Organizing Committee
Abstract

The celebrated Boltzmann equation is the foundation of the kinetic theory for dilute collections of particles, which undergo elastic binary collisions. The Boltzmann theory is at the center of a series of multi-scaled physical models that connect microscopic multiparticle models to macroscopic fluid models such as the Navier-Stokes equations:

Particles → Boltzmann → Fluids

The first arrow refers the Boltzmann-Grad limit, while the second arrow refers to various hydrodynamic limits which lead to the fundamental equations of fluids. The Boltzmann theory therefore provides a practical tool and machinery for deriving macroscopic models in broad physical applications. Due to its importance, there has been an explosion of mathematical studies, both theoretical and numerical, for the Boltzmann equation.A major open problem that remains is to determine whether or not smooth initial data would lead to a unique global-in-time solution of the Boltzmann equation. Nevertheless, there have been exciting new developments in recent years. The focus of the program is to bring computational and theoretical people together to investigate problems of fundamental importance.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, November 7, 2011
TimeEventLocationMaterials
8:30 - 8:55am ESTRegistration and Welcome Coffee  
8:55 - 9:00am ESTWelcome - Jill Pipher, Director, ICERM11th Floor Lecture Hall 
9:00 - 9:45am ESTFrom the Vlasov-Maxwell-Boltzmann System to Incompressible viscous electro-magneto-hydrodynamics, part I - Laure Saint-Raymond, Ecole Normale Supérieure & University Paris 611th Floor Lecture Hall 
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTExact summation of the Chapman- Enskog expansion, a primer - Marshall Slemrod, University of Wisconsin11th Floor Lecture Hall
11:30 - 12:15pm ESTA Collision-Based Hybrid Method for Linear Transport - Cory Hauck, Oak Ridge National Laboratory11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:15pm ESTThe Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems - Tong Yang, City University of Hong Kong11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break  
4:00 - 4:45pm ESTCorrelation among elemental relaxation and driven-flow problems for a rarefied gas - Shigeru Takata, Kyoto University11th Floor Lecture Hall
Tuesday, November 8, 2011
TimeEventLocationMaterials
9:00 - 9:45am ESTLarge time behavior of coagulation-fragmentation equations with degenerate diffusion - Laurent Desvillettes, École Normale Supérieure de Cachan11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTFourier Law and Non-Isothermal Boundary in the Boltzmann Theory - Chanwoo Kim, University of Cambridge11th Floor Lecture Hall
11:30 - 12:15pm ESTEfficient methods for solving the Boltzmann equation for nanoscale transport applications - Nicolas Hadjiconstantinou, Massachusetts Institute of Technology11th Floor Lecture Hall 
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:15pm ESTRiemann Problem for a Boltzmann shock wave with the hard sphere model - Shih-Hsien Yu, National University of Singapore11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTTraffic Flow Modeling - Tong Li, University of Iowa11th Floor Lecture Hall
Wednesday, November 9, 2011
TimeEventLocationMaterials
9:00 - 9:45am ESTBose condensates in interaction with excitations - a kinetic model - Anne Nouri, Aix-Marseille University11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTKac's Program in Kinetic Theory - Stephane Mischler, Université de Paris-Dauphine11th Floor Lecture Hall
11:30 - 12:15pm ESTOptimal Large-Time Decay Rates for Collisional Kinetic Equations in the Whole Space - Robert Strain, University of Pennsylvania11th Floor Lecture Hall 
12:30 - 12:40pm ESTGroup Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:15pm ESTDerivation of MHD equations from the Vlasov-Maxwell-Boltzmann system - Juhi Jang, University of California, Riverside11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTCompeting interactions in kinetic models for fluids - Rossana Marra, University of Roma Tor Vergata11th Floor Lecture Hall
Thursday, November 10, 2011
TimeEventLocationMaterials
9:00 - 9:45am ESTGhost effect by curvature - Raffaele Esposito, Università di L'Aquila11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTFrom the Vlasov-Maxwell-Boltzmann System to Incompressible viscous electro-magneto-hydrodynamics, part II - Diogo Arsenio, École Normale Supérieure11th Floor Lecture Hall 
11:30 - 12:15pm ESTHypocoercivity for some Linear Kinetic Equations with a Boundary - Frederic Herau, Université de Nantes11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:15pm ESTUnique moment set from the order of magnitude method - Henning Struchtrup, University of Victoria11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTHydrodynamic limit and boundary layers - Nader Masmoudi, New York University11th Floor Lecture Hall 
Friday, November 11, 2011
TimeEventLocationMaterials
9:00 - 9:45am ESTEuler limit for Boltzmann equation with Maxwell boundary condition - Claude Bardos, Université de Paris VII (Denis Diderot)11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 10:35am ESTSurvey Distribution  
10:35 - 11:20am ESTFluid Approximations from Boltzmann Equations for Domains with Boundary - C. David Levermore, University of Maryland11th Floor Lecture Hall
11:35 - 12:20pm ESTEstimates and approximations to the non-linear Boltzmann equation - Irene Gamba, University of Texas11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:00pm ESTDiscussions11th Floor Lecture Hall 
3:00 - 3:30pm ESTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:45pm ESTDiscussions11th Floor Lecture Hall 

Tutorial Week Schedule

Monday, October 31, 2011
TimeEventLocationMaterials
1:30 - 2:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
2:00 - 4:00pm EDTAn introduction to Collisional (Boltzmann-type) models in Kinetic theory - Robert Strain, University of Pennsylvania11th Floor Lecture Hall 
Tuesday, November 1, 2011
TimeEventLocationMaterials
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, November 2, 2011
TimeEventLocationMaterials
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, November 3, 2011
TimeEventLocationMaterials
1:50 - 2:00pm EDTICERM Long Term Visitor Group Photo11th Floor Lecture Hall 
2:00 - 4:00pm EDTAn introduction to spectral approximation for Boltzmann equation - Francis Filbet, Universite Claude Bernard, Lyon I11th Floor Lecture Hall 
4:00 - 4:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, November 4, 2011
TimeEventLocationMaterials
10:00 - 12:00pm EDTAn introduction to spectral approximation for Boltzmann equation - Francis Filbet, Universite Claude Bernard, Lyon I10th Floor Classroom 
2:00 - 4:00pm EDTAsymptotic analysis for boundary-value problems of the Boltzmann equation - Kazuo Aoki, Kyoto University10th Floor Classroom 
4:00 - 4:30pm EDTCoffee/Tea Break10th Floor 

Problems

Problem 1: Boundary Effects.

Boundary effects play an important role in the dynamics of particles confined in a bounded region. Yet its mathematical study is at an early stage. This is due to the fact that solutions to the Boltzmann equation in general will develop singularities. The focus is to investigate the formation and propagation of singularities, both from numerical and theoretical points of view.

Problem 2: Hydrodynamic Limits.

There have been lots of studies of hydrodynamic limits of the Boltzmann equation. The focus in our program will be on error estimates and higher-order expansions of hydrodynamic limits both from the theoretical point of view and from the point of view of numerical simulation. Boundary and initial layer analysis for hydrodynamic limits, which has been barely studied, is an important area that is ready for investigation.

Problem 3: Boltzmann-Grad Limit.

There has been little mathematical work in this direction since the work of Lanford. The focus will be on boundary effects in the Boltzmann-Grad limit, and on the application of Lanford's proof to establish the Boltzmann-Grad limit for other particle systems of physical importance. Numerical simulations at the particle level will play an key role.

Associated Semester Workshops

Kinetic Theory and Computation
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Vlasov Models in Kinetic Theory
Image for "Vlasov Models in Kinetic Theory"

Lecture Videos

Unique moment set from the order of magnitude method

Henning Struchtrup
University of Victoria
November 10, 2011

Ghost effect by curvature

Raffaele Esposito
Università di L'Aquila
November 10, 2011

Competing interactions in kinetic models for fluids

Rossana Marra
University of Rome Tor Vergata
November 9, 2011

A Collision-Based Hybrid Method for Linear Transport

Cory Hauck
Oak Ridge National Laboratory
November 7, 2011