Processes associated with plasma self-organization in tokamaks are presented the possible logical sequence. The resulting picture of physical processes self-organized plasmas is predicted based on nonrequiibrium thermodynamic approach, which uses Smoluchowski-type equation for energy balance. magnetized leads to formation universal MHD structure, where normalized pressure profiles similar. Fina...

In this section we will consider the general properties of the solution p(r, t) of the Smoluchowski equation in the case that the force field is derived from a potential, i.e., F (r) = −∇U(r) and that the potential is finite everywhere in the diffusion doamain Ω. We will demonstrate first that the solutions, in case of reaction-free boundary conditions, obey an extremum principle, namely, that ...

IKP, Forschungszentrum Jülich, D-52425 Jülich, Germany †IKP, Westfälische Wilhelms–Universität, D-48149 Münster, Germany Institute of Nuclear Physics, PL-31-342 Cracow, Poland ‡M. Smoluchowski Institute of Physics, Jagellonian University, PL-30-059 Cracow, Poland §Uppsala University, S-75121 Uppsala, Sweden ¶ZEL, Forschungszentrum Jülich, D-52425 Jülich, Germany Institute of Physics, University...

Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and oneand two-body potentials, a Smoluchowski-type evolution equation is rigorously derived for the one-particle distribution function. This new equation includes a novel definition of the diffusion tensor. A comparison with existing formulati...

Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.

In applications such as molecular dynamics it is of interest to fit Smoluchowski and Langevin equations to data. Practitioners often achieve this by a variety of seemingly ad hoc procedures such as fitting to the empirical measure generated by the data and fitting to properties of autocorrelation functions. Statisticians, on the other hand, often use estimation procedures, which fit diffusion p...

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, rectification, and pumping. Recently, it has been shown that the nanofabricated synthetic pores could be considered as analogous to biological channels with respect to their transport characteristics [P. Yu. Apel et al., Nucl. Instrum. Methods Phys. Res. B 184, 337 (2001); Z. S...

The utility of an approximate heuristic version of Kramers' theory of reaction rates that was earlier used [Chaudhury and Cherayil, J. Chem. Phys. 125, 024904 (2006)] to successfully describe the nonexponential waiting time distributions of the enzyme beta-galactosidase is reassessed. The original model, based on the Smoluchowski equation, is reformulated in terms of the phase space variables o...

In this article we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuous medium and structure them by their degree of malfunctioning. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and agglomeration of soluble polymers of am...