Related papers: Symmetry-Breaking Bifurcations for Compartmental R…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of inter-particle interaction to inter-well tunneling. Here, we elucidate the…
We introduce a system composed of two (2+1)-dimensional baby-skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core…
A general symmetry-controlled mechanism is proposed for realizing dual flat-bands of bound state in the continuum (BIC) and its radiative counterpart in photonic crystal slabs. By breaking the vertical mirror symmetry of slab,…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
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…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
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…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse,…
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
In this work we developed a RAFT polymerization model taking into account the main reactions of the experimental RAFT process and implemented that model in dissipative particle dynamics (DPD). With a help of a kinetic model based on the…
Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing…
We investigate the emergence of sustained spatio-temporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
In this work, we focus on an autocatalytic reaction-diffusion model and carry out multiple scale weakly nonlinear analysis. A cubic and a quadratic autocatalytic reaction system is analysed. We develop a framework to identify the critical…
We study a model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field together with membrane fluidity and bending elasticity. We prove the existence of a plethora of equilibria in the large,…
It is well known that a symmetric soliton in coupled nonlinear Schroedinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of its energy, featuring a transition into an asymmetric soliton via a subcritical…
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…