We study the coupled rotational diffusion in a two-particle chain on the basis of a Smoluchowski equation and calculate time-correlation functions that are measurable in an experiment. This might be used to explore hydrodynamic interactions in the limit where lubrication theory is valid. PACS numbers: 05.45.Xt, 47.15.Gf, 47.85.Np, 82.70.Dd, 82.60.Yz

The existence of inertial manifolds for a Smoluchowski equation—a nonlinear and nonlocal Fokker–Planck equation which arises in the modelling of colloidal suspensions—is investigated. The difficulty due to first-order derivatives in the nonlinearity is circumvented by a transformation. Mathematics Subject Classification: 35Kxx, 70Kxx

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via twoscale convergence techniques, allows the investigation of deposition effects in porous materials in the...

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.

A stochastic theory of diffusion-controlled reaction is developed with the emphasis on the many-body aspects which rigorous stochastic theories inevitably encounter. The field operator method developed in our previous paper is extensively used in the analysis. The classical Smoluchowski theory is shown to be strictly valid in the long-time scale, and its relation to the Boltzmann equation is di...

We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion-type, specifically Smoluchowski, processes. The notion of entropy production is analyzed. The role of the Helmholtz extremum principle is contrasted to that of the more familiar entropy extremum principles. PACS numbers: 02.50.Ey, 05.20.-y, 05.40.Jc

P. Bizoń, T. Chmaj, A. Rostworowski, B. G. Schmidt, and Z. Tabor M. Smoluchowski Insitute of Physics, Jagiellonian University, Kraków, Poland H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland Cracow University of Technology, Kraków, Poland Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Golm, Germany Department of Biophysics, Jagel...

According to the Smoluchowski-Kramers approximation, the solution of the equation μq̈ t = b(q μ t ) − q̇ t + Σ(q t )Ẇt, q 0 = q, q̇ 0 = p converges to the solution of the equation q̇t = b(qt) + Σ(qt)Ẇt, q0 = q as μ → 0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.

This paper concentrates on breaching the gap between the Smoluchowski coagulation equations for Marcus-Lushnikov processes and the theory of random graphs. It is known that in many cases the cluster dynamics of a random graph process can be replicated with the corresponding coalescent process. The cluster dynamics of a coalescent process (without merger history) is reflected in a auxiliary proc...