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...

‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

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...

The Helmholtz resonator is a prototype of a single acoustic resonance, which can be modeled with a digital resonator. This paper extends this concept by coupling several Helmholtz resonators. The resulting structure is called a Helmholtz resonator tree. The height of the tree is defined by the number of resonator layers that are interconnected. The overall number of resonance frequencies of a H...