相关论文: The Gap-Tooth Method in Particle Simulations
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
By applying a hybrid Molecular dynamics and mesoscopic simulation technique, we study the classic convection-diffusion problem of Taylor dispersion for colloidal discs in confined flow. We carefully consider the time and length-scales of…
In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic…
The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
Dissipative particle dynamics (DPD) is now a well-established method for simulating soft matter systems. However, its applicability was recently questioned because some investigations showed an upper coarse-graining limit that would prevent…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
We propose a new method for implementing process tomography that is based on the information extracted from temporal correlations between observables, rather than on state preparation and state tomography. As such, the approach is…
We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for…
The diffuse medium in and around galaxies can exist in a multi-phase state: small, cold gas clouds contributing significantly to the total mass embedded in pressure equilibrium with a hotter, more diffuse volume-filling component. Modeling…
Starting from a particle model we derive a macroscopic aggregation-diffusion equation for the evolution of slime mold under the assumption of propagation of chaos in the large particle limit. We analyze properties of the macroscopic model…
When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets…
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of first order. We also analyze the large-time behavior of the approximated solution by obtaining the first term in the asymptotic…
We propose a dynamical model for the erosive growth of a channel in a granular medium driven by subsurface water flow. The model is inferred from experimental data acquired with a laser-aided imaging technique. The evolution equation for…
Growth-elasticity is a powerful model framework for understanding complex shape development in soft biological tissues. At each instant, by mapping how continuum building blocks have grown geometrically and how they respond elastically to…