Related papers: Convergence of methods for coupling of microscopic…
We develop a coarse grained (CG) approach for efficiently simulating calcium dynamics in the endoplasmic reticulum membrane based on a fine stochastic lattice gas model. By grouping neighboring microscopic sites together into CG cells and…
The generator coordinate method (GCM) casts the wavefunction as an integral over a weighted set of non-orthogonal single determinantal states. In principle this representation can be used like the configuration interaction (CI) or shell…
This paper provides an error estimate for the u-series method of the Coulomb interaction in molecular dynamics simulations. We show that the number of truncated Gaussians $M$ in the u-series and the base of interpolation nodes $b$ in the…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…
We propose a new multi-scale molecular dynamics simulation method which can achieve high accuracy and high sampling efficiency simultaneously without aforehand knowledge of the coarse grained (CG) potential and test it for a biomolecular…
This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…
Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for the reaction diffusion model. Using only three properties, this analysis provides convergence results for several conforming and…
Many biochemical systems appearing in applications have a multiscale structure so that they converge to piecewise deterministic Markov processes in a thermodynamic limit. The statistics of the piecewise deterministic process can be obtained…
We present a parallel-scalable method for simulating non-dilute suspensions of deformable particles immersed in Stokesian fluid in three dimensions. A critical component in these simulations is robust and accurate collision handling. This…
\noindent\textbf{Background:} While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics.…
Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavour, determining nucleation mechanisms and rates for phase separation requires an…
Markov Chain Monte Carlo methods are algorithms used to sample probability distributions, commonly used to sample the Boltzmann distribution of physical/chemical models (e.g., protein folding, Ising model, etc.). This allows us to study…
Many modern production and measurement facilities incorporate multiphase systems at low pressures. In this region of flows at small, non-zero Knudsen- and low Mach numbers the classical mesoscopic Monte Carlo methods become increasingly…
We consider two volume-surface reaction-diffusion systems arising from cell biology. The first system describes the localisation of the protein Lgl in the asymmetric division of Drosophila SOP stem cells, while the second system models the…
The small magnitude and long-range character of non-covalent interactions pose a significant challenge for computational quantum chemical and electronic-structure methods alike. State-of-the-art coupled cluster (CC) theory and…
The direct numerical simulation of particulate systems offers a unique approach to study the dynamics of fluid-solid suspensions by fully resolving the submerged particles and without introducing empirical models. For the lattice Boltzmann…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…