The Smoluchowski coagulation-diffusion PDE is a system of partial differential equations modelling the evolution in time of mass-bearing Brownian particles which are subject to shortrange pairwise coagulation. This survey presents a fairly detailed exposition of the kinetic limit derivation of the Smoluchowski PDE from a microscopic model of many coagulating Brownian particles that was undertak...

Thermostats are dynamical equations used to model thermodynamic variables such as temperature and pressure in molecular simulations. For computationally intensive problems such as the simulation of biomolecules, we propose to average over fast momentum degrees of freedom and construct thermostat equations in configuration space. The equations of motion are deterministic analogues of the Smoluch...

We discuss equilibria, dynamics and regularity for Smoluchowski equations coupled to Navier-Stokes equations. Introduction We consider mixtures of fluids and microscopic inclusions. The microscopic inclusions are characterized by state variables m ∈ M , where M is a compact smooth Riemannian manifold without boundary. The simplest example is that of microscopic rods with directors m ∈ S. The mi...

We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples theMaier-Saupe short-range interaction, dipole-dipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field...

A numerical study of 3D electrokinetic flows through micromixers was performed. The micromixers considered here consisted of heterogeneous rectangular microchannels with prescribed patterns of zeta-potential at their walls. Numerical simulation of electroosmotic flows within heterogeneous channels requires solution of the Navier-Stokes, Ernest-Plank and species concentration equations. It is kn...

The formation of a distribution of cluster sizes is a common feature in a wide variety of situations. Examples include astrophysics, atmospheric physics and polymer science, [2, 3, 8]. In this paper we discuss some mathematical aspects of the Smoluchowski coagulation equation which is a model for the dynamics of cluster growth. This model involves a coupled infinite system of ordinary different...

We consider a generalized class of Keller-Segel models describing the chemo-taxis of biological populations (bacteria, amoebae, endothelial cells, social insects ,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion pri...

We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples theMaier-Saupe short-range interaction, dipole-dipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field...

We show that the Perron-Frobenius equation of microscopic chaos based on double symmetric maps leads to an inhomogeneous Smoluchowski equation with a source term. Our perturbative analysis reveals that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. In addition, our result proves that in the zeroth-order limit, the position dist...