相关论文: A thermo-diffusion system with Smoluchowski intera…
Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential…
In 1917, Marian von Smoluchowski presented a simple mathematical description of diffusion-controlled reactions on the scale of individual molecules. His model postulated that a reaction would occur when two reactants were sufficiently close…
We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to…
We investigate experimentally phenomenon of turbulent thermal diffusion of micron-size solid particles in an inhomogeneous convective turbulence forced by one vertically-oriented oscillating grid in an air flow. This effect causes formation…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
An uncoupled multi-scale homogenization approach is used to estimate the effective thermal conductivities of plain weave C/C composites with a high degree of porosity. The geometrical complexity of the material system on individual scales…
We propose an efficient and fast numerical algorithm of finding a \emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable…
We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such…
A system of stochastic differential equations describing diffusive phenomena, which has arbitrary friction depending on both state and distribution is investigated. The Smoluchowski-Kramers approximation is seen to describe dynamics in the…
The Smoluchowski diffusion equation describes diffusion in the presence of external forces. Studying the mechanical response of soft materials to linear forces, such as shear, results in a boundary value problem involving an…
The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature -- the thermal entrance length -- is a consequence of diffusion…
Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities with constant rate coefficients, the temperature-dependent…
We investigate the evolution of a system of colloidal particles, trapped at a fluid interface and interacting via capillary attraction, as function of the range of the capillary interaction and temperature. We address the collapse of an…
This paper deals with the homogenization of the $p$-Laplacian reaction-diffusion problems in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of pure-reactive type. We generalize…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a…
In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface…
We use direct numerical simulations to investigate the interaction between the temperature field of a fluid and the temperature of small particles suspended in the flow, employing both one and two-way thermal coupling, in a statistically…
We report a molecular dynamics simulation of a supercooled simple monatomic glass-forming liquid. It is found that the onset of the supercooled regime results in formation of distinct domains of slow diffusion which are confined to the…