Related papers: Pattern Formation in a Coupled Membrane-Bulk React…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…
Biomolecular condensates formed through the phase separation of proteins and nucleic acids are widely observed, offering a fundamental means of organizing intracellular materials in a membrane-less fashion. Traditionally, these condensates…
A model predicting the structure of repulsive, spherically symmetric, monodisperse particles confined between two walls is presented. We study the buckling transition of a single flat layer as the double layer state develops. Experimental…
We describe and analyze a bistable reaction-diffusion (RD) model for two interconverting chemical species that exhibits a phenomenon of wave-pinning: a wave of activation of one of the species is initiated at one end of the domain, moves…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
In order to understand the long known anomalies in the composition dependence of diffusion and viscosity of binary mixtures, we introduce here two new models and carry out extensive molecular dynamic simulations. In these models, the two…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane,…
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high…
We study dynamics emergent from a two-dimensional reaction--diffusion process modelled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution…
We implement molecular dynamics simulations in canonical ensemble to study the effect of confinement on a $2d$ crystal of point particles interacting with an inverse power law potential proportional to $r^{-12}$ in a narrow channel. This…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…