Organizing Committee
- Irene Gamba
University of Texas at Austin - Axel Klar
Universität Kaiserslautern - Benoit Perthame
Universite de Paris VI (Pierre et Marie Curie) - Christian Ringhofer
Arizona State University - Chi-Wang Shu
Brown University
Abstract
There are several fundamental applications involving kinetic theory and computations. They range from semiconductor modeling involving kinetic and quantum charged transport, radiative transfer in cosmology, conservative and dissipative phenomena in rarefied gas dynamics in mixtures, and grain and polymer flows.
Issues to be addressed involve the derivation and multi-scale modeling due to different scales of effective constants, spatial heterogeneities and strength of boundary conditions. Because the basic drift-diffusion, hydrodynamic and quantum models may interact through interfaces, a basic understanding of boundary conditions as well as phase transitions are critical. An example of such modeling problem appears naturally in semiconductors devices where the electron and holes density flows through a highly heterogeneous crystal lattice.
It is well established that drift-diffusion models are currently inadequate for the simulations of submicron devices where effective fields become very strong. As a consequence, kinetic transport modeling and even quantum modeling corrections are necessary to accurately model the current flow through devices. Mathematically it is critical to address the analytical and approximating properties of hydrodynamic and kinetic models of Euler and Boltzmann type coupled to Poisson's equation, as well as the Schrödinger and quantum Boltzmann equations that become relevant in different scaling regimes.
Recently, there have been new applications to biological systems, chain supply dynamics and quantitative finance, where statistical methods for multi-agent systems have given raised to of extension of Boltzmann equation to models for particle swarms, networks or the dynamics of information. This is a mathematical area that is not as well developed as its semiconductor counterpart. Our program will pay special attention to these new developments in an attempt to set basic benchmarks of terms of analytical as well as numerical modeling.
Confirmed Speakers & Participants
Talks will be presented virtually or in-person as indicated in the schedule below.
- Speaker
- Poster Presenter
- Attendee
- Virtual Attendee
-
Martial Agueh
University of Victoria
-
Giacomo Albi
Università di Ferrara
-
Kazuo Aoki
Kyoto University
-
Dieter Armbruster
Arizona State University
-
Francois Baccelli
University of Texas, Austin
-
Weizhu Bao
National University of Singapore
-
Alethea Barbaro
Case Western Reserve University
-
Claude Bardos
University of Paris
-
Vincent Calvez
Ecole Normale Superior of Lyon
-
Heesun Choi
Seoul National University
-
Andrew Christlieb
Michigan State University
-
Zhenlu Cui
Fayetteville State University
-
Marie Doumic
Institut National de Recherche en Informatique Automatique (INRIA)
-
Yong Duk
Seoul National University
-
Miguel Escobedo
Universidad del País Vasco
-
Emre Esenturk
University of Pittsburgh
-
Francis Filbet
Universite de Lyon II
-
Irene Gamba
University of Texas at Austin
-
Simone Göttlich
University of Mannheim
-
Yaman Guclu
Michigan State University
-
Wei Guo
Colorado School of Mines
-
Yan Guo
Brown University
-
Seung Ha
Seoul National University
-
Jeffrey Haack
University of Texas at Austin
-
Nicolas Hadjiconstantinou
Massachusetts Institute of Technology
-
George Hagstrom
New York University
-
Cory Hauck
Oak Ridge National Laboratory
-
Andong He
Brown University
-
Reinhard Illner
University of Victoria
-
Juhi Jang
University of Southern California
-
Ahmed Kaffel
University of Wisconsin
-
Axel Klar
Universität Kaiserslautern
-
Ji Oon Lee
Korea Advanced Institute of Science and Technology
-
Charles Levermore
University of Maryland
-
Fengyan Li
Rensselaer Polytechinic Institute
-
Armando Majorana
Università di Catania
-
Nader Masmoudi
Courant Institute of Mathematical Sciences at NYU
-
Jose Morales
University of Texas at Austin
-
Anne Nouri
Aix-Marseille University
-
Vladislav Panferov
California State University
-
Lorenzo Pareschi
Università di Ferrara
-
Gustavo Perla Menzala
Laboratorio Nacional de Computacao Cientifica
-
Benoit Perthame
Universite de Paris VI (Pierre et Marie Curie)
-
Xueke Pu
Chongqing University
-
Jingmei Qiu
University of Houston
-
Amelie Rambaud
Institut Camille Jordan, Universite Lyon 1
-
Kui Ren
University of Texas at Austin
-
Thomas Rey
Universite Claude-Bernard (Lyon I)
-
Matthew Reyna
Rensselaer Polytechnic Institute
-
Christian Ringhofer
Arizona State University
-
Jesus Rosado Linares
University of California, Los Angeles
-
Chi-Wang Shu
Brown University
-
Ravi Srinivasan
The University of Texas at Austin
-
Robert Strain
University of Pennsylvania
-
Walter Strauss
Brown University
-
Eitan Tadmor
University of Maryland
-
Daniela Tonon
International School for Advanced Studies (SISSA/ISAS)
-
Ariane Trescases
Ecole Normale Superior Paris-Saclay
-
Tetsuro Tsuji
Kyoto University
-
Kent Van Vels
University of Texas at Austin
-
Dongming Wei
University of Wisconsin
-
Miles Wheeler
New York University Courant Institute of Mathematical Sciences
-
Lei Wu
Brown University
-
Bokai Yan
University of Wisconsin
-
Xu Yang
New York University
-
He Yang
Rensselaer Polytechnic Institute
-
Yanzhi Zhang
Missouri University of Science and Technology
-
Chenglong Zhang
University of Texas at Austin
Workshop Schedule
Monday, October 17, 2011
Tuesday, October 18, 2011
Wednesday, October 19, 2011
Thursday, October 20, 2011
Friday, October 21, 2011
Tutorial Week Schedule
Tuesday, October 11, 2011
| Time | Event | Location | Materials |
|---|---|---|---|
| 3:30 - 4:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
| 4:30 - 5:30pm EDT | Professional Development Roundtable Discussion: Papers & Journals | 11th Floor Lecture Hall |
Wednesday, October 12, 2011
| Time | Event | Location | Materials |
|---|---|---|---|
| 3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, October 13, 2011
| Time | Event | Location | Materials |
|---|---|---|---|
| 10:30 - 11:30am EDT | Deterministic numerical methods for Boltzmann-Poisson systems, Part I - Yingda Cheng, Michigan State University | 11th Floor Lecture Hall | |
| 2:00 - 3:00pm EDT | Deterministic numerical methods for Boltzmann-Poisson systems, Part II - Yingda Cheng, Michigan State University | 11th Floor Lecture Hall | |
| 3:00 - 3:30pm EDT | Coffee and Tea Break | 11th Floor Collaborative Space | |
| 3:30 - 4:30pm EDT | Deterministic numerical methods for Boltzmann-Poisson systems, Part III - Yingda Cheng, Michigan State University | 11th Floor Lecture Hall |
Friday, October 14, 2011
| Time | Event | Location | Materials |
|---|---|---|---|
| 2:00 - 3:00pm EDT | The production planning problem: Clearing functions, variable leads times, delay equations and partial differential equations, Part I - Dieter Armbuster, Arizona State University | 11th Floor Lecture Hall | |
| 3:00 - 3:30pm EDT | Coffee and Tea Break | 11th Floor Collaborative Space | |
| 3:30 - 4:30pm EDT | The production planning problem: Clearing functions, variable leads times, delay equations and partial differential equations, Part II - Dieter Armbuster, Arizona State University | 11th Floor Lecture Hall |
Problems
Problem 1: Boundary Effects.
A major open area is to solve a hydrodynamic model in two or three dimensions with boundary conditions of contact type. So far this has been accomplished only in one dimension and for some reduced stationary models in two dimensions. These issues have raised important open questions about how to design numerical schemes for such hydrodynamic models.
Problem 2: Computational Issues in Quantum Modeling.
For quantum-based computations of resonant tunneling diodes in semiconductors, high-dimensional computations are very expensive because of the high oscillations. However, in the most effective designs of devices the highest oscillations occur along preferred directions which naturally select appropriate homogenized model reductions. This is an example where the mathematics can efficiently reduce the solution structure to make the computations feasible.
Problem 3: Quantum Boltzmann Theory.
Despite its importance, there has been very little work on quantum Boltzmann equations because of their severe nonlinearity. Our program will attempt to numerically compute and analytically construct global-in-time solutions near a Bose-Einstein distribution and to investigate the phenomenon of Bose-Einstein condensation.
Problem 4: Statistical Multi-agent Modeling.
Another area of focus will be the modeling of swarms, information percolation, Pareto tail distributions and chain supply dynamics. These models exhibit a new sort of difficulty; in fact, their stationary states are not Maxwellian. New approaches to reduced dimensionality via hydrodynamic limits or moment methods are being considered. In addition, some social-biological interactions are modeled by systems of kinetic equations which remain broadly unaddressed.
