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We analyze the collective surface diffusion coefficient, $D_c$, near a first-order phase transition at which two phases coexist and the surface coverage, $\te$, drops from one single-phase value, $\te_+$, to the other one, $\te_-$. Contrary…
A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here we develop a numerically-exact…
Here, an approach in terms of shot noise is proposed to study and characterize surface diffusion and low vibrational motion when having interacting adsorbates on surfaces. In what we call statistical limit, that is, at long times and high…
Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or "space charge") near the electrodes on Faradaic reaction kinetics. The full model…
The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…
Despite the simplicity of one-particle dynamics, explicit expressions for the one-dimensional propagator on a circle suitable to numerical evaluation are surprisingly lacking -- not only in the presence of potentials but even in the free…
Dirac energy-dispersions are responsible of the extraordinary transport properties of graphene. This motivated the quest for engineering such energy dispersions also in photonics, where they have been predicted to lead to many exciting…
We consider the reaction zone that grows between separated regions of diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the framework of the mean-fieldlike reaction-diffusion equations. For distances from the centre…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
Diffusion of a tagged particle near a constraining biological surface is examined numerically by modeling the surface-water interaction by an effective potential. The effective potential is assumed to be given by an asymmetric double well…
In this article, we perform an asymptotic analysis of a nonlocal reaction-diffusion equation, with a fractional laplacian as the diffusion term and with a nonlocal reaction term. Such equation models the evolutionary dynamics of a…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…