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Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and…
The theory of nucleation with depletion zones is discussed. The approach of stochastic effects of solitary droplet is analyzed. The negative features of a solution with fixed boundary are outlined. A new solution with effective fixed…
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
This paper is concerned with a chemotaxis model with logarithmic sensitivity and fast diffusion, which possesses strong singularities for the sensitivity at zero-concentration of chemical signal, and for the diffusion at zero-population of…
We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics…
We prove existence of weak solutions and weak-strong uniqueness for a mathematical model which couples the evolution of a phase-parameter $\varphi$ satisfying a Cahn-Hilliard type relation with the one of an additional variable $\sigma$…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
This paper develops a comprehensive Hamilton-Jacobi framework to analyze asymptotic propagation dynamics in a field-road system featuring unidirectional advection and Wentzell-type boundary conditions. We rigorously derive a Hamilton-Jacobi…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
We study initial transient stages in directional solidification by means of a non-variational phase field model with fluctuations. This model applies for the symmetric solidification of dilute binary solutions and does not invoke…
Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are…
We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…
In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a double-well…
Biomolecular condensates provide distinct chemical environments, which control various cellular processes. The diffusive dynamics and chemical kinetics inside phase-separated condensates can be studied experimentally by fluorescently…
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2$ population densities. We introduce a discrete multi-phase…
We introduce two simple models of forward-backward stochastic differential equations with a singular terminal condition and we explain how and why they appear naturally as models for the valuation of CO2 emission allowances. Single phase…