Related papers: Point-particle method to compute diffusion-limited…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
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.…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption at a reactive surface, which takes into account stochastic switching of a diffusing particle's conformational state. For simplicity,…
We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…
Yeh and Hummer's simplified estimation method has often been adopted to obtain diffusion coefficients for solute molecules using molecular dynamic simulation. However, the simplified formula is not necessarily valid when a small basic cell…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
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…
In this paper, a diffusion-based molecular communication channel is modeled in presence of a probabilistic absorber. The probabilistic absorber is an absorber which absorbs molecules upon collision with probability q. With random walk…
The calculation of the diffusion-controlled reaction rate for partially absorbing, non-spherical boundaries presents a formidable problem of broad relevance. In this paper we take the reference case of a spherical boundary and work out a…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells,…
Many applications seek to measure a sample's absorption coefficient spectrum to retrieve the chemical makeup. Many real world samples are optically turbid, causing scattering confounds which many commercial spectrometers cannot address.…
Solvation is a notoriously difficult and nagging problem for the rigorous theoretical description of chemistry in the liquid phase. Successes and failures of various approaches ranging from implicit solvation modeling through dielectric…
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an…