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Vlasov Models in Kinetic Theory (September 19-23, 2011)

Tutorial Week (September 12-16, 2011)

Organizing Committee

vlasov

 

[Image courtesy of NASA, ESA and Hubble Heritage Team]

 

Description

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.

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.

DatesTitleOrganizers
September 19-23, 2011Vlasov Models in Kinetic TheoryPierre Degond, Francis Filbet, Robert Glassey, Jingmei Qiu, Gerhard Rein

Video Links
Description Speaker
Video
Abstract
Slides
MondaySeptember 12th 2011
Time Description Speaker Location Slides
1:30 - 3:00 Introduction to Kinetic Theory Clement Mouhot, University of Cambridge 11th Floor Lecture Hall
3:00 - 3:30 Coffee/Tea Break   11th Floor Collaborative Space
3:30 - 5:00 Introduction to Kinetic Theory Clement Mouhot, University of Cambridge 11th Floor Lecture Hall
TuesdaySeptember 13th 2011
Time Description Speaker Location Slides
10:30 - 12:00 Numerical methods for the Vlasov Equation Eric Sonnendrucker, Université de Strasbourg I (Louis Pasteur) 10th Floor Seminar Room
PDF
2:30 - 4:00 Numerical methods for the Vlasov Equation Eric Sonnendrucker, Université de Strasbourg I (Louis Pasteur) 11th Floor Lecture Hall
PDF
4:00 - 4:30 Coffee/Tea Break   11th Floor Collaborative Space
4:30 - 5:30 Professional Development
(postdocs and graduate students)
  11th Floor Lecture Hall
WednesdaySeptember 14th 2011
Time Description Speaker Location Slides
10:00 - 12:00 Computation Working Group Eric Sonnendrucker, Université de Strasbourg I (Louis Pasteur) 10th Floor Seminar Room
3:00 - 4:30 Introduction to Kinetic Theory Clement Mouhot, University of Cambridge 11th Floor Lecture Hall
4:30 - 5:00 Coffee/Tea Break   11th Floor Collaborative Space
ThursdaySeptember 15th 2011
Time Description Speaker Location Slides
10:30 - 12:00 TBA Chi-Wang Shu, Brown University 10th Floor Seminar Room
2:30 - 4:00 TBA Chi-Wang Shu, Brown University 11th Floor Lecture Hall
4:00 - 5:30 Welcome Reception   11th Floor Collaborative Space
FridaySeptember 16th 2011
Time Description Speaker Location Slides
2:30 - 4:00 Introduction to Kinetic Theory Clement Mouhot, University of Cambridge  
4:00 - 4:30 Coffee/Tea Break   11th Floor Collaborative Space
MondaySeptember 19th 2011
Time Description Speaker
Abstract
Slides
9:00 - 9:30 Registration and Welcome Coffee  
9:30 - 10:00 Welcome  
10:00 - 11:00

On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian

Hyung Ju Hwang, Pohang University of
Science and Technology (POSTECH)

PDF Word
11:00 - 12:00 Kinetic equations for swarming: mean
field limit and qualitative properties
Jose Antonio Carrillo, Autonomous University of Barcelona
PDF Word
PDF
12:00 - 2:00 Break for Lunch
Free Time
 
2:00 - 3:00 A conservative semi-Lagrangian method
for the gyrokinetic Vlasov equation
Eric Sonnendrucker, Universite de Strasbourg
PDFWord
PDF
3:00 - 4:00 Long time behaviour for a Vlasov-Fokker-Planck equation

Francois Bolley, Universite de Paris-Dauphine

PDF Word
4:00 - 6:00 Welcome Reception  
TuesdaySeptember 20th 2011
Time Description Speaker
Abstract
Slides
9:30 - 10:30

 

Computing Multivalued Solutions of Pressureless
Gas Dynamics by Deterministic Particle Methods

Alina Chertok, North Carolina State University
PDF Word
PDF
10:30 - 11:00 Coffee/Tea Break
(Bagels and fruit provided)
 
11:00 - 12:00 The mean-field limit for a regularized
relativistic Vlasov-Maxwell dynamics
Francois Golse, École Polytechnique
PDF Word
PDF
12:00 - 2:00 Break for Lunch
Free Time
 
2:00 - 3:00 Well posedness for non linear transport models Pierre-Emmanuel Jabin, Universite de Nice Sophia Antipolis
PDF Word
PDF
3:00 - 4:00 Efficiant computation of the semi classical limit of the Schrödinger equation Giovanni Russo, Università di Catania
4:00 - 4:30 Coffee/Tea Break
(Cookies & Fruit provided)
 
4:30 Discussions on applications to plasma physics  
WednesdaySeptember 21st 2011
Time Description Speaker
Abstract
Slides
9:30 - 10:30 Orbital Stability of Spherical Galactic Models Mohammed Lemou, Centre National de
la Recherche Scientifique (CNRS)
PDF Word
PDF
10:30 - 11:00 Coffee/Tea Break
(Bagels and fruit provided)
 
11:00 - 12:00 A self-similar solution of the Einstein-Vlasov system Alan Rendall, Max Planck Institute für Gravitationsphysik,
Albert-Einstein-Institut
PDFWord
PDF
12:00 - 2:00 Break for Lunch
Free Time
 
2:00 - 3:00 Black hole formation for Vlasov matter
from a complete regular past
Hakan Andreasson, AAAS
PDF Word
3:00 - 4:00 On the Hamiltonian-Jacobi variational formulation of the Vlasov equation Phil Morrison, University of Texas
PDF Word
4:00 - 4:10 Group Photo in Lecture Hall  
4:10 - 4:30 Coffee/Tea Break
(Cookies & Fruit provided)
 
4:30 Discussions on gravitational models  
ThursdaySeptember 22nd 2011
Time Description Speaker
Abstract
Slides
9:30 - 10:30 Numerical and analytical issues for Vlasov-Boltzmann-Maxwell systems Irene Gamba, University of Texas
PDF Word
10:30 - 11:00 Coffee/Tea Break
(Bagels and fruit provided)
 
11:00-12:00 Simulations of Vlasov-Poisson equations
for infinite homogeneous stellar systems
Yingda Cheng, University of Texas
PDF Word
PDF
12:00 - 2:00 Break for Lunch
Free Time
 
2:00 - 3:00 Some polymeric fluid flow models: steady states & large-time convergence Anton Arnold, Technische Universität Wien
PDF Word
PDF
3:00 - 4:00 Advanced particle methods for collisionless plasma simulations Andrew Christlieb, Michigan State University
PDF
4:00 - 4:30 Coffee/Tea Break
(Cookies & Fruit provided)
 
4:30 New Applications for Vlasov Models  
FridaySeptember 23rd 2011
Time Description Speaker
Abstract
Slides
9:30 - 10:30 Global Existence for the Vlasov-Poisson System with Steady Spatial Asymptotic Behavior Jack Schaeffer, Carnegie Mellon
PDF Word
10:30 - 11:00 Coffee/Tea Break
(Bagels and fruit provided)
 
11:00 - 11:10 Survey Distribution
Please return to 11th floor reception desk
 
11:10 - 12:10 Dynamics of spatially homogeneous solutions to the Einstein-Vlasov system Simone Calogero, University of Granada
12:10 - 2:00 Break for Lunch
Free Time
 
2:00 - 3:00 Free Discussions  
4:00 - 4:30 Coffee/Tea Break
(Cookies & Fruit provided)
 
4:00 - 4:50 Free Discussions