Partial differential equations in kinetic theories
KIT
16 August 2010 to 22 December 2010
Programme theme
Kinetic equations occur naturally in the modelling of the collective motion of large individual particle ensembles such as molecules in rarefied gases, beads in granular materials, charged particles in semiconductors and plasmas, dust in the atmosphere, cells in biology, or the behaviour of individuals in economical trading; Generally, huge interacting particle systems cannot efficiently be described by the individual dynamics of all particles due to overwhelming complexity but clearly some input from the microscopic behaviour is needed in order to bridge from microscopic dynamics to the macroscopic world, typically rendered in terms of averaged quantities. This leads to classical equations of mathematical physics: the Boltzmann equation of rarified gas dynamics, the fermionic and bosonic Boltzmann equations and the relativistic Vlasov-Maxwell system of particle physics, the quantistic Wigner-Poisson system, to name just a few.
Kinetic theory has produced as a spin-off many new mathematical tools in the last 20 years: renormalized solutions of transport equations by R DiPerna and P-L Lions, averaging lemmas by the French kinetic school, entropy dissipation tools which have been extended methodologically and used far beyond kinetic theory are just some highlights of new analytical PDE methods stemming from kinetic theory. Another recent landmark in this field has been the proof of the hydrodynamic limit process of the renormalized solutions of the Boltzmann equation towards (weak) Leray solutions of the Navier-Stokes equations by F Golse and L Saint-Raymond. On the other hand, kinetic theory has different scientific viewpoints ranging from applied mathematical and physical modelling to stochastic analysis, numerical analysis of PDEs and in many important cases extensive numerical simulations.
The main objective of this program is aimed at advancing Partial Differential Equations (PDEs) research in kinetic theories and its impact in the applied sciences highlighting selected modern application areas. This effort has to be understood from a global perspective of research in PDEs bringing together mathematical modelling, analysis, numerical schemes and simulation in a feedback loop of synergies. The three selected newly emerging application areas of kinetic theories are kinetic modelling in biology, coupled fluid-particle models and PDE Models for quantum fluids.
As part of the program, several workshops will take place in the Newton Institute, and one satellite workshop at the ICMS in Edinburgh. There are also two series of seminars which will take place weekly at the Newton Institute:
- A weekly seminar, on Tuesdays at 14:00 in seminar room 2.
- A series of lectures on Landau damping, given by Clément Mouhot, every Monday in October at 14:00 in seminar room 1.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Partial differential equations in kinetic theories, where work on this paper was undertaken. This work was supported by EPSRC grant EP/F005431/1.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme | Publication Date |
|---|---|---|---|
The cumulant lattice Boltzmann equation in three dimensions: Theory and validationAuthors: Andrea Pasquali, Martin Geier, Martin Schönherr, Manfred Krafczyk |
2010 | KIT | 2 March 2017 |
Derivation of the Lattice Boltzmann model for relativistic hydrodynamicsAuthors: BM Boghosian, HJ Herrmann, M Mendoza, Sauro Succi |
2010 | KIT | 21 October 2016 |
On the speed of approach to equilibrium for a collisionless gasAuthors: Francois Golse, Kazuo Aoki |
2010 | KIT | 21 October 2016 |
Finite time blow up in Kaniadakis-Quarati model of Bose-Einstein particlesAuthors: Giuseppe Toscani |
2010 | KIT | 21 October 2016 |
Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problemAuthors: JA Carillo, C-W Shu, Blanca Ayuso De Dios |
2010 | KIT | 21 October 2016 |
Reconstruction of the early universe, Zeldovich approximation and Monge-Ampère gravitationAuthors: Y Brenier |
2010 | KIT | 21 October 2016 |
A hierarchy of models related to nanoflows and surface diffusionAuthors: P Charrier, Pierre Degond, Kazuo Aoki |
2010 | KIT | 21 October 2016 |
Stochastic mean-field limit: Non-Lipschitz forces and swarmingAuthors: Jose A Carrillo, François Bolley, JA Canizo |
2010 | KIT | 21 October 2016 |
Exponential convergence to equilibrium for kinetic Fokker-Planck equations on Riemannian manifoldsAuthors: Simone Calogero |
2010 | KIT | 21 October 2016 |
Steady flows of a highly rarefied gas induced by non-uniform wall temperatureAuthors: Kazuo Aoki, Shigeru Takata, R Hattori, D Sakai, S Kosuge |
2010 | KIT | 21 October 2016 |
Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilitiesAuthors: Christian Schmeiser, Min Tang, N Vauchelet, B Perthame |
2010 | KIT | 21 October 2016 |
Analysis of nonlinear noisy integrate\&fire neuron models: blow-up and steady statesAuthors: Jose A Carrillo, B Perthame, Maria Cáceres |
2010 | KIT | 21 October 2016 |
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equationsAuthors: JA Canizo, Stéphane Mischler, Maria Cáceres |
2010 | KIT | 21 October 2016 |
A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of determinantsAuthors: Thanos Tzavaras, A Miroshnikov |
2010 | KIT | 21 October 2016 |
Transport coefficients in the 2-dimensional Boltzmann equationAuthors: Alexander Bobylev, Raffaele Esposito |
2010 | KIT | 21 October 2016 |
Numerical studies of a granular gas in a host mediumAuthors: Giampiero Spiga, Marzia Bisi, Sergej Rjasanow |
2010 | KIT | 21 October 2016 |
Optimal bounds for self-similar solutions to coagulation equations with multiplicative kernelAuthors: Juan Velazquez, B Niethammer |
2010 | KIT | 21 October 2016 |
A numerical model of the Boltzmann equation related to the discontinuous Galerkin methodAuthors: Armando Majorana |
2010 | KIT | 21 October 2016 |
On a relativistic Fokker-Planck equation in kinetic theoryAuthors: JAA Felix, Simone Calogero |
2010 | KIT | 21 October 2016 |
From individual to collective behaviour of coupled velocity jump processes: a locust exapleAuthors: J Haskovec, Radek Erban |
2010 | KIT | 21 October 2016 |
Excluded-volume effects in the diffusion of hard spheresAuthors: SJ Chapman, M Bruna-estrach |
2010 | KIT | 21 October 2016 |
Cross diffusion preventing blow up in the two-dimensional Keller-Segel modelAuthors: A Jungel, Sabine Hittmeir |
2010 | KIT | 21 October 2016 |
Structured populations, cell growth and measure valued balance lawsAuthors: RM Colombo, Piotr Gwiazda, Agnieszka Ulikowska, Jose A Carrillo |
2010 | KIT | 21 October 2016 |
Mean-field limit for the stochastic Vicsek modelAuthors: J Canizo, Jose A Carrillo, François Bolley |
2010 | KIT | 21 October 2016 |
Nonlocality and the critical Reynolds numbers of the minimum state magnetohydrodynamic turbulenceAuthors: S Oughton, Ye Zhou |
2010 | KIT | 21 October 2016 |
Numerical methods for computing ground state and dynamics of nonlinear relativistic Hartree equation for boson starsAuthors: Xuanchun Dong, Weizhu Bao |
2010 | KIT | 21 October 2016 |
A short note on simplified pseudospectral methods for computing ground state and dynamics of spherically symmetric Schrödinger-Poisson-Slater systemAuthors: Xuanchun Dong |
2010 | KIT | 21 October 2016 |
Workshops
Partial differential equations in kinetic theories: tutorials for graduate students
23 August 2010 to 3 September 2010
Fluid-kinetic modelling in biology, physics & engineering
6 September 2010 to 10 September 2010
PDEs in kinetic theories: kinetic description of biological models
8 November 2010 to 12 November 2010
Evolutionary dynamics of structured populations
22 November 2010 to 22 November 2010
PDE models for quantum fluids
13 December 2010 to 17 December 2010
Seminars
| Tuesday 14th September 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Pauline Lafitte Université des Sciences et Technologies de Lille |
Room 2 | 
|
| 14:50 to 15:35 |
Shigeru Takata Kyoto University |
Room 2 |
|
| Tuesday 21st September 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Li-Shi Luo Old Dominion University |
Room 1 |
|
| 15:00 to 15:45 |
Sergej Rjasanow Universität des Saarlandes |
Room 1 |
|
| Tuesday 28th September 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Tai-Ping Liu Stanford University |
Room 1 |
|
| 15:00 to 15:45 |
Alexander Bobylev Karlstad University |
Room 1 |
|
| Monday 4th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| 15:15 to 16:00 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| Tuesday 5th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Alina Chertock North Carolina State University |
Room 1 |
|
| 15:00 to 15:45 |
Bertram During University of Sussex |
Room 1 |
|
| Monday 11th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| 15:15 to 16:00 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| Tuesday 12th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Irene Gamba Japan Atomic Energy Agency & University of Texas at Austin |
Room 1 |
|
| 15:00 to 15:45 |
Vladislav Panferov California State University |
Room 1 |
|
| Monday 18th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| 15:15 to 16:00 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| Tuesday 19th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Walter Strauss Brown University |
Room 1 | |
| 15:00 to 15:45 |
François Bolley CNRS & Université Paris-Dauphine |
Room 1 |
|
| Monday 25th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| 15:15 to 16:00 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| Tuesday 26th October 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Patrick Gerard Université Paris Saclay |
Room 1 |
|
| 15:00 to 15:55 |
Philippe Laurencot Université Paul Sabatier Toulouse III |
Room 1 |
|
| Monday 1st November 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| 15:15 to 16:00 |
Clément Mouhot University of Cambridge |
Room 1 |
|
| Tuesday 2nd November 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Anne Nouri Aix Marseille Université |
Room 1 | |
| 15:00 to 15:45 |
Stéphane Mischler CNRS & Université Paris-Dauphine |
Room 1 | |
| Monday 15th November 2010 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Cedric Villani Institut Henri Poincaré |
Room 1 |
|
| 17:00 to 18:00 |
Cedric Villani Institut Henri Poincaré |
Centre for Mathematical Sciences |
|
| Tuesday 16th November 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Rossana Marra Università degli Studi di Roma Tor Vergata |
Room 1 |
|
| 15:00 to 15:45 |
Marco Di Francesco Università degli Studi dell'Aquila |
Room 1 |
|
| Tuesday 23rd November 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Ingenuin Gasser Technische Universität Hamburg-Harburg |
Room 1 |
|
| 15:00 to 15:45 |
Decay estimates towards equilibrium for a quantum kinetic equation |
Room 1 |
|
| Monday 29th November 2010 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Wolfgang Wagner Weierstraß-Institut für Angewandte Analysis und Stochastik |
Room 1 |
|
| Tuesday 30th November 2010 | |||
|---|---|---|---|
| 14:00 to 14:45 |
Jose A Carrillo ICREA and Universitat Autonoma de Barcelona |
Room 1 |
|
| 15:00 to 15:45 |
Nonlinear integrate and fire neuron models, part II: existence, uniqueness, and asymptotics |
Room 1 |
|
Organisers
- Jose A Carrillo ICREA and Universitat Autonoma de Barcelona
- Shi Jin University of Wisconsin-Madison
- Peter Markowich University of Cambridge
Speakers
- Alexander Bobylev Karlstad University
- François Bolley CNRS & Université Paris-Dauphine
- Jose A Carrillo ICREA and Universitat Autonoma de Barcelona
- Alina Chertock North Carolina State University
- Marco Di Francesco Università degli Studi dell'Aquila
- Bertram During University of Sussex
- Irene Gamba Japan Atomic Energy Agency & University of Texas at Austin
- Ingenuin Gasser Technische Universität Hamburg-Harburg
- Patrick Gerard Université Paris Saclay
- Pauline Lafitte Université des Sciences et Technologies de Lille
- Philippe Laurencot Université Paul Sabatier Toulouse III
- Tai-Ping Liu Stanford University
- Li-Shi Luo Old Dominion University
- Rossana Marra Università degli Studi di Roma Tor Vergata
- Stéphane Mischler CNRS & Université Paris-Dauphine
- Clément Mouhot University of Cambridge
- Anne Nouri Aix Marseille Université
- Vladislav Panferov California State University
- Sergej Rjasanow Universität des Saarlandes
- Walter Strauss Brown University
- Shigeru Takata Kyoto University
- Cedric Villani Institut Henri Poincaré
- Wolfgang Wagner Weierstraß-Institut für Angewandte Analysis und Stochastik
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