Asymptotics, Numerics, Analysis
of the
network
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Asymptotics, Numerics, Analysis |
of the network |
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A. Multiscale phenomena and limiting structures
- 1. Kinetic and relaxation methods for conservation laws and moment systems
(Derivation and validation of models using diffusive and hydrodynamic limits, ...)- 2. Multiscale phenomena for charged particle systems
(Modeling, analysis and numerics of hybrid semiconductor and plasma models, ...)- 3. Mass transportation and entropy methods
(Large-time asymptotics for kinetic and parabolic equations, ...)- 4. Eulerian-Lagrangian methods
(Multiphase flows, particles and solids in fluids and sprays, ...)- 5. Continuum and kinetic models of phase transitions
(Coagulation/fragmentation, Bose condensation, kinetic relations, ...)- 6. Quantum evolution equations
(Hartree-Fock equation, Dirac equation, semiclassical/nonrelativistic limits, ...)
B. Collisional evolution equations
- 7. Transport and collisions
(Analysis of and numerics for the Boltzmann equation, traffic flow problems, ...)- 8. Many-particle systems
(Asymptotic limits, derivation of: kinetic equations, fluid models, and nonlinear one-particle approximations, ...)- 9. Collision and dispersive quantum models
(Derivation of "quantum Boltzmann" equations, electron-phonon interaction, weak coupling limits, interaction with random media, ...)- 10. Kinetic models for granular media and materials
(Derivation, analysis and numerics for models with inelastic collisions and/or mean fields, thin film magnetism, ...)
C. Nonlinear waves and hyperbolic systems
- 11. Structural properties of hyperbolic systems
(Zero-viscosity limits, diffusive and dispersive effects, non-strict hyperbolicity, ...)- 12. Stability of nonlinear waves and boundary layers
(Over-/undercompressible shock phenomena, discrete shock profiles, ...)- 13. Hamilton-Jacobi equations and geometrical optics
(Thin film magnetism, mesh generation, pressureless gas, ...)- 14. Fluid dynamics equations
(Navier-Stokes equation, rotating flows, atmospheric and oceanic flows, dynamo equations, ...)
D. Numerical methods and simulations
- 15. Numerical methods for balance laws and dispersive equations
(Central schemes, relaxation schemes, kinetic schemes, schemes for nonlinear Schrödinger eq., ...)- 16. Computational singular (in)compressible flows
(Magneto-hydrodynamics, multiphase models, shallow water equation, semiconductor simulations, Euler equations, Navier-Stokes equations, ...)