Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer probability approach

Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two dimensional (2-D) and three dimensional (3-D) cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for the Boltzmann-type of collisions and for the absorption-type of collisions (the later are typical for dusty plasmas and some other systems). Validity of the Einstein's relation for the Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For the Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, e.g., absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasma in the framework of the PT approach. The relation between this force, negative collecting friction force and scattering and collecting drag forces is established.+AFwAXA- The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.+AFwAXA- PACS number(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-yComment: 18 page

Cosmic Physics: The High Energy Frontier

Cosmic rays have been observed up to energies $10^8$ times larger than those of the best particle accelerators. Studies of astrophysical particles (hadrons, neutrinos and photons) at their highest observed energies have implications for fundamental physics as well as astrophysics. Thus, the cosmic high energy frontier is the nexus to new particle physics. This overview discusses recent advances being made in the physics and astrophysics of cosmic rays and cosmic gamma-rays at the highest observed energies as well as the related physics and astrophysics of very high energy cosmic neutrinos. These topics touch on questions of grand unification, violation of Lorentz invariance, as well as Planck scale physics and quantum gravity.Comment: Topical Review Paper to be published in the Journal of Physics G, 50 page