Natural boundaries for the Smoluchowski equation and affiliated diffusion processes

Natural boundaries for the Smoluchowski equation and affiliated diffusion processes.

The Schrödinger problem of deducing the microscopic dynamics from the inputoutput statistics data is known to admit a solution in terms of Markov diffusions.The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion.By choosing a reference Smoluchowski diffusion,we automatically fix the Feynman-Kac potential and the field of local acceleration...

Smoluchowski diffusion equation for active Brownian swimmers.

We study the free diffusion in two dimensions of active Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers and analytically solved in the long-time regime for arbitrary values of the Péclet number; this allows us to analyze the out-of-eq...

The diffusion in the quantum Smoluchowski equation

A novel quantum Smoluchowski dynamics in an external, nonlinear potential has been derived recently. In its original form, this overdamped quantum dynamics is not compatible with the second law of thermodynamics if applied to periodic, but asymmetric ratchet potentials. An improved version of the quantum Smoluchowski equation with a modified diffusion function has been put forward in L. Machura...

Diffusion Equation and Stochastic Processes.

Smoluchowski equation and the colloidal charge reversal.

Smoluchowski equation and the Monte Carlo simulations are used to study the conditions leading to the reversal of the electrophoretic mobility. Zeta (zeta) potential is identified with the diffuse potential at the shear plane which, we argue, must be placed at least one ionic diameter away from the colloidal surface. For sufficiently strongly charged colloids, zeta potential changes sign as a f...