Nonlinear mean-field Fokker-Planck equations and their applications in physics, astrophysics and biology
arXiv:cond-mat/0611087 · doi:10.1016/j.crhy.2006.01.004
Abstract
We discuss a general class of nonlinear mean-field Fokker-Planck equations [P.H. Chavanis, Phys. Rev. E, 68, 036108 (2003)] and show their applications in different domains of physics, astrophysics and biology. These equations are associated with generalized entropic functionals and non-Boltzmannian distributions (Fermi-Dirac, Bose-Einstein, Tsallis,...). They furthermore involve an arbitrary binary potential of interaction. We emphasize analogies between different topics (two-dimensional turbulence, self-gravitating systems, Debye-Hückel theory of electrolytes, porous media, chemotaxis of bacterial populations, Bose-Einstein condensation, BMF model, Cahn-Hilliard equations,...) which were previously disconnected. All these examples (and probably many others) are particular cases of this general class of nonlinear mean-field Fokker-Planck equations.
Cited by in corpus (5)
- Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
- Logotropic distributions
- Hamiltonian and Brownian systems with long-range interactions: III. The BBGKY hierarchy for spatially inhomogeneous systems
- Kinetic and hydrodynamic models of chemotactic aggregation
- Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot