Related papers: SLE(6) and the geometry of diffusion fronts
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
We describe the accelerated propagation wave arising from a non-local reaction-diffusion equation. This equation originates from an ecological problem, where accelerated biological invasions have been documented. The analysis is based on…
The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in…
Fronts are regions of transition from one state to another in a medium. They are present in many areas of science and applied mathematics, and modelling them and their evolution is often an effective way of treating the underlying phenomena…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
Active droplets undergoing micellar solubilization can self-propel themselves by emitting filled micelles from their surface and are by nature anti-chemotactic. These droplets get repelled by their own trail of filled micelles or by other…
We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…
We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…
The concept of percolation is combined with a self-consistent treatment of the interaction between the dynamics on a lattice and the external drive. Such a treatment can provide a mechanism by which the system evolves to criticality without…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$…