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We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
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…
Biofilms are bacterial aggregates that grow on moist surfaces. Thin homogeneous biofilms naturally formed on the walls of conducts may serve as biosensors, providing information on the status of microsystems (MEMS) without disrupting them.…
We construct a phase field model including hydrodynamics and elasticity in one-component systems. It can be used to investigate solid-liquid and liquid-liquid phase transitions. Upon first-order phase transition, a velocity field is induced…
It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
One of the promising frontiers of bioengineering is the controlled release of a therapeuticdrug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a two-phase mathematical model describing…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…
Building upon the classical chemo-mechanical theory of Larch{\'e} and Cahn for equilibrium, numerous studies have investigated the transport of species in solids, with or without trapping phenomena. In most applications -- such as the…
In this paper the model for a highly viscous droplet sliding down an inclined plane is analyzed. It is shown that, provided the slope is not too steep, the corresponding moving boundary problem possesses classical solutions. Well-posedness…
Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…
Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead…
We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral…
We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the…
Bacteria are ubiquitous in our daily lives, either as motile planktonic cells or as immobilized surface-attached biofilms. These different phenotypic states play key roles in agriculture, environment, industry, and medicine; hence, it is…
We use numerical simulations to examine two-dimensional particle mixtures that strongly phase separate in equilibrium. When the system is externally driven in the presence of quenched disorder, plastic flow occurs in the form of meandering…
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the…