Organizing Committee
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.

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Image courtesy of Christoffer A Rasmussen
Author: Vedexent at en wikipedia

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, October 17, 2011
TimeEventLocationMaterials
9:00 - 9:20am EDTRegistration and Welcome Coffee11th Floor Collaborative Space 
9:20 - 9:30am EDTWelcome11th Floor Lecture Hall 
9:30 - 10:30am EDTSystem Dynamic Models and Real-time Simulation of Complex Material Flow Systems - Simone Goettlich, University of Mannheim11th Floor Lecture Hall
10:30 - 11:30am EDTTransport Equations for Internet Transmission Control - Francois Baccelli, INRIA-Paris-Rocquencourt11th Floor Lecture Hall 
11:30 - 1:30pm EDTBreak for Lunch Free Time  
1:30 - 2:30pm EDTAveraged kinetic models for particle flows on complex networks - Christian Ringhofer, Arizona State University11th Floor Lecture Hall
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:00 - 4:00pm EDTRecent progress on the modeling of flocking and synchronization phenomena - Seung-Yeal Ha, Seoul National University11th Floor Lecture Hall
4:00 - 5:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, October 18, 2011
TimeEventLocationMaterials
9:30 - 10:30am EDTThe jam equation, a functional-differential equation arising from a traffic flow model - Reinhard Illner, The University of Victoria, Canada11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTA scalar conservation law with discontinuous flux for supply chains with finite buffers - Dieter Armbruster, Arizona State University11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for Lunch Free Time  
2:00 - 3:00pm EDTContinuum descriptions for dynamics of self-propelled particles - Vladislav Panferov, California State University at Northridge11th Floor Lecture Hall
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTEstimating the division rate in size-tructured populations, merging deterministic and statistical approaches - Marie Doumic-Jauffret, INRIA-Paris-Rocquencourt11th Floor Lecture Hall
4:30 - 5:30pm EDTKinetic and mean-field game models of information propagation - Ravi Srinivasan, The University of Texas at Austin11th Floor Lecture Hall
Wednesday, October 19, 2011
TimeEventLocationMaterials
9:30 - 10:30am EDTAnalysis of PDE models for neuronal networks - Benoit Perthame, University Pierre et Marie Curie, Paris11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTA new model for self-organized dynamics, from particle to hydrodynamic descriptions - Eitan Tadmor, University of Maryland11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for Lunch Free Time  
2:00 - 3:00pm EDTSome new remarks on a kinetic equation for Compton scattering - Miguel Escobedo, Universidad del Pais Vasco11th Floor Lecture Hall
3:00 - 3:10pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
3:10 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTKinetic models for bacterial waves - Vincent Calvez, école Normale Supérieure de Lyon11th Floor Lecture Hall
4:30 - 5:30pm EDTDiscussions11th Floor Collaborative Space 
Thursday, October 20, 2011
TimeEventLocationMaterials
9:30 - 10:30am EDTMultiphase traffic theories and traffic oscillations - Axel Klar, Technische Universität Kaiserslautern11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTSome considerations on radiometric effects - Kazuo Aoki, Kyoto University11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for Lunch Free Time  
2:00 - 3:00pm EDTInverse transport and diffusion problems in photoacoustic imaging and device modeling - Kui Ren, University of Texas at Austin11th Floor Lecture Hall
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTUniqueness of the compactly supported weak solution to the relativistic Vlasov-Darwin system. - Martial Agueh, The University of Victoria, Canada11th Floor Lecture Hall
4:30 - 5:30pm EDTDiscussions11th Floor Collaborative Space 
Friday, October 21, 2011
TimeEventLocationMaterials
9:30 - 10:30am EDTAn application of the discontinuous Galerkin method for solving kinetic equations. - Armando Majorana, University of Catania, Italy11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:10am EDTSurvey Distribution Please return to 11th floor reception desk.  
11:10 - 12:10pm EDTHigh-order, Entropy-based Models for Linear Transport in Slab Geometries - Cory Hauck, Oak Ridge National Laboratory11th Floor Lecture Hall
12:10 - 2:00pm EDTBreak for Lunch Free Time  
2:00 - 3:00pm EDTBinary interaction algorithms for the simulation of flocking and swarming dynamics - Lorenzo Pareschi, University of Ferrara, Italy11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTA discontinuous Galerkin scheme for front propagation with obstacles - Chi-Wang Shu, Brown University11th Floor Lecture Hall
4:30 - 4:35pm EDTClosing remarks11th Floor Lecture Hall 

Tutorial Week Schedule

Tuesday, October 11, 2011
TimeEventLocationMaterials
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:30 - 5:30pm EDTProfessional Development Roundtable Discussion: Papers & Journals11th Floor Lecture Hall 
Wednesday, October 12, 2011
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, October 13, 2011
TimeEventLocationMaterials
10:30 - 11:30am EDTDeterministic numerical methods for Boltzmann-Poisson systems, Part I - Yingda Cheng, Michigan State University11th Floor Lecture Hall 
2:00 - 3:00pm EDTDeterministic numerical methods for Boltzmann-Poisson systems, Part II - Yingda Cheng, Michigan State University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee and Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTDeterministic numerical methods for Boltzmann-Poisson systems, Part III - Yingda Cheng, Michigan State University11th Floor Lecture Hall 
Friday, October 14, 2011
TimeEventLocationMaterials
2:00 - 3:00pm EDTThe production planning problem: Clearing functions, variable leads times, delay equations and partial differential equations, Part I - Dieter Armbuster, Arizona State University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee and Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTThe production planning problem: Clearing functions, variable leads times, delay equations and partial differential equations, Part II - Dieter Armbuster, Arizona State University11th 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.

Associated Semester Workshops

Kinetic Theory and Computation
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Vlasov Models in Kinetic Theory
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Boltzmann Models in Kinetic Theory
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Lecture Videos

Analysis of PDE models for neuronal networks

Benoit Perthame
Universite de Paris VI (Pierre et Marie Curie)
October 19, 2011