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Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and $p/$He spectral anomalies. Most of the CR models use diffusive propagation that is inaccurate for weakly scattered energetic particles. So, some parts of the spectra affected by the heliospheric modulation, for example, cannot be interpreted. I discuss and adopt an exact solution of the Fokker-Planck equation arXiv1610.01584, which gives a complete description of a ballistic, diffusive and transdiffusive (intermediate between the first two) propagation regimes. I derive a simplified version of an exact Fokker-Planck propagator that can easily be employed in place of the Gaussian propagator, currently used in major Solar modulation and other CR transport models.
An analytic solution for a Fokker-Planck equation that describes propagation of energetic particles through a scattering medium is obtained. The solution is found in terms of an infinite series of mixed moments of particle distribution. The spatial d
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does not fully
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise
It is commonly known that the Fokker-Planck equation is exactly solvable only for some particular systems, usually with time-independent drift coefficients. To extend the class of solvable problems, we use the intertwining relations of SUSY Quantum M
The Fokker-Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Usually this equation is solved b