Organizing Committee
Abstract

Vlasov-type models deal with continua of particles where the electric charges dominate the collisions, so that the collisions are ignored. They occur in physical plasmas, including astrophysical plasmas and fusion reactors.

There are many examples of astrophysical plasmas of this type, such as the solar wind. When a fusion reactor is very hot, the relevant times scales are so short that collisions can be ignored. Vlasov theory also models systems where the dominant force is gravity, such as clusters of stars or galaxies.

Image courtesy of NASA, ESA and Hubble Heritage Team

Confirmed Speakers & Participants

Workshop Schedule

Monday, September 19, 2011
TimeEventLocationMaterials
9:00 - 9:30Registration and Welcome Coffee  
9:30 - 10:00Welcome  
10:00 - 11:00On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian - Hyung Ju Hwang, Pohang University of Science and Technology11th Floor Lecture Hall
11:00 - 12:00Kinetic equations for swarming, mean field limit and qualitative properties - Jose Antonio Carrillo, Autonomous University of Barcelona11th Floor Lecture Hall
12:00 - 2:00Break for Lunch Free Time  
2:00 - 3:00A conservative semi-Lagrangian method for the gyrokinetic Vlasov equation - Eric Sonnendrucker, Universite de Strasbourg11th Floor Lecture Hall
3:00 - 4:00Long time behavior for a Vlasov Fokker Planck equation - Francois Bolley, Universite de Paris-Dauphine11th Floor Lecture Hall
4:00 - 6:00Welcome Reception  
Tuesday, September 20, 2011
TimeEventLocationMaterials
9:30 - 10:30Computing Multivalued Solutions of Pressureless Gas Dynamics by Deterministic Particle Methods - Alina Chertok, North Carolina State University11th Floor Lecture Hall
10:30 - 11:00Coffee and Tea Break (Bagels and fruit provided)11th Floor Collaborative Space 
11:00 - 12:00The mean-field limit for a regularized relativistic Vlasov-Maxwell dynamics - Francois Golse, École Polytechnique11th Floor Lecture Hall
12:00 - 2:00Break for Lunch Free Time  
2:00 - 3:00Well posedness for non linear transport models - Pierre-Emmanuel Jabin, Universite de Nice Sophia Antipolis11th Floor Lecture Hall
3:00 - 4:00Efficiant computation of the semi classical limit of the Schrödinger equation - Giovanni Russo, Università di Catania11th Floor Lecture Hall 
4:00 - 4:30Coffee and Tea Break (Cookies & Fruit provided)11th Floor Collaborative Space 
4:30 - 6:00Discussions on applications to plasma physics  
Wednesday, September 21, 2011
TimeEventLocationMaterials
9:30 - 10:30Orbital Stability of Spherical Galactic Models - Mohammed Lemou, Centre National de la Recherche Scientifique (CNRS)11th Floor Lecture Hall
10:30 - 11:00Coffee and Tea Break (Bagels and fruit provided)11th Floor Collaborative Space 
11:00 - 12:00A self-similar solution of the Einstein-Vlasov system - Alan Rendall, Max Planck Institute für Gravitationsphysik, Albert-Einstein-Institut11th Floor Lecture Hall
12:00 - 2:00Break for Lunch Free Time  
2:00 - 3:00Black hole formation for Vlasov matter from a complete regular past - Hakan Andreasson, AAAS11th Floor Lecture Hall
3:00 - 4:00On the Hamiltonian-Jacobi variational formulation of the Vlasov equation - Phil Morrison, University of Texas11th Floor Lecture Hall
4:00 - 4:10Group Photo in Lecture Hall11th Floor Lecture Hall 
4:10 - 4:30Coffee and Tea Break (Cookies & Fruit provided)11th Floor Collaborative Space 
4:30 - 6:00Discussions on gravitational models  
Thursday, September 22, 2011
TimeEventLocationMaterials
9:30 - 10:30Numerical and analytical issues for Vlasov-Boltzmann-Maxwell systems - Irene Gamba, University of Texas11th Floor Lecture Hall
10:30 - 11:00Coffee and Tea Break (Bagels and fruit provided)11th Floor Collaborative Space 
11:00 - 12:00Simulations of Vlasov-Poisson equations for infinite homogeneous stellar systems - Yingda Cheng, University of Texas11th Floor Lecture Hall
12:00 - 2:00Break for Lunch Free Time  
2:00 - 3:00Some polymeric fluid flow models steady states & large-time convergence - Anton Arnold, Technische Universität Wien11th Floor Lecture Hall
3:00 - 4:00Advanced particle methods for collisionless plasma simulations - Andrew Christlieb, Michigan State University11th Floor Lecture Hall
4:00 - 4:30Coffee and Tea Break (Cookies & Fruit provided)11th Floor Collaborative Space 
4:30 - 6:00New Applications for Vlasov Models  
Friday, September 23, 2011
TimeEventLocationMaterials
9:30 - 10:30Global Existence for the Vlasov-Poisson System with Steady Spatial Asymptotic Behavior - Jack Schaeffer, Carnegie Mellon11th Floor Lecture Hall
10:30 - 11:00Coffee and Tea Break (Bagels and fruit provided)11th Floor Collaborative Space 
11:00 - 11:10Survey Distribution Please return to 11th floor reception desk.  
11:10 - 12:10Dynamics of spatially homogeneous solutions to the Einstein-Vlasov system - Simone Calogero, University of Granada11th Floor Lecture Hall
12:10 - 2:00Break for Lunch Free Time  
2:00 - 3:00Free Discussions11th Floor Collaborative Space 
4:00 - 4:30Coffee and Tea Break (Cookies & Fruit provided)11th Floor Collaborative Space 
4:00 - 4:50Free Discussions11th Floor Collaborative Space 

Tutorial Week Schedule

Monday, September 12, 2011
TimeEventLocationMaterials
1:30 - 3:00Introduction to Kinetic Theory - Clement Mouhot, University of Cambridge11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 5:00Introduction to Kinetic Theory - Clement Mouhot, University of Cambridge11th Floor Lecture Hall 
Tuesday, September 13, 2011
TimeEventLocationMaterials
10:30 - 12:00Numerical methods for the Vlasov Equation - Eric Sonnendrucker, Université de Strasbourg I (Louis Pasteur)10th Floor Seminar Room 
2:30 - 4:00Numerical methods for the Vlasov Equation - Eric Sonnendrucker, Université de Strasbourg I (Louis Pasteur)11th Floor Lecture Hall 
4:00 - 4:30Coffee/Tea Break11th Floor Collaborative Space 
4:30 - 5:30Professional Development (postdocs and graduate students)11th Floor Lecture Hall 
Wednesday, September 14, 2011
TimeEventLocationMaterials
10:00 - 12:00Computation Working Group - Eric Sonnendrucker, Université de Strasbourg I (Louis Pasteur)10th Floor Seminar Room 
3:00 - 4:30Introduction to Kinetic Theory - Clement Mouhot, University of Cambridge11th Floor Lecture Hall 
4:30 - 5:00Coffee/Tea Break11th Floor Collaborative Space 
Thursday, September 15, 2011
TimeEventLocationMaterials
10:30 - 12:00TBA - Chi-Wang Shu, Brown University10th Floor Seminar Room 
2:30 - 4:00TBA - Chi-Wang Shu, Brown University11th Floor Lecture Hall 
4:00 - 5:30Welcome Reception11th Floor Collaborative Space 
Friday, September 16, 2011
TimeEventLocationMaterials
2:30 - 4:00Introduction to Kinetic Theory - Clement Mouhot, University of Cambridge11th Floor Lecture Hall 
4:00 - 4:30Coffee/Tea Break11th Floor Collaborative Space 

Problems

Problem 1: Stability of Equilibria.

There are a lot of steady states in the Vlasov theory and their stability has been a major focus of interest. Stability requires both very long-time computations as well as theoretical analysis in order to make progress. A fundamental open problem in Vlasov theory is the question of whether there are any periodic BGK modes that are stable under arbitrary perturbations of the same period. Another open problem is to find unstable galaxy configurations in stellar dynamics. Collaborations in these problems between numerical and theoretical researchers are particularly crucial.

Problem 2: Boundary Effects.

Boundary effects play an major role physical plasmas. Many effects can occur at boundaries, for instance, chemical reactions with the surface material. An important focus of our program will be to design numerical schemes to capture possible singularity formation at boundaries and the propagation of singularities in a general 3D domain.

Problem 3: Landau Damping.

The concept of Landau damping has been a major source of controversy in the physics community for decades. In principle it could be checked numerically except it requires very long-time computations. The need for great accuracy is a challenge to the numerical community. Recent work has established Landau damping for the case of analytic data for the Vlasov-Poisson system. A central question is to investigate a possible Landau damping effect in the presence of a magnetic field.

Problem 4: Well-posedness.

A major open problem is whether the three- dimensional Vlasov-Maxwell system is globally well-posed as a Cauchy problem. All that is known is, on the one hand, global existence but not uniqueness of weak solutions and, on the other, well-posedness and regularity of solutions assuming either some symmetry or almost neutrality. Computation of asymmetric solutions should shed light on the general problem.

Associated Semester Workshops

Kinetic Theory and Computation
Boltzmann Models in Kinetic Theory

Lecture Videos

Advanced particle methods for collisionless plasma simulations

Andrew Christlieb
Michigan State University
September 22, 2011

A self-similar solution of the Einstein-Vlasov system

Alan Rendall
Max Planck Institute fur Gravitationsphysik, Albert-Einstein-Institut
September 21, 2011

Orbital Stability of Spherical Galactic Models

Mohammed Lemou
Centre National de la Recherche Scientifique (CNRS)
September 21, 2011