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Rampf, Cornelius (U. Heidelberg)  WPI, OMP 1, Seminar Room 08.135  Mon, 18. Dec 17, 14:00 
Shellcrossing in quasionedimensional flow  
Blowup of solutions for the cosmological fluid equations, often dubbed shellcrossing or orbit crossing, denotes the breakdown of the singlestream regime of the colddarkmatter fluid. At this instant, the velocity becomes multivalued and the density singular. Shellcrossing is well understood in one dimension (1D), but not in higher dimensions. This talk is about quasionedimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shellcrossing using the EulerPoisson equations written in Lagrangian coordinates. The signature of shellcrossing is then just the vanishing of the Jacobian of the Lagrangian map, a regular perturbation problem. In essence the problem of the first shellcrossing, which is highly singular in Eulerian coordinates, has been desingularized by switching to Lagrangian coordinates, and can then be handled by perturbation theory. Allorder recursion relations are obtained for the timeTaylor coefficients of the displacement field, and it is shown that the Taylor series has an infinite radius of convergence. This allows the determination of the time and location of the first shellcrossing, which is generically shown to be taking place earlier than for the unperturbed 1D flow. The time variable used for these statements is not the cosmic time t but the linear growth time $tau sim t^{2/3}$. For simplicity, calculations are restricted to an Einsteinde Sitter universe in the Newtonian approximation, and tailored initial data are used. However it is straightforward to relax these limitations, if needed.  

Colombi, Stephane (I.Astrophysique Paris)  WPI, OMP 1, Seminar Room 08.135  Mon, 18. Dec 17, 15:30 
Phasespace structure of dark matter protohalos: pre and postcollapse regimes  
During this talk I'll discuss the formation of primordial dark matter halos from smooth initial conditions. To simplify furthermore the context, we shall consider structures seeded by 3 sine waves of various amplitudes. Phasespace evolution of these objects will be studied from the computational point of view, by using a state of the art Vlasov solver, and the theoretical point of view, by comparing the numerical results to predictions of Lagrangian perturbation theory. While these latter are in principle only calculable prior to collapse, extension to multistreaming regime will be discussed, with actual implementation in the 1D cosmological case of "postcollapse" Lagrangian perturbation theory.  

Nguyen, Toan (U. Pennsylvania)  WPI, OMP 1, Seminar Room 08.135  Tue, 19. Dec 17, 9:30 
Longtime estimates for VlasovMaxwell in the nonrelativistic limit  
I will present a joint work with D. HanKwan and F. Rousset on establishing long time estimates for VlasovMaxwell systems near stable homogeneous equilibria, which are valid for times of an arbitrarily large polynomial order of the speed of light in the nonrelativistic limit.  

Lesur, Maxime (U. Lorraine)  WPI, OMP 1, Seminar Room 08.135  Tue, 19. Dec 17, 14:30 
Plasma turbulence and transport dominated by nonlinear kinetic effects  
In hot plasmas, collisions are so rare that microscopic vortexlike structures develop in the phasespace of the particle distribution: coupling both real space and velocity (or energy) space. In this work, we focus on magnetic confinement fusion plasmas (in toroidal geometry). We base our approach on a reduced kinetic model [1, 2], akin to the VlasovPoisson model. Our numerical simulations indicate the nonlinear selforganisation, within the turbulence, of finescale velocityspace (or energyspace) structures, which can drive most of the macroscopic radial transport in some regimes.  

Brenier, Yann (CNRS X Palaiseau):  WPI, OMP 1, Seminar Room 08.135  Wed, 20. Dec 17, 9:30 
On the MAK reconstruction method for the early universe  
I will report on some very recent progress made on the MAK method for the numerical reconstruction of the early universe (in particular by Bruno Lévy and JeanDavid Benamou), based either on the geometric algorithm of Mérigot for the MongeAmpère equation or on the entropic regularization method (going back to Schrödinger in the 30s) for the optimal mass transport problem with quadratic cost.  

Gürcan, Özgür (U. PMC Paris)  WPI, OMP 1, Seminar Room 08.135  Wed, 20. Dec 17, 14:30 
Dynamics of a shell model of bounced averaged gyrokinetic Vlasov Equation  
Development of a shell model for a bounced averaged gyrokinetic Vlasov equation is presented. First, the linear dynamics is compared with a linear solver based on solving the linear dispersion relation numerically. Then the nonlinear dynamics is studied by analyzing the wavenumber spectrum of quadratic conserved quantities. The resulting spectra seems to show a cascade spectrum at high k and predatorprey like oscillations in low k. Future perspectives including a logarithmically discretized three dimensional version of the model, which is 2D in space and 1D in energy, is discussed.  

Diamond, Patrick (UC San Diego)  WPI, OMP 1, Seminar Room 08.135  Thu, 21. Dec 17, 9:30 
QuasiGeostrophic Fluids and Vlasov Plasmas: Parallels and Intersections  
This talk explores connections and contrasts between the nonlinear dynamics of two prototypical systems in plasmas and fluids. The first is the quasigeostrophic fluid, which evolves by conservative advection of potential vorticity. The QG system is the minimal model for largescale atmospheric waves and the jet stream (zonal flow). The second is the Vlasov–Poisson system, in which the Vlasov equation describes the conservative advection of a phase space density. Many interesting connections between these two systems already have been noted. This talk will expand the list and suggest directions for future crossfertilization .  

Uhlemann, Cora (U. Cambridge)  WPI, OMP 1, Seminar Room 08.135  Thu, 21. Dec 17, 15:00 
Finding closure  what SchrödingerPoisson can teach us about cumulant hierarchies  
Since dark matter almost exclusively interacts gravitationally, the dynamics of its phase space distribution is described by VlasovPoisson. One key property of VlasovPoisson is that it corresponds to an infinite tower of coupled equations for its cumulants. Hence, determining the timeevolution of dark matter density and velocity demands solving the full cumulant hierarchy. While the perfect pressureless fluid model is the only consistent truncation, it cannot describe the dynamics in the multistreaming regime. Given this inadequacy of truncations for the cumulant hierarchy, I suggest to take a closer look at closure schemes that rely on recurrence. To this end, I will introduce SchrödingerPoisson as theoretically motivated and phenomenologically viable approximation to VlasovPoisson. I will show how SchrödingerPoisson generates cumulants at all orders consistently and hence can serve as inspirational example for finding closure schemes.  

Germain, Pierre (NYU Courant)  WPI, OMP 1, Seminar Room 08.135  Fri, 22. Dec 17, 10:00 
Recent mathematical progress on weak turbulence”  
I will present two recent rigorous results on weak turbulence: the first one is on the local wellposedness of the kinetic wave equation (with A. Ionescu and M.B. Tran). And the second one on the derivation of the kinetic wave equation from the nonlinear Schrodinger equation (work in progress, with T. Buckmaster, Z. Hani, and J. Shatah).  

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