Related papers: Well posedness of fluid/solid mixture models for b…
Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…
We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…
The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses,…
We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and…
We introduce and analyze a model for osmotically spreading biofilm colonies at solid-air interfaces that includes wetting phenomena, i.e. surface forces. The model combines a hydrodynamic description for biologically passive liquid…
Tuning cell rearrangements is essential in collective cell movement that underlies cancer progression, wound repair, and embryonic development. A key question is how tissue material properties and morphology emerge from cellular factors…
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial direction and the displacement of the vessel wall from rest. We…
Biofilms are ubiquitous macro-colonies of bacteria that develop at various interfaces (solid-liquid, solid-gas or liquid-gas). The formation of biofilms starts with the attachment of individual bacteria to an interface, where they…
This paper is devoted to the study of propagation dynamics for a large class of non-monotone evolution systems. In two directions of the spatial variable, such a system has two limiting systems admitting the spatial translation invariance.…
We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models both in the context of finite…
We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin…
Multicomponent lipid mixtures exhibit complex phase behavior, including coexistence of nanoscopic fluid phases in ternary mixtures mimicking the composition of the outer leaflet of mammalian plasma membrane. The physical mechanisms…
Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few-mode-model. It is derived from the proper hydrodynamic balance…
Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The…
In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity,…