Boltzmann Models in Kinetic Theory (November 7-11, 2011)


Organizing Committee
Description

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.


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.

  • Vedran Sohinger
    (Pennsylvania State University)
  • Robert Strain*
    (University of Pennsylvania)
  • Walter Strauss
    (Brown University)
  • Henning Struchtrup*
    (University of Victoria)
  • Shigeru Takata*
    (Kyoto University)
  • Maja Taskovic
    (University of Texas at Austin)
  • Daniela Tonon
    (International School for Advanced Studies SISSA/ISAS)
  • Minh-Binh Tran
    (Université de Paris XIII Paris-Nord)
  • Arianne Trescases
    (École Normale Supérieure de Cachan)
  • Tetsuro Tsuji
    (Graduate School of Engineering, Kyoto University)
  • Kent Van Vels
    (University of Texas)
  • Li Wang
    (University of Wisconsin)
  • Dongming Wei
    (University of Wisconsin)
  • Miles Wheeler
    (Brown University)
  • Lei Wu
    (Brown University)
  • Xiang Xu
    (Carnegie Mellon University)
  • Bokai Yan
    (University of Wisconsin)
  • He Yang*
    (Rensselaer Polytechnic Institute)
  • Chang Yang
    (Université de Lyon)
  • Tong Yang*
    (City University of Hong Kong)
  • Takeru Yano
    (Osaka University)
  • Shih-Hsien Yu*
    (National University of Singapore)
  • Huihui Zeng
    (Georgetown University)
  • Chenglong Zhang
    (University of Texas)
  • Keya Zhu
    (Pennsylvania State University)
Monday October 31st 2011
Time Description Speaker Location Abstracts
1:30 - 2:00 Coffee/Tea Break   11th Floor Collaborative Space
2:00 - 4:00 An introduction to Collisional (Boltzmann-type) models in Kinetic theory Robert Strain, University of Pennsylvania 11th Floor Lecture Hall
Tuesday November 1st 2011
Time Description Speaker Location Abstracts
2:30 - 3:00 Coffee/Tea Break   11th Floor Collaborative Space
Wednesday November 2nd 2011
Time Description Speaker Location Abstracts
2:30 - 3:00 Coffee/Tea Break   11th Floor Collaborative Space
Thursday November 3rd 2011
Time Description Speaker Location Abstracts
1:50 - 2:00 ICERM Long Term Visitor Group Photo   11th Floor Lecture Hall
2:00 - 4:00 An introduction to spectral approximaton for Boltzmann equation Francis Filbet, Universite Claude Bernard, Lyon I 11th Floor Lecture Hall
4:00 - 4:30 Coffee/Tea Break   11th Floor Collaborative Space
Friday November 4th 2011
Time Description Speaker Location Abstracts
10:00 - 12:00 An introduction to spectral approximaton for Boltzmann equation Francis Filbet, Universite Claude Bernard, Lyon I 10th Floor Classroom
2:00 - 4:00 Asymptotic analysis for boundary-value problems of the Boltzmann equation Kazuo Aoki, Kyoto University 10th Floor Classroom
4:00 - 4:30 Coffee/Tea Break   10th Floor
Monday November 7th 2011
Time Description Speaker Location Abstracts
8:30 - 8:55 Registration and Welcome Coffee    
8:55 - 9:00 Welcome Jill Pipher, Director, ICERM 11th Floor Lecture Hall
9:00 - 9:45 From the Vlasov-Maxwell-Boltzmann System to Incompressible viscous electro-magneto-hydrodynamics, part I Laure Saint-Raymond, Ecole Normale Supérieure & University Paris 6 11th Floor Lecture Hall
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10:00 - 10:30 Coffee/Tea Break   11th Floor Collaborative Space
10:30 - 11:15 Exact summation of the Chapman- Enskog
expansion: a primer
Marshall Slemrod, University of Wisconsin 11th Floor Lecture Hall
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11:30 - 12:15 A Collision-Based Hybrid Method for Linear Transport Cory Hauck, Oak Ridge National Laboratory 11th Floor Lecture Hall
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12:30 - 2:30 Break for Lunch and Free Time  
2:30 - 3:15 The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems Tong Yang, City University of Hong Kong 11th Floor Lecture Hall
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3:30 - 4:00 Coffee/Tea Break   11th Floor Collaborative Space
4:00 - 4:45

Correlation among elemental relaxation and driven-flow problems for a rarefied gas

Shigeru Takata, Kyoto University

11th Floor Lecture Hall
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5:00 - 6:30 Welcome Reception   11th Floor Collaborative Space
Tuesday November 8th 2011
Time Description Speaker Location Abstracts
9:00 - 9:45 Large time behavior of coagulation-fragmentation equations with degenerate diffusion Laurent Desvillettes, École Normale Supérieure de Cachan 11th Floor Lecture Hall
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10:00 - 10:30 Coffee/Tea Break   11th Floor Collaborative Space
10:30 - 11:15 Fourier Law and Non-Isothermal Boundary in the Boltzmann Theory Chanwoo Kim, University of Cambridge 11th Floor Lecture Hall
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11:30 - 12:15 Efficient methods for solving the Boltzmann equation for nanoscale transport applications Nicolas Hadjiconstantinou, Massachusetts Institute of Technology 11th Floor Lecture Hall
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12:30 - 2:30 Break for Lunch and Free Time  
2:30 - 3:15 Riemann Problem for a Boltzmann shock wave with the hard sphere model Shih-Hsien Yu, National University of Singapore 11th Floor Lecture Hall
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3:30 - 4:00 Coffee/Tea Break   11th Floor Collaborative Space
4:00 - 4:45 Traffic Flow Modeling Tong Li, University of Iowa 11th Floor Lecture Hall
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Wednesday November 9th 2011
Time Description Speaker Location Abstracts
9:00 - 9:45 Bose condensates in interaction with excitations - a kinetic model Anne Nouri, Aix-Marseille University 11th Floor Lecture Hall
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10:00 - 10:30 Coffee/Tea Break   11th Floor Collaborative Space
10:30 - 11:15 Kac's Program in Kinetic Theory Stephane Mischler, Université de Paris-Dauphine 11th Floor Lecture Hall
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11:30 - 12:15 Optimal Large-Time Decay Rates for Collisional Kinetic Equations in the Whole Space Robert Strain, University of Pennsylvania 11th Floor Lecture Hall
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12:30 - 12:40 Group Photo in Lecture Hall   11th Floor Lecture Hall
12:40 - 2:30 Break for Lunch and Free Time  
2:30 - 3:15 Derivation of MHD equations from the Vlasov-Maxwell-Boltzmann system Juhi Jang, University of California, Riverside 11th Floor Lecture Hall
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3:30 - 4:00 Coffee/Tea Break   11th Floor Collaborative Space
4:00 - 4:45 Competing interactions in kinetic models for fluids Rossana Marra, University of Roma Tor Vergata 11th Floor Lecture Hall
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Thursday November 10th 2011
Time Description Speaker Location Abstracts
9:00 - 9:45 Ghost effect by curvature Raffaele Esposito, Università di L'Aquila 11th Floor Lecture Hall
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10:00 - 10:30 Coffee/Tea Break   11th Floor Collaborative Space
10:30 - 11:15 From the Vlasov-Maxwell-Boltzmann System to Incompressible viscous electro-magneto-hydrodynamics, part II Diogo Arsenio, École Normale Supérieure 11th Floor Lecture Hall
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11:30 - 12:15 Hypocoercivity for some Linear Kinetic Equations with a Boundary Frederic Herau, Université de Nantes 11th Floor Lecture Hall
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12:30 - 2:30 Break for Lunch and Free Time  
2:30 - 3:15 Unique moment set from the order of magnitude method Henning Struchtrup, University of Victoria 11th Floor Lecture Hall
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3:30 - 4:00 Coffee/Tea Break   11th Floor Collaborative Space
4:00 - 4:45 Hydrodynamic limit and boundary layers Nader Masmoudi, New York University 11th Floor Lecture Hall
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Friday November 11th 2011
Time Description Speaker Location Abstracts
9:00 - 9:45 Euler limit for Boltzmann equation with Maxwell boundary condition Claude Bardos, Université de Paris VII (Denis Diderot) 11th Floor Lecture Hall
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10:00 - 10:30 Coffee/Tea Break   11th Floor Collaborative Space
10:30 - 10:35 Survey Distribution    
10:35 - 11:20 Fluid Approximations from Boltzmann Equations for Domains with Boundary C. David Levermore, University of Maryland 11th Floor Lecture Hall
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11:35 - 12:20 Estimates and approximations to the non-linear Boltzmann equation
Irene Gamba, University of Texas 11th Floor Lecture Hall
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12:30 - 2:30 Break for Lunch and Free Time  
2:30 - 3:00 Discussions
  11th Floor Lecture Hall
3:00 - 3:30 Coffee/Tea Break   11th Floor Collaborative Space
3:30 - 4:45 Discussions   11th Floor Lecture Hall