The Smoluchowski equations of coagulation are solved analytically in two cases involving a finite cut-off of the system: the constant kernel set to zero for any j > N on the one hand, and the general three-particle case on the other. Both are seen to exhibit rather unusual large-time behaviour. The first model can be used to account for large particles precipitating out of a system and its beha...

We study a general class of nonlinear mean field Fokker-Planck equations in relation with an effective generalized thermodynamical formalism. We show that these equations describe several physical systems such as: chemotaxis of bacterial populations, Bose-Einstein condensation in the canonical ensemble, porous media, generalized Cahn-Hilliard equations, Kuramoto model, BMF model, Burgers equati...

We study a model system in which lipid bilayers are created using variable (precisely known) proportions of phosphatidylcholine and cholesterol. The model membranes exhibit cholesterol-enriched microdomains that are analogous to the so-called "lipid rafts" that form in living cells. After briefly presenting some experimental results, we formulate and solve a novel mathematical model based on th...

The Smoluchowski coagulation equation is a mean-field model for the growth of clusters (particles, droplets,...) by binary coalescence, that is, the driving growth mechanism is the merger of two particles into a single one. In the simple situation where each particle is fully identified by its volume, it describes the dynamics of the volume distribution function f = f(t, x) ≥ 0 of particles of ...

Direct observations of solution-phase nanoparticle growth using in situ liquid transmission electron microscopy (TEM) have demonstrated the importance of "non-classical" growth mechanisms, such as aggregation and coalescence, on the growth and final morphology of nanocrystals at the atomic and single nanoparticle scales. To date, groups have quantitatively interpreted the mean growth rate of na...

Several recent theories of the kinetics of diffusion influenced excited-state association--dissociation reactions are tested against accurate Brownian dynamics simulation results for a wide range of parameters. The theories include the relaxation time approximation (RTA), multiparticle kernel decoupling approximations and the so-called kinetic theory. In the irreversible limit, none of these th...