Partial Differential Equations in Kinetic Theories

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.Read more at http://www.newton.ac.uk/programmes/KIT/index.html

Recent Episodes
  • 'The Hughes' model for pedestrian flow
    Nov 22, 2010 – 42:32
  • A class of self-similar solutions for the Vlasov-Einstein system
    Sep 14, 2010 – 57:13
  • A completely integrable toy model of nonlinear Schrodinger equations without dispersion
    Oct 27, 2010 – 51:32
  • A modified least action principle allowing mass concentrations for the early universe reconstruction problem
    Sep 7, 2010 – 48:37
  • A Numerical Scheme for the Quantum Boltzmann Equation Efficient in the Fluid Regime
    Dec 17, 2010 – 49:14
  • A stochastic individual velocity jump process modelling the collective motion of locusts
    Sep 9, 2010 – 27:06
  • A stochastic min-driven coalescence process and its hydrodynamical limit
    Oct 27, 2010 – 43:37
  • Adaptation in continuous populations with migration and genetic drift
    Nov 24, 2010 – 46:54
  • Aggregation-pattern due to repulsive-aggregating interaction potentials
    Sep 15, 2010 – 43:32
  • An Eulerian surface hopping method for the Schrödinger equation with conical crossings
    Dec 15, 2010 – 47:51
  • An integro-differential model to study evolution
    Sep 13, 2010 – 27:09
  • Analysis of diffusive quantum fluid models
    Dec 16, 2010 – 49:02
  • Analysis of Dynamics of Doi-Onsager Phase Transition
    Sep 8, 2010 – 32:48
  • Asymptotic dynamics of a population density: a model with a survival threshold
    Sep 10, 2010 – 24:56
  • Asymptotic spreading in general heterogeneous media
    Nov 24, 2010 – 53:13
  • Asymptotic-preserving schemes for some kinetic equations
    Sep 3, 2010 – 01:12:05
  • Bifurcation problems for structured population dynamics models
    Nov 24, 2010 – 57:43
  • Bloch Decomposition-Based Gaussian Beam Method for the Schrödinger equation with Periodic Potentials
    Dec 16, 2010 – 43:53
  • Blow-up Conditions for a System of Nonlinear Schrödinger Equations
    Dec 21, 2010 – 32:07
  • Continuations of the nonlinear Schrodinger solutions beyond the singularity
    Dec 16, 2010 – 53:45
  • Convolution inequalities for the Boltzmann operator and the inhomogeneous BTE with soft potentials for initial data near Maxwellian states
    Oct 19, 2010 – 58:58
  • Decay estimates towards equilibrium for a quantum kinetic equation
    Nov 24, 2010 – 54:13
  • DSMC-fluid solver with dynamic localisation of kinetic effects
    Sep 15, 2010 – 37:41
  • Dynamical modelling of nonequilibrium condensates
    Dec 21, 2010 – 57:14
  • Existence and uniqness of solution to the Lifshitz-Slyozov system with monomers spatial diffusion
    Sep 14, 2010 – 34:25
  • Fluid models of swarming behavior
    Sep 14, 2010 – 24:18
  • Fokker-Planck models for Bose-Einstein particles
    Sep 14, 2010 – 57:29
  • From Gross-Pitaevskii to KdV and KP
    Dec 21, 2010 – 59:55
  • Ghost effect by curvature
    Nov 22, 2010 – 40:13
  • Global Ray Tracing
    Dec 16, 2010 – 32:31
  • Gradient flow scheme for nonlinear fourth order equations
    Oct 8, 2010 – 32:13
  • Hilbert sixth problem
    Oct 1, 2010 – 58:11
  • Homogenization of the linear Boltzmann equation in a periodic system of holes
    Sep 7, 2010 – 01:02:59
  • Hydrodynamic limits, Knudsen layers and Numerical fluxes
    Sep 10, 2010 – 56:22
  • Interaction dynamics of singular wave fronts computed by particle methods
    Oct 7, 2010 – 43:32
  • Kinetic description and connectivity of old and new models of flocking
    Sep 14, 2010 – 32:11
  • Kinetic equations and Markov jump processes
    Dec 6, 2010 – 01:00:10
  • Kinetic models for bacterial chemotaxis
    Sep 13, 2010 – 40:08
  • Kinetic models in material science
    Sep 9, 2010 – 37:58
  • Kinetic models of chemotaxis
    Sep 13, 2010 – 39:46
  • Large time behavior of collisionless plasma
    Sep 15, 2010 – 32:30
  • Lattice Boltzmann equation: what Do We Know and What Can We Do With It?
    Sep 30, 2010 – 57:09
  • LBM: Approximate Invariant Manifolds and Stability
    Sep 9, 2010 – 37:21
  • Linear Boltzmann equation and some Dirichlet series
    Oct 1, 2010 – 38:55
  • Macroscopic limits and decay to equilibrium for kinetic equations with relaxation collision kernels and mass conservation
    Sep 15, 2010 – 59:51
  • Mathematical Modeling of Selection and Orientational Aggregation in Population Dynamics
    Sep 14, 2010 – 59:10
  • Mean field limit of stochastic particle systems
    Oct 21, 2010 – 51:11
  • Modelling Aspects of Solid Tumour Growth
    Sep 10, 2010 – 56:00
  • Nonlinear coherent states and Ehrenfest time for Schrodinger equation
    Dec 16, 2010 – 51:38
  • Nonlinear Cross-Diffusion Models for Size Exclusion
    Sep 7, 2010 – 39:38
Recent Reviews
Similar Podcasts
Disclaimer: The podcast and artwork on this page are property of the podcast owner, and not endorsed by UP.audio.