Related papers: Calculating Effective Diffusivities in the Limit o…
We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the…
Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
Denoising diffusion probabilistic models have transformed image generation with their impressive fidelity and diversity. We show that they also excel in estimating optical flow and monocular depth, surprisingly, without task-specific…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
We describe and discuss the properties of three numerical methods for solving the diffusion equation for the transport of the chemical species and of the angular momentum in stellar interiors. We study through numerical experiments both…
We present an efficient numerical scheme based on Monte Carlo integration to approximate statistical solutions of the incompressible Euler equations. The scheme is based on finite volume methods, which provide a more flexible framework than…
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
An upper bound on the mixing efficiency is derived for a passive scalar under the influence of advection and diffusion with a body source. For a given stirring velocity field, the mixing efficiency is measured in terms of an equivalent…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
The paper proposes Monte Carlo algorithms for the computation of the information rate of two-dimensional source/channel models. The focus of the paper is on binary-input channels with constraints on the allowed input configurations. The…
A heuristic approach for collisionless perpendicular diffusion of energetic particles is presented. Analytic forms for the corresponding diffusion coefficient are derived. The heuristic approach presented here explains the parameter $a^2$…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified (i.e., test-particle) shocks. The computer code uses a single algorithmic sequence to smoothly span the range from…
We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and…
We present a version of the T-moves approach for treating nonlocal pseudopotentials in diffusion Monte Carlo which has much smaller time-step errors than the existing T-moves approaches, while at the same time preserving desirable features…
We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of…
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…