Related papers: Spiking at the edge
We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
Particles diffusing near interfaces face anisotropic resistance to motion due to hydrodynamic interactions. While this has been extensively studied near \textit{hard} interfaces since the works of Lorentz and Brenner, our understanding of…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
The phase separation mechanism of a binary liquid mixture off-critically quenched in its miscibility gap is nucleation and growth, its homogeneous phase reaching a metastable equilibrium state. The successive stages of growth of the…
The competing influence of two types of interactions on surface diffusion is investigated: one of them, epsilon, acts between adsorbed particles, while the other one, eta, between activated and adsorbed particles. To this end, a specific…
In nonlinear topological systems, edge solitons either originate from linear topological edge modes or emerge as nonlinearity-induced localized states without topological protection. While electric circuits (ECs) provide a platform for…
An activator-inhibitor-substrate model of side-branching used in the context of pulmonary vascular and lung development is considered on the supposition that spatially localized concentrations of the activator trigger local side-branching.…
Spin waves are promising chargeless information carriers for the future, energetically efficient beyond-CMOS systems. Among many advantages there are the ease of achieving nonlinearity, the variety of possible interactions, and excitation…
We study the mechanism of the `pearling' instability seen recently in experiments on lipid tubules under a local applied laser intensity. We argue that the correct boundary conditions are fixed chemical potentials, or surface tensions…
Diffusion in cell membranes is not just simple two-dimensional Brownian motion, but typically depends on the timescale of the observation. The physical origins of this anomalous sub-diffusion are unresolved, and model systems capable of…
We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication. Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of…
Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…
We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble,…
Addiction to internet-based social media has increasingly emerged as a critical social problem, especially among young adults and teenagers. Based on multiple research studies, excessive usage of social media may have detrimental…
Topological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic…
Topology plays an increasing role in physics beyond the realm of topological insulators in condensed mater. From geophysical fluids to active matter, acoustics or photonics, a growing family of systems presents topologically protected…
A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid and flat surface and the tip of an incoming projectile. We develop a comprehensive theory for this viscous approach stage of…