اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn Exact Solution of the Fokker-Planck Equation for Isotropic Scattering
66
0
0.0
(
0
)
تأليف
M.A. Malkov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 dispersion of a particle cloud released at t=0 evolves through three phases, ballistic (t<Tc), transdiffusive (t~Tc) and diffusive (t>>Tc), where Tc is the collision time.The ballistic phase is characterized by a decelerating expansion of the initial point source in form of a box distribution with thickening walls. The next, transdiffusive phase is marked by the box walls thickened to its size and a noticeable slow down of expansion. Finally, the evolution enters the conventional diffusion phase.
قيم البحث
اقرأ أيضاً
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. Mos
t 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.
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
generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and L{e}vy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.
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
describe the long time limit of this problem. Instead this limit is characterized by an infinite covariant density. This non-normalizable density yields the mean square displacement of the particles, which for a certain range of parameters exhibits anomalous diffusion. In a symmetric potential with an asymmetric initial condition, the average position decays anomalously slowly. This problem also has applications outside the thermal context, as in the diffusion of the momenta of atoms in optical molasses.
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
y expanding the solution into a series of spherical harmonics, which in this case is a complex and cumbersome procedure. This article presents the implementation procedure and some results of the numerical solution of the Fokker-Planck equation using the finite element method. A method for creating a sequence of triangular grids on the surface of a sphere based on an inscribed icosahedron is described. The equations of the finite element method are derived and examples of numerical solutions are presented. The processes of magnetization and demagnetization under heating of a particle with cubic magnetic anisotropy are simulated.
Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is introduced. The stru
cture related to the energy conservation is skew-symmetry in mathematical sense, and the action-reaction law in physical sense. A thermal relaxation term is obtained by using integration-by-parts on a volume integral of the energy moment equation, so the discontinuous Galerkin method is selected to preserve the skew-symmetry. The discontinuous Galerkin method enables ones to introduce the nonlinear upwind flux without violating the conservation laws. Some experiments show that the conservative scheme maintains the mass-energy-conservation only with round-off errors, and analytic equilibria are reproduced only with truncation errors of its formal accuracy.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
