Related papers: A Two-Region Diffusion Model for Current-Induced I…
The growth of crystal surfaces, under non-equilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus governed by a…
We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate…
The distinction between absolute and convective instabilities is well known in the context of hydrodynamics and plasma physics. In this Letter, we examine an epitaxial crystal growth model from this point of view and show that a…
A discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We study the meandering instability during growth of an isolated nanostructure, a crystalline cone, consisting of concentric circular steps. The onset of the instability is studied analytically within the framework of the standard…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
Separated flows past complex geometries are modelled by discrete vortex techniques. The flows are assumed to be rotational and inviscid, and a new technique is described to determine the streamfunctions for linear shear profiles. The…
The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both…
Motivated by strategies for targeted microfluidic transport of droplets, we investigate how sessile droplets can be steered toward a preferred direction using travelling waves in substrate wettability or deformations of the substrate. To…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
An analytical theory is presented for linear, local, short-wavelength instabilities in swirling flows, in which axial shear, differential rotation, radial thermal stratification, viscosity, and thermal diffusivity are all taken into…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
In this paper, we study the large time behaviour of solutions of multistable reaction-diffusion equations in $\mathbb{R}^N$, with a spatially periodic heterogeneity. By multistable, we mean that the problem admits a finite -- but…