Related papers: Effect of a membrane on diffusion-driven Turing in…
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
This paper deals with the analysis of qualitative properties involved in the dynamics of Keller-Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the…
The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation…
We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This…
This paper proves that contractive ordinary differential equation systems remain contractive when diffusion is added. Thus, diffusive instabilities, in the sense of the Turing phenomenon, cannot arise for such systems. An important…
first-principles numerical simulation model for crumpling of a stiff tethered membrane is introduced. In our model membranes, wrinkles, ridge formation, ridge collapse, as well as the initiation of stiffness divergence, are observed. The…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
Membranes are of great technological and biological as well as theoretical interest. Two main classes of membranes can be distinguished: Fluid membranes and polymerized, tethered membranes. Here, we review progress in the theoretical…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset \R^d$ containing a set of small subdomains or interior…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
From the perspective of physical properties, the cell membrane is an exotic two-dimensional material that has a dual nature: it exhibits characteristics of fluids, i.e., lipid molecules show lateral diffusion, while also demonstrating…
A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…
We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local…
We show that some boundary conditions assumed at a thin membrane may result in normal diffusion not being the stochastic Markov process. We consider boundary conditions defined in terms of the Laplace transform in which there is a linear…