Related papers: Boundary-reaction-diffusion model for oscillatory …
Oscillatory zoning, i.e. self-formation of spatial quasi-periodic oscillations in the composition of solid growing from aqueous solution, is analyzed theoretically. Keeping in mind systems like (Ba,Sr)SO4 we propose a 1D model that takes…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
We investigate the mechanism of growth of nanocrystals from solution using the case of ZnO. Spanning a wide range of values of the parameters, such as the temperature and the reactant concentration, that control the growth, our results…
We report the physical origin of transient off-centre convective zones (oCZs) that arise in mass accreting stellar models. Using detailed MESA simulations of binary evolution, we find that these oCZs are not numerical artefacts but emerge…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
Oscillons, i.e., immobile spatially localized but temporally oscillating structures, are the subject of intense study since their discovery in Faraday wave experiments. However, oscillons can also disappear and reappear at a shifted spatial…
We study non-isothermal diffusive transport of a weakly-soluble two-component substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. Particular attention is given to the example case of…
The shear-transformation-zone (STZ) theory has been remarkably successful in accounting for broadly peaked, frequency-dependent, viscoelastic responses of amorphous systems near their glass temperatures $T_g$. This success is based on the…
The phase-separation process of a binary mixture with order-parameter-dependent mobility under shear flow is numerically studied. The ordering is characterized by an alternate stretching and bursting of domains which produce oscillations in…
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to…
Non-linear behavior in interstellar chemical models has been recognized for 25 years now. Different mechanisms account for the possibility of multiple fixed-points at steady state, characterized by the ionization degree of the gas. Chemical…
We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the…
We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…
Based on the formula for the number density of vacancies in a solid under the stress or tension, the model of grain boundary diffusion in crystalline solids is developed. We obtain the activation energy of grain boundary diffusion…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
In this work we present the homogenization of a reaction-diffusion model that includes an evolving microstructure. Such type of problems model, for example, mineral dissolution and precipitation in a porous medium. Hence, we are dealing…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
We prove that the famous diffusive Brusselator model can support more complicated spatial-temporal wave structure than the usual temporal-oscillation from a standard Hopf bifurcation. In our investigation, we discover that the diffusion…