Related papers: Effect of a membrane on diffusion-driven Turing in…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing…
Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently,…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…
In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the…
We study chemical pattern formation in a fluid between two flat plates and the effect of such patterns on the formation of convective cells. This patterning is made possible by assuming the plates are chemically reactive or release reagents…
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
Context: The thermal instability is one of the dynamical agents for turbulence in the diffuse interstellar medium, where both, turbulence and thermal instability interact in a highly non-linear manner. Aims: We study basic properties of…
Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…
We consider a problem of stability of a membrane of an infinite span and a finite chord length, submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov (1985) has shown that an…
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz, and the…
We propose a mechanism for the stabilization/destabilization of cell membranes by multivalent ions with an emphasis on its implications for the division and fusion of cells. We find that multivalent cations preferentially adsorbed onto a…
We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3D) inviscid fluid flow. We apply small initial…
Understanding the mechanical instabilities of two-dimensional membranes has strong connection to the subjects of structure instabilities, morphology control and materials failures. In this work, we investigate the plastic mechanism…
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…