitly represented. The framework consists of a collection of abstract argument systems connected via mediators. The mediators integrate information coming from connected argument systems - possibly solving conflicts within this information - and provide the context used in a particular argumentation module. We show how the framework can be used for hierarchic argumentation as typically found in legal reasoning, and we show how it can be used to model group argumentation processes.

• Thematic program: Foundations of Knowledge and Information Handling (2007)

n this talk I will consider computational problems that (A) can be solved in polynomial time for graphs of bounded treewidth and (B) where the order of the polynomial time bound is expected to depend on the treewidth of the instance. Among the considered problems are coloring problems, factor problems, orientation problems and satisfiability problems. I will present an algorithmic meta-theorem (an extension of Courcelle's Theorem) that provides a convenient way for establishing (A) for some of the considered problems and I will explain how concepts from parameterized complexity theory can be used to establish (B).

• Thematic program: Foundations of Knowledge and Information Handling (2007)

Due to the ongoing miniaturization of semiconductor devices it is necessary to derive new models for the transport of electrons. One such model is the energy transport model, which includes the energy density and the energy current in addition to the electron density and the electron current which occur in the standard drift-diffusion model. We will present the techniques to calculate solutions in two dimensions and will present some results.

• WK student seminar

We investigate the transfer of the classical entropy method to open quantum systems in Lindblad form. A first result for a simple system is presented.

• WK student seminar

The steady laminar flow of a two-dimensional incompressible boundary layer disturbed by a shallow three-dimensional hump is studied by means of a three-dimensional extension of the triple-deck theory. The most striking feature then is the emergence of a ‘corridor’ in the wake of the hump, which stays at constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. An asymptotic analysis of the flow quantities far downstream in this region then yields to similarity solutions of the triple-deck flow as well as to a condition for the hump geometry for the occurrence of the ‘corridor effect’.

• WK student seminar

If-then rules, which are arguably the most common form of knowledge representation in Artificial Intelligence, are ambiguous. They can be interpreted both as logic programs having the form if conditions then conclusions and as production rules having the form if conditions then do actions. The relationship between these different kinds of rules has received little attention in the AI literature, and, when it has, different authors have reached entirely different conclusions. Some authors, such as Russell and Norvig in their textbook Introduction to Artificial Intelligence, view production rules as just logical implications used to reason forward, while Herbert Simon in the MIT Encyclopedia of Cognitive Science views the logic programming language Prolog as one of many production system languages. On the other hand, Thagard in his Introduction to Cognitive Science denies any relationship between logic and production rules at all. In this talk, I will explore the relationships between logic programs and production rules and propose a framework that combines the two kinds of rules and eliminates the overlap between them. The framework uses production rules for sentences of the form if conditions then achieve goals, and it uses logic programs both to evaluate conditions and to achieve goals by reducing goals to sub-goals. I will discuss the problems of giving the resulting framework both a declarative, model-theoretic semantics and an operational semantics in the form of a transition system.

• Thematic program: Foundations of Knowledge and Information Handling (2007)

The setting of the Banach Gelfand triple (S0,L2,SO') allows to describe in a clean functional analytic way how a given continuous problem (such as applying a pseudo-differential operator given by its Kohn-Nirenberg symbol that should be applied to a given L2-function, or finding the spreading function of an operator) can be approximated at least in a qualitative way in a constructive way. The setting involves the use of function spaces, Fourier transforms and generalized functions, and aims at the reduction of a continuous problem to a finite-dimensional setting, which in principle is available for numerical implementation, e.g. using MATLAB or any other mathematical software.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

Our aim is to emphasize the main known limitations to the use of Wigner measures for Schr"odinger equations.
After a short review of successful applications of Wigner measures to study the semi-classical limit of solutions to Schr"odinger equations, we list some examples where Wigner measures cannot be a good tool to describe high frequency limits. Typically, the Wigner measures may not capture effects which are not negligible at the pointwise level, or the propagation of Wigner measures may be an ill-posed problem. In the latter situation, two families of functions may have the same Wigner measures at some initial time, but different Wigner measures for a larger time. In the case of systems, this difficulty can partially be avoided by considering more refined Wigner measures such as two-scale Wigner measures; however, we give examples of situations where this quadratic approach fails.

This is joint work with Remi Carles, Clotilde ermanian-Kammerer and Hans-Peter Stimming, Comm. Pure and Applied Analysis, (1) 2009

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

We consider a class of pseudodifferential operators defined by smooth symbols which may have almost exponential growth or decay at infinity in phase space. They can be considered as symbol-global type operators, studied by many authors in the context of PDE. In the present lecture, we use time-frequency methods/Gabor frames in the study of spectral asymptotics. Almost exponential growth/decay of symbols is handled by the use of techniques from ultra-distribution theory.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

Consider the solution to the time-dependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin in 1989 that there exists f in the Sobolev space $H^s(mathbb{R}^n), ; s=n/2$ such that tangential convergence can not be widened to convergence regions. We show that the corresponding result holds when $-Delta_x$ is replaced by an operator $varphi(D)$, with special conditions on $varphi$. More explicitly we consider the solution to the equation $(varphi(D)+ipartial_t )u =0,$ with the initial condition u(x,0)=f(x). Here $varphi$ should be real-valued and its radial derivatives of first and second order ($varphi' =varphi'_r$ and $varphi'' =varphi''_{rr}$) should be continuous, outside a compact set containing origin. Furthermore, we will require some appropriate conditions on the growth $varphi'$ and $varphi''$. In particular the function $varphi(xi)=|xi|^a$ will satisfy these conditions, for a> 1.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

The Weyl calculus is an important part within the theory of pseudo-differential operators. In physics, the calculus links classcal mechanics with quantum mechanics in the sense that an observable in classical mechanics corresponds to an operator in quantum mechanics. In general, this operator is the Weyl operator, at least with good approximations.
The composition of two such operators corresponds to a somewhat complicated product between the observables. This product is the so called Weyl product.
In the talk we present some continuity results for this product in background of the theory of modulation spaces. Furthermore, the Weyl product, on the Fourier transform side, is equal to a twisted convolution. Consequently, any continuity result for the Weyl product on modulation spaces gives rise to a similar continuityresult for the twisted convolution on Fourier modulation spaces. We show how these results can be used to get continuity for twisted convolutions on weighted Lebesgue spaces.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

It is well known that the continuous wavelet transform has the ability to identify the set of singularities of a function or distribution. It was recently shown that certain multidimensional generalizations of the wavelet transform are useful to capture additional information about the geometry of the singularities.
The continuous shearlet transform, recently introduced by the author and his collaborators is a novel approach which combines the power of multiscale analysis with ability to deal with the anisotropy and directional features of multidimensional data. In this talk, we show that the continuous shearlet transform can capture both the location and geometry of singularities. This is useful to identify and characterize the geometrical information of the edges in natural images. Numerical examples of edge analysis and detection will also be presented.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

ABSTRACT: The limit Wigner measure of a WKB function satisfies a simple transport equation in phase-space and is well suited for capturing oscillations at scale of order $O(epsilon)$, but it fails, for instance, to provide the correct amplitude on caustics where different scales appear. We define the semi-classical Wigner function of an $N$-dimensional WKB function, as a suitable formal approximation of its scaled Wigner function. The semi-classical Wigner function is an oscillatory integral that provides an $epsilon$-dependent regularization of the limit Wigner measure, it obeys a transport-dispersive evolution law in phase space, and it is well defined even at simple caustics.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

In the 90's there was wide interest in the use of Wigner and smoothed Wigner transforms in signal processing; several libraries for their computation were created at that time. However, it is fair to say that these transforms are not as widely used today, and one of the reasons is that their computation is "unreasonably" expensive, when compared e.g. to spectrograms. Motivated by a recent scheme for the simulation of caustic development and propagation, we present a new library for the computation of Wigner and smoothed Wigner transforms. The main improvement in comparison to the state of the art is a parallelization of all steps of the process (including output, e.g. plotting) which allows a better behavior for much larger signals.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

Informal discussion, in order to share experience of the speaker on the subject (dating back to his PhD work and habilitation at TU Vienna) with the workshop participants.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

Several deep results in time-frequency analysis, known as Feichtinger-Groechenig theory, are crucial for understanding Gabor frames. We point out a few aspects.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

Phase-space methods such as Wigner transforms have long been used for the study of semiclassical limits. Regularized objects, such as Husimi transforms, have often been proposed as an interesting alternative, but have not been widely used, due to the lack of an appropriate framework to study the equations governing them.
We present a new framework, in which exact smoothed Wigner and Husimi equations can be formulated rigorously for a wide class of problems, and the convergence to semiclassical limits can be established. It must be noted that there are several similarities to the Gelfand-Shilov functions of type $S^{b,B}$. Special emphasis is based on the points where this constitutes a strengthening of the existing Wigner-transform-based state of the art. In particular, it is seen that the coarse-scale approach works with less regular potentials.

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

• Event: Workshop on "Applied Analysis and Fast Computation in Phase-Space 2008" (2008)

We consider the semi-relativistic Hartree system in attractive Coulomb case. We prove existence of the minimizers of the energy functional under a constraint which comprises an appropriately chosen Casimir functional. For the existence of such minimizers the concentration-compactness property of the density which is needed to tackle the limit of the potential energy along the minimizing sequences is studied.

• WK student seminar

In this talk a constructive existence proof for travelling wave solutions of a reactive kinetic equation will be presented. The density of the kinetic profile is shown to be asymptotically close to the travelling wave solution of the Fisher equation, which is a reaction-diffusion model commonly used to describe population dynamics.

• WK student seminar

• WK seminar

• WK student seminar

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

• Event: Workshop on "American and Bermudan Options" (2008)

The phenomenon of matter wave interference lies at the heart of quantum physics. It has been observed in many contexts in the limit of non-interacting particles as a single particle effect. We observe and control many-body matter wave interference, which is driven by nonlinear particle interactions. In a multipath matter wave interferometer the macroscopic many-body wave function of an interacting atomic Bose-Einstein condensate develops a regular interference pattern, allowing us to directly visualize the effect of interaction induced phase shifts as time progresses. We demonstrate coherence for the nonlinear phase evolution in a matter wave spin-echo-type experiment when we stop and reverse the interaction driven evolution by first nulling the strength of the interaction and then driving the multipath phase shifts with opposite signs by means of an external potential. Alternatively, we balance the effect of interactions by means of the external potential and observe persistent Bloch oscillations. If time permits, we discuss experiments in which we confine the matter wave sample to a one-dimensional geometry and study Bloch osciallations and transport in a one-dimensional gas.

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

Using the continuous and the discrete time-dependent GPE, we probe the Bogoliubov spectrum of a Bose-Einstein condensate in a 1D optical lattice. The presence of the optical lattice not only reduces the sound velocity, but is also responsible for phenomena which arise due to the interplay of interactions and periodic potential, like dynamical instabilities for a moving condensate. Moreover, the time-dependent GPE allows to go beyond the Bogoliubov description by entering the non-linear regime, where one can observe saturation and self-trapping effects. Finally, we include an external trapping potential to simulate situations closer to the experimental ones.

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

I review existence of stationary and moving gap solitons in the Gross--Pitaevskii equation with a small periodic potential. These solitons are approximated by the explicit solutions of the coupled-mode system. We show, however, that exponentially decaying traveling solutions of the Gross--Pitaevskii equation do not generally exist in the presence of a periodic potential due to bounded oscillatory tails ahead and behind the moving solitary waves. The oscillatory tails are not accounted in the coupled-mode formalism and are estimated by using techniques of spatial dynamics and local center-stable manifold reductions. Existence of bounded traveling solutions of the Gross--Pitaevskii equation with a single bump surrounded by oscillatory tails on a large interval of the spatial scale is proven by using these techniques.

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

In this talk, we introduce the Bloch-decomposition based time-splitting spectral method to conduct numerical simulations of the dynamics of (non)linear SchrÄodinger equations subject to periodic and confining potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattice Bose-Einstein condensates in the superfluid regime. Joint work with Shi Jin, Peter A. Markowich, and Christof Sparber

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

We investigate the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with spatially-periodic scattering lengths. This type of "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii (GP) equation with a nonlinearity coefficient that varies periodically in space. For the case of a sinusoidal coefficient, we examine the dynamics of spatially-extended states (modulated amplitude waves) that we construct analytically using the method of averaging. For the case of piecewise-constant coefficient, we examine the dynamics of solitary waves that we construct using a "stitching" technique.

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of Bose-Einstein condensates (BEC) in a rotational frame. As preparatory steps, we take the 3D Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale it to obtain a four-parameter model and show how to reduce it to 2D GPE in certain limiting regimes. Then we study numerically and asymptotically the ground states, excited states and quantized vortex states as well as their energy and chemical potential diagram in rotating BEC. Some very interesting numerical results are observed. Finally, we study numerically stability and interaction of quantized vortices in rotating BEC. Some interesting interaction patterns will be reported. This talk is based on joint work with Qiang Du, Peter Markowich, Hanquan Wang and Yanzhi Zhang.

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

I report on a recent joint work together with R. Carles and P. Markowich, where we consider the time-dependent Gross-Pitaevskii equation modeling Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension-reduction for this nonlinear and nonlocal Schrödinger equation.

• Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Gyrokinetic Plasma Turbulence (2008)
• Event: Workshop and Minicourse "Kinetic Equations, Numerical Approaches and Fluid Models for Plasma Turbulence" (2008)

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

Banach Gelfand triples are an important subset from the modulation spaces. Starting from the Segal algbra S_0(Rd) and its dual one can use the notion of (unitary) Banach Gelfand triple isomorphism to describe e.g. the Fourier transform, or the mapping between operator kernels and their Kohn-Nirenberg symbol or their spreading distribution in a technically not so difficult way, building on standard functional analytic concepts only.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

We investigate how pseudodifferential operators behave with respect to Gabor frames. If the symbol is taken in a special class of non-smooth symbols that is one of the standard modulation spaces and is known as the Sjöstrand class then the operator is almost diagonalized by time-frequency shifts (phase-space shifts or coherent states) of a single function. In contrast to other almost diagonalization results, the quality of the almost diagonalization characterizes the symbol class. Various modifications and approximation results will be discussed.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

The theme of this talk is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau-Weyl operators". The link between standard Weyl calculus and Landau-Weyl calculus is made explicit by the use of an infinite family of intertwining "windowed wavepacket transforms"; this makes possible the use of the theory of modulation spaces to study various regularity properties. Our techniques allow us not only to recover easily the eigenvalues and eigenfunctions of the Hamiltonian operator of a charged particle in a uniform magnetic field, but also to prove global hypoellipticity results, and to study the regularity of the solutions to Schrödinger equations. This is joint work with Franz Luef.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

This lecture is dedicated to the jubilee of 25 years since the first technical report on modulation spaces was written. Nowadays, modulation spaces are recognized as the most important spaces of functions/distributions in the growing field of time-frequency analysis and its various applications. In particular, modulation spaces are designed to perform local analysis in time-frequency plane. Our aim is to perform micro-local analysis in the background of modulation spaces. The starting point is to give a reasonable definition of wave-front sets in modulation spaces. This leads to an equivalent notion of wave front sets in Fourier Lebesgue spaces. As applications, we describe (local) products in modulation spaces by the means of the corresponding wave front sets, and show that usual properties for a class of pseudo-differential operators which are valid for classical wave front sets also hold in our framework. The results are the part of ongoing research project with Stevan Pilipovic and Joachim Toft.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

In this talk, I will introduce how to use the frequency-uniform decomposition method to study the cauchy problem of nonlinear Schrodinger equations. I mainly show the global well-posedness of solutions to NLS equations with small rough data in certain modulation spaces.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

We present some characterizations of classical function spaces, e.g. the Schwartz space of test functions or Gelfand-Shilov spaces, in terms of the short-time Fourier transform. This talk surveys results originally obtained by Feichtinger, Groechenig and Zimmermann.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

Modulation spaces play a similar role with respect to Gabor families and within time-frequency analysis as the more classical function spaces (of Besov and Triebel Lizorkin type) with respect to wavelet bases. They can be defined via uniform (as opposed to dyadic) decompositions of the Fourier transform side, and have a natural continous description in terms of the STFT (short-time or gliding window Fourier Transform). On the Fourier transform side they are typical examples of so-called Wiener amalgam spaces, which are a very flexible tool to describe the global behaviour of certain local properties. Especially the convolution relations between Wiener amalgam spaces (decoupling of local and global properties) are a powerful tool.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

We consider the problem of high-frequency asymptotics for the time-dependent one-dimensional Schrodinger equation with rapidly oscillating initial data. This problem is commonly studied via the WKB method. An alternative method is based on the limit Wigner measure. This approach recovers geometrical optics, but, like the WKB method, it fails at caustics. To remedy this deficiency we employ the semiclassical Wigner function which is a formal asymptotic approximation of the scaled Wigner function but also a regularization of the limit Wigner measure. We obtain Airy-type asymptotics for the semiclassical Wigner function as solutions to the Wigner equation.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

Wigner functions were introduced as a phase space formulation of quantum mechanics, designed especially for the "semiclassical limit" according to the "correspondence principle". In the last 15 years the Wigner measures, as the weak limit of sequences of Wigner functions, have become a mathematical tool on their own for a wide class of "homogenization" problems. We present the key ideas of the concept of Wigner transforms and the problems where they are more or less useful.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

A review of old and recent results concerning coherent states will be presented, including semiclassical quantum propagation. We will also show how coherent states allow to construct objects localised in higher dimensional submanifolds of the underlying phase-space, up to the lagrangian case, and the importance, especially for long time evolution, of the freedom that provides continuous representation versus the discrete frame vision.

• Thematic program: Applied Analysis and Fast Computation in Phase-Space (2008)
• Event: Workshop "Applied Analysis and Fast Computation in Phase-Space (2008)" (2008)

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• Event: Workshop "Nanostructures in biology and physics" (2008)

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• Event: Workshop "Nanostructures in biology and physics" (2008)

Density functional theory (DFT) of classical systems provides a versatile and powerful framework to study on equal footing inhomogeneous density distribution and thermodynamics of nanostructures. The key problem of DFT is to construct and to test the accuracy of a functional that allows one to describe the system of interest, characterized by its interparticle interaction. Once a DFT for a given system is constructed, the system can be studied in any external field by minimizing the DFT.

In this talk I will give a brief introduction into the general formalism of DFT and present a density functional for charged hard spheres. The DFT for charged hard spheres allows one to study packing effects at high densities and short distances as well as screening of the electric field at larger distances. Applications to biological problems are outlined.

• Event: Workshop "Nanostructures in biology and physics" (2008)

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• Event: Workshop "Nanostructures in biology and physics" (2008)

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• Event: Workshop "Nanostructures in biology and physics" (2008)

A model of the ryanodine receptor (RyR) calcium-selective biological ion channel is used to study the energetics of ion binding selectivity (i.e., ion adsorption). RyR is a calcium-selective channel with four aspartates (a DDDD locus) in the selectivity filter, similar to the four glutamates (the EEEE locus) of the L-type calcium channel. While the affinity of RyR for Ca2+ is in the millimolar range (as opposed to the micromolar range of Ca2+ the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity.
A Poisson-Nernst-Planck/Density Functional Theory model of RyR is used to calculate the energetics of selectivity. In RyR, ion selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter.
While electrostatic terms dominate Ca2+ selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N mutation of RyR that is analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca2+ selectivity found in both theory and experiments.

• Event: Workshop "Nanostructures in biology and physics" (2008)

lectrical double layers (DL) are formed in a phase containing mobile charge carriers near a charged surface. Depending on the material carrying the mobile charges, DLs appear in electrolytes, molten salts, ionic liquids, plasmas, and even fast ion conductors (solid electrolytes). DLs in solutions of dissolved ions have special importance in electrochemistry, biology, and colloid chemistry. DLs near electrodes are different from DLs near charged objects carrying fixed surface charge (such as colloids, macromolecules, porous bodies) because the surface charge on the electrode can be controlled by applying an external voltage.
The electrical DL was a topic of extensive research using various methods from the Poisson-Boltzmann theory to state of the art statistical mechanical methods such as density functional theory. Recently, computer simulations became the dominant tool to study DLs according to their flexibility and accuracy. To exploit the advantages of symmetry, studies of DLs are commonly performed in the planar geometry where the elctrolyte is located between two charged surfaces. Monte Carlo simulations can be performed in the constant charge ensemble (where the surface charges on the elecrodes are fixed) or in the constant voltage ensemble (where the potential difference between the electrodes is fixed). It is advantageous to simulate the electrolyte in the grand canonical ensemble where the chemical potentials of the various ionic species are fixed. An overview of these various simulation techiques with a general introduction to Monte Carlo simulations will be given.
Simulations provide the charge density in the simulation cell from which the potential profile in the DL is computed by solving Poisson's equation using appropriate boundary conditions. The use of various boundary conditions (Neumann, Dirichlet) will be discussed in relation to the ensemble used in the simulation. Results for various situations and comparison with various theories will be presented.
Examples include the behavior of the DL capacitance at low temperatures, the effect of asymmetries of size and charge of ions on the DL potential, the competition of various ions at a higly charged electrode, the structure of the DL at dielectric interfaces, the effect of DL structure on the conductance of nanopores, and the importance of DLs in the behavior of ion channels.

• Event: Workshop "Nanostructures in biology and physics" (2008)

Natural systems excel at discriminating between molecules on the basis of subtle differences. Membrane-spanning protein channels, for example,are exquisitely designed to differentiate between Na+ (sodium) and K+(potassium) ions despite their identical charges and only sub-Angstrom differences in size. Consequently nearly all cells can selectively transport these ions across their membranes, a process that underlies such diverse physiological tasks as nerve cell signaling, heart rhythm control, and kidney function.
While scientists have long known that ion selectivity lies in the ability of the channel to satisfy or frustrate ion solvation requirements, the persistent question revolves around how channels and other biological structures give rise to such a subtle effect between Na+ and K+. By understanding ion discrimination in natural systems, we can potentially learn how to harness nature’s design principles in nano-scale devices that mimic biological function for varied applications, including fast, efficient water desalination. Here we present a novel explanation for ion discrimination in the celebrated potassium-selective protein channels, we contrast this explanation of natural ion discrimination with the unexpectedly antithetical mechanism found in a natural potassium-selective ion carrier, and finally we describe current work toward implementing ion selectivity in synthetic channels.

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• Event: Workshop "Nanostructures in biology and physics" (2008)

BioFEDs (biologically sensitive field-effect devices) are field-effect biosensors with semiconductor transducers. Their device structure is similar to an ISFET (ion-selective field-effect transistor), but the surface of the transducer is functionalized with receptor molecules. Conductance modulations of the transducer after binding of the analyte to the surface receptors provide the detection mechanism. The main advantage of BioFEDs is label-free operation.

In recent experiments, DNA strands and tumor markers were detected by silicon-nanowire devices. Despite the experimental successes, a quantitative theory to explain the functioning of the biosensors and to understand the experiments has been missing. The modeling of the biosensors is complicated by the fact that they consist of a biomolecular and a nanoelectronic part with different length scales, yet both parts have to be considered self-consistently.

We present the first self-consistent model for the quantitative analysis of BioFEDs. It is centered around a multi-scale model involving homogenized interface conditions for the Poisson equation for cylindrical and planar geometries (i.e., for nanowires and nanoplates). The mathematical analysis shows that not only the surface charge density, but also the dipole moment density of the biofunctionalized surface layer influences the conductance of the transducers. These simulation results are the first quantitative explanation of the functioning of BioFEDs.

• Event: Workshop "Nanostructures in biology and physics" (2008)

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• Event: Workshop "Nanostructures in biology and physics" (2008)

You may download the abstract of the talk

• Event: Workshop "Nanostructures in biology and physics" (2008)

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• Event: Workshop "Nanostructures in biology and physics" (2008)

We present measurements on direct radio-frequency pumping of ion channels and pores bound in bilipid membranes. We make use of newly developed microcoaxes, which allow delivering the high frequency signal in close proximity to the membrane bound proteins and ion channels. We find rectification of the radio-frequency signal, which is used to pump ions through the channels and pores.

• Event: Workshop "Nanostructures in biology and physics" (2008)

Networks are widely used in complex systems, for example, to identify closely related groups of participants in the system (called modules, clusters or communities). The network clustering program CFinder identifies densely internally connected groups of nodes (modules) in networks and allows explicitly for overlaps among the identified modules. Recently, we have extended CFinder to weighted and directed networks.
In both graph models and directed real graphs we identify two types of directed network modules: in- and out-modules based on whether the overlaps of the modules contain mainly in- or out-hubs. We find in-modules in: the directed graph of Google's own webpages and a large word association net of English words. We find out-modules in an e-mail web and the transcription regulatory network of yeast.
In biological and other networks, too, modules and the "background" are often hard to tell apart, and one cannot draw sharp boundaries for the modules. The extension of CFinder to weighted graphs allows one to identify densely internally connected groups of nodes (proteins in a PPI network) with higher confidence.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

We present a network model for supply chains with policy attributes using kinetic equations. The proposed network model is an extension of the single lane model with policy attributes presented by Degond et. al.
The single lane model is extended to the network case using suitable moment closures. Numerical results are presented for several different examples.

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• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

In this talk, I will show how to derive a gas-kinetic equation from an underlying simple microscopic model, and, in turn, a non-local macroscopic model from the gaskinetic model. In contrast to other approaches, the collision term will be explicitely evaluated in the transition from the kinetic to the macroscopic model. This enables to relate the macroscopic "pressure term" or "anticipation term" to microscopic statistical properties.
In the second part, I will derive analytic criteria for the flow stability for nonlocal macroscopic models in closed and open systems, and show that the flow stability is equivalent to the microscopic string stability of the intelligent-driver model and related modell classes. Finally, I will define a set of general stability classes applicable for both microscopic and macroscopic models. By simulation of open systems with a bottleneck, I will demonstrate that micro and macromodels of the same stability class produce identical sets of spatiotemporal states, i.e., the same "phase diagrams".

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• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Understanding the dynamical properties of large crowds is of great practical importance. Emergency situations require efficient evacuation strategies to avoid casualties and reduce the number of injured persons.
In many cases legal requirements have to be fulfilled, e.g. for aircraft or cruise ships. For tests already in the planning stage reliable simulation models are required to avoid additional costs for changes in the construction.
From a physics point of view pedestrian dynamics is challenging due to the large variety of collective phenomena that can be observed, e.g. formation of lanes in counterflow.
In this talk we give an overview on the empirical and theoretical results on pedestrian dynamics. The focus will be on a cellular automaton model (the floor field model) in which interactions are implemented in analogy to the process of chemotaxis.

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• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Can we reliably predict and quantitatively describe how large groups of people move? One approach to this problem is based on the quantitative methods of statistical physics. In cases when the interactions between the members of a group are relatively well defined (e.g, pedestrian traffic) the corresponding models reproduce relevant aspects of the observed phenomena.
People moving in the same environment typically develop specific patterns of collective motion including the formation of lanes, flocking or jamming at bottlenecks. We simulate such phenomena assuming realistic interactions between particles representing humans.
The two specific cases to be discussed in more detail are waves produced by crowds at large sporting events and the main features of pedestrian escape panic under various conditions. Our models allow the prediction of crowd behavior even in cases when experimental methods are obviously not applicable and, thus, are expected to be useful in assessing the level of security in situations involving large groups of excited people.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Ants build and use a transport system that has many similarities with human-build highway networks. The main mechanism for the formation of these ant trails is a special form of communication on a chemical basis, called chemotaxis.
Using a stochastic cellular automaton model which is an extension of the Asymmetric Simple Exclusion Process (ASEP) that takes into account the effects of chemotaxis we discuss the basic properties of the traffic flow on existing trails.
Surprisingly it is found that in certain regimes the average speed of the ants can vary non-monotonically with their density. This is in sharp contrast to highway traffic. The observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.
The predictions of the model approach are in qualitative agreement with empirical observations on natural ant trails for which we have determined fundamental diagrams, velocity and headway distributions etc. by video analysis.

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• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

We consider Enskog-Boltzmann models for traffic flows and derive under a suitable scaling the corresponding Fokker-Planck equations.
Connections with the Vlasov-Fokker-Planck model recently introduced by Illner & coauthors are discussed. Some numerical results are also presented.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

After a brief survey of traffic models I will discuss three questions: Existence and univalence (or multivalence) of the fundamental diagram, the link between kinetic and macroscopic models, and the emergence of moving traffic jams in dense traffic.
The latter phenomenon will be discussed for a macroscopic model derived from a Vlasov type kinetic model (with reasonable nonlocalities) which possesses classes of traveling wave solutions.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

• WK student seminar

The semantic characterization of answer sets as classical models of a logic program satisfying all loop formulas, due to Lin and Zhao [2004], showed that answer sets can be understood as solutions to a set of (Boolean) constraints. This observation has led to the development of answer set solvers that exploit solvers for classical propositional logic as back-end inference engines. Recently, our group in Potsdam developed the new answer set solver "clasp", also relying on (Boolean) constraints, e.g. in backjumping and conflict-driven learning, which are some of the key techniques natively supported within "clasp". To our knowledge, "clasp" is the first and sill the only answer set solver that combines answer set and (Boolean) constraint solving techniques in an efficient way. The talk introduces the semantic basis of "clasp", its disjunctive spin-off "claspD", and finally, we consider related issues arising in answer set programming, like grounding and incrementality.

• Thematic program: Foundations of Knowledge and Information Handling (2007)
• Thematic program: Foundations of Knowledge and Information Handling (2007)

In many technical applications, e.g. flows in transonic diffusers, flow situations occur where a shock generated in a supersonic flow regime, where viscous effects are negligible for large Reynolds numbers, interacts with a viscous boundary layer at a wall eventually leading to flow separation. A formulation of the resulting unsteady viscous inviscid interaction problem for laminar flows by means of asymptotic analysis will be given under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes one-dimensional in the leading order approximation. In the following several numerical approaches for the time integration of the governing system of PDEs (implicit Lax-Wendroff scheme, method of lines: implicit Euler scheme and TR-BDF2 scheme) will be discussed.

• WK student seminar

Steady three dimensional transonic flows through channels so narrow that the classical boundary layer approach fails are considered. Under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes two dimensional to the leading order. The resulting interaction problem is formulated, by using asymptotic analysis for large Reynolds numbers.

• WK student seminar

To solve the optimal consumption and investment problem, there exist two different methods. This talk will concentrate on the martingale approach ("the dual approach"). The market setting is a geometric Ornstein-Uhlenbeck market. Estimates for long-term behavior will be presented.

• WK student seminar

• WK student seminar

The biological process of chemotaxis, i.e. the direct movement of a biological population towards a chemical signal, can be modeled by the so-called Keller-Segel system describing the evolution of the population density and of the chemical con- centration. In this talk we will present this model and its main mathematical properties, i.e. a priori estimates, global existence and blow-up in dimension $dge2$.

• WK seminar

We start with a short introduction to the idea of an entropy method, demonstrated for a simple Fokker-Planck equation. Afterwards, we will discuss the possibility to use such a method for open quantum systems. Particular focus will be given to recent results and the main problems with this approach.

• WK student seminar

• WK student seminar

• WK seminar

• Thematic program: Motility: from the molecular to the population scale (2008)
• WK seminar

• Event: Workshop and Minicourse on 'Multiscale Problems and Models in Traffic Flow' (2008)

• Event: Workshop and Minicourse on 'Multiscale Problems and Models in Traffic Flow' (2008)