Related papers: A scheme for simulating one-dimensional diffusion …
We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
The astonishing growth of generative tools in recent years has empowered many exciting applications in text-to-image generation and text-to-video generation. The underlying principle behind these generative tools is the concept of…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
In this work we study the diffusion mechanisms in lithium disilicate melt using molecular dynamics simulation, which has an edge over other simulation methods because it can track down actual atomic rearrangements in materials once a…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Diffusion models are getting popular in generative image and video synthesis. However, due to the diffusion process, they require a large number of steps to converge. To tackle this issue, in this paper, we propose to perform the diffusion…
The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of…
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J.…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…
We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation…