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Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

We propose a kinetic Ising model to study phase separation driven by surface diffusion. This model is referred to as "Model S", and consists of the usual Kawasaki spin-exchange kinetics ("Model B") in conjunction with a kinetic constraint.…

To study epitaxial thin-film growth, a new model is introduced and extensive kinetic Monte Carlo simulations performed for a wide range of fluxes and temperatures. Varying the deposition conditions, a rich growth diagram is found. The model…

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the…

We report growth of superconducting Sr2RuO4 films by oxide molecular beam epitaxy (MBE). Careful tuning of the Ru flux with an electron beam evaporator enables us to optimize growth conditions including the Ru/Sr flux ratio and also to…

We examine the budding of a nanoscale particle through a lipid bilayer using molecular dynamics simulations, free energy calculations, and an elastic theory, with the aim of determining the extent to which equilibrium elasticity theory can…

We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after…

This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…

We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of…

In this paper a simple (2+1) solid-on-solid model of the epitaxial films growth based on random deposition followed by breaking particle-particle lateral bonds and particles surface diffusion is introduced. The influence of the critical…

In recent years, deep learning-based image compression, particularly through generative models, has emerged as a pivotal area of research. Despite significant advancements, challenges such as diminished sharpness and quality in…

Equivariant diffusion models have achieved impressive performance in 3D molecule generation. These models incorporate Euclidean symmetries of 3D molecules by utilizing an SE(3)-equivariant denoising network. However, specialized equivariant…

Significant strides have been made using large vision-language models, like Stable Diffusion (SD), for a variety of downstream tasks, including image editing, image correspondence, and 3D shape generation. Inspired by these advancements, we…

Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…

We report results of the first computer simulation studies of a physically adsorbed gas on a quasicrystalline surface, Xe on decagonal Al-Ni-Co. The grand canonical Monte Carlo method is employed, using a semi-empirical gas-surface…

Electron-beam (e-beam) lithography is widely employed in fabrication of 2-D patterns and 3-D structures. A certain type or shape of the sidewall in the remaining resist profile may be desired in an application, e.g., an undercut for…

The presence of atomic-scale defects at multilayer interfaces significantly degrades performance in CdTe-based photovoltaic technologies. The ability to accurately predict and understand defect formation mechanisms during overlayer growth…

Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…

We present a mathematical model based on a system of partial differential equations (PDEs) with cross-diffusion and reaction terms to describe ecological interactions between multiple bacterial species and substrates within microaggregates,…