Related papers: Boundary-reaction-diffusion model for oscillatory …
Transport phenomena are studied for a binary (AB) alloy on a rigid square lattice with nearest-neighbor attraction between unlike particles, assuming a small concentration $c_v$ of vacancies $V$ being present, to which $A(B)$ particles can…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
Granular crystallisation is an important phenomenon whereby ordered packing structures form in granular matter under vibration. However, compared with the well-developed principles of crystallisation at the atomic scale, crystallisation in…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
Reorientation of the segregation pattern of a binary granular mixture on a two-dimensional hor- izontally oscillating tray is numerically realized. The mixture consists of large-and-heavy particles and small-and-light particles, the…
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…
Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of…
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk diffusion equation with a non-linear boundary condition. Cell…
The atomic structure of the supercooled liquid has often been discussed as a key source of glass formation in metals. The presence of icosahedrally-coordinated clusters and their tendency to form networks have been identified as one…
It is known that gas bubbles on the surface bounding a fluid flow can change the coefficient of friction and affect the parameters of the boundary layer. In this paper, we propose a method that allows us to create, in the near-wall region,…
A survey is presented of the dynamic features of non-itinerant off-center defects in crystals, such as rotation-like reorientation of isolated species by either impurity or host ions. The occurrence of off-center displacements in…
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary…
We introduce a schematic non-linear diffusion model where density fluctuations induce a rich out of equilibrium dynamics. The properties of the model are studied by numerical simulations and analytically in a mean field approximation. At…
Oriented attachment (OA) has become a well-recognized mechanism for the growth of metal, ceramic, and biomineral crystals. While many computational and experimental studies of OA have shown that particles can attach with some misorientation…