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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.…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We study gas mixing in a simulated Milky Way-mass galaxy's circumgalactic medium (CGM) using cosmological `zoom-in' simulations. We insert tracer dyes in the CGM with different gas flows (shearing, coherent, and static) and diverse physical…
Molecular Dynamics - Green's Functions Reaction Dynamics (MD-GFRD) is a multiscale simulation method for particle dynamics or particle-based reaction-diffusion dynamics that is suited for systems involving low particle densities. Particles…
The dispersion measure (DM) of fast radio bursts (FRBs) provides a unique way to probe ionised baryons in the intergalactic medium (IGM). Cosmological models with different parameters lead to different DM-redshift ($\mathrm{DM}-z$)…
An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as…
In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This…
In this paper, we investigate the diffusion least mean square (DLMS) algorithm over fading channel, where in addition to channel noise and path-loss the inter-node-interference (INI) among neighboring nodes of a host node is also taken into…
We develop an online optimisation algorithm for in situ calibration of collision models in simulations of rarefied gas flows. The online optimised collision models are able to achieve similar accuracy to Direct Molecular Simulation (DMS) at…
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…
Particle diffusion in rotating drums is studied via computer simulations using a full 3-D model which does not involve any arbitrary input parameters. The diffusion coefficient for single-component systems agree qualitatively with previous…
Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used…
The diffusion approximation of stochastic gradient descent (SGD) in current literature is only valid on a finite time interval. In this paper, we establish the uniform-in-time diffusion approximation of SGD, by only assuming that the…
We present a systematic study of the self-diffusion coefficient for a fluid of particles interacting via the square-well pair potential by means of molecular dynamics simulations in the canonical (N,V,T) ensemble. The discrete nature of the…
We propose a mean field (MF) theory for a homogeneously driven granular gas of inelastic particles with Coulomb friction. The model contains three parameters, a normal restitution coefficient $r_n$, a maximum tangential restitution…
In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study…
The dynamics of interacting particles in orbital magnetic fields are notoriously difficult to study, as this physics is inherently connected to electronic correlations in two-dimensional systems, for which no straightforward theoretical…
Systems of particles with long range interactions present two important processes: first, the formation of out-of-equilibrium quasi-stationary states (QSS), and the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much…
Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…
Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on…