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New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a…
Strongly coupled, recurrent, balanced network models have been successful in describing and predicting many phenomena observed in cortical neural recordings. However, most balanced network models use current-based synapse models in place of…
We use cluster dynamical mean field theory to study the phase diagram of the square lattice bilayer Hubbard model with an interlayer interaction. The layers are populated by two-component fermions, and the densities in both layers and the…
Cell shape changes are largely controlled by the actin cytoskeleton, a dynamic filament network beneath the plasma membrane. Several cell types can form extended free-standing protrusions not supported by an extracellular substrate or…
Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion,…
We theoretically investigate the relaxation dynamics of a nearly-flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion in each…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
The study of interactions between biomimetic membranes and micron-sized particles is crucial for understanding various biological processes. Here, we control microparticle spontaneous engulfment by giant lipid vesicles by tuning particle…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized…
We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a nonlinear generalisation of the…
We revisit the Glauber model to study the heavy ion reaction cross sections and elastic scattering angular distributions at low and intermediate energies. The Glauber model takes nucleon-nucleon cross sections and nuclear densities as…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
The structure of membrane-active peptides and their interaction with lipid bilayers can be studied in oriented lipid membranes deposited on solid substrates. Such systems are desirable for a number of surface-sensitive techniques. Here we…
Accurate estimation of surface wettability for various degrees of hydrophobicity becomes increasingly important in the molecular design of membrane. In this paper, we develop simple yet physically realistic model for estimating contact…
We present a theoretical model for the evolution of mixture concentrations in a micro-pervaporation device, similar to those recently presented experimentally. The described device makes use of the pervaporation of water through a thin PDMS…
The 2-fold degeneracy of the ground state of a quasi-one-dimensional system allows it to support topological excitations such as solitons. We study the combined effects of Coulomb interactions and confinement due to interchain coupling on…
The acoustic mismatch model and the diffuse mismatch model have been widely used to predict the thermal interface conductance. However, the acoustic mismatch model (diffuse mismatch model) is based on the hypothesis of a perfectly smooth…
The two-dimensional Active Brownian Particles system is meant to be composed of hard disks, that show excluded volume interactions, usually simulated via molecular dynamics using pure repulsive potentials. We show that the softness of the…
Two models for quasistatic adhesive unilateral contact delaminating in mixed fracture mode, i.e. distinguishing the less-dissipative Mode I (opening) from the more-dissipative Mode II (shearing), and allowing rigorous mathematical and…