Related papers: Generation and motion of interfaces in a mass-cons…
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…
With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the non-linear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model…
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
A bio tissue model consisting of multilayer spherical cells including four nested radial domains (nucleus, nuclear membrane, cytoplasm and plasma membrane) is worked out to derive the cell heating dynamics in presence of membrane…
Spatial profiling technologies in biology, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate high-dimensional, multi-channel data with strong spatial alignment and complex inter-channel relationships.…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
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…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact ``localized states." The formation of space-filling patterns from…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical…
Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be…
We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the…
It has been suggested recently that growth and division of a protocell could be modeled by a chemically active droplet with simple chemical reactions driven by an external fuel supply. This model is called the continuum model. Indeed it's…
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are…
The effective mixing behavior of solutes in porous media is fundamentally connected to the development of a local mixing interface between the two initial solutions, which is characterized by a complex lamellar structure. The deformation of…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…