Related papers: Variational Percolation Bounds for Cellular Membra…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
A modified Poisson-Nernst-Planck system in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. It describes the concentrations of ions immersed in a polar solvent and the correlated electric potential due to the…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
Biological membranes are able to exhibit various morphology due to the fluidity of the lipid molecules within the monolayers. The shape transformation of membranes has been well described by the classical Helfrich theory, which consists…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
We analyze enhanced optical transmission through subwavelength apertures using a modal formulation for the two fundamental polarizations, transverse electric (TE) and transverse magnetic (TM). Within this framework, the fields inside the…
As nutrients travel through microcirculation and are absorbed, their availability continuously decreases. However, a uniform nutrient distribution is critical, as it prevents tissue death in poorly supplied areas. How, then, do vascular…
Lipid membranes, the barrier defining living cells and many of their sub-compartments, bind to a wide variety of nano- and micro-meter sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the…
Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…
We give a description of cell diffusion in a soft tissue, paying special attention to the coupling of force, matter, and microforce balance laws through a suitable dissipation principle. To this end, we cast our framework into a multi-level…
Nonequilibrium dynamics of biomembranes with active inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with ATP ligands. As protein…
Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…
Atomic diffusion affects the properties of various engineering materials, which predominantly occur in the polycrystalline state. A rigorous description of polycrystalline diffusion must therefore account for crystallographic defects,…
One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production…
Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of…
Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first, factor proportional to a power of the number of mesh…
We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating…
Major efforts in recent years have been directed towards understanding molecular transport in polymeric membranes, in particular reverse osmosis and nanofiltration membranes. Transition-state theory is an increasingly common approach to…