相关论文: Splitting instability of cellular structures in th…

Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface, by analysing a model of mechanically-regulated tissue growth in the…

We study domain structures in bistable systems such as the Ginzburg-Landau equation. The size of domains can be controlled by a global negative feedback. The domain-size control is applied for a localized spiral pattern.

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a…

We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…

Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and…

In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…

In the tangent space of some spatially extended dissipative systems one can observe "physical" modes which are highly involved in the dynamics and are decoupled from the remaining set of hyperbolically "isolated" degrees of freedom…

Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…

Pattern-forming processes, such as electrodeposition, dielectric breakdown or viscous fingering are often driven by instabilities. Accordingly, the resulting growth patterns are usually highly branched, fractal structures. However, in some…

We develop a simple computational model for cell boundary evolution in plastic deformation. We study the cell boundary size distribution and cell boundary misorientation distribution that experimentally have been found to have scaling forms…

Interfaces in tissues are ubiquitous, both between tissue and environment as well as between populations of different cell types. The propagation of an interface can be driven mechanically. % e.g. by a difference in the respective…

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld…

We consider a model proposed earlier by us for describing a form of plastic instability found in creep experiments . The model consists of three types of dislocations and some transformations between them. The model is known to reproduce a…

We explore the dynamics of a flexible fiber transported by a viscous flow in a Hele-Shaw cell of height comparable to the fiber height. We show that long fibers aligned with the flow experience a buckling instability. Competition between…

A simple one-dimensional mechanical model is proposed for splitting instability in swollen membranes. The splitting instability occurs by ring constriction. The bifurcation can be both subcritical and supercritical, depending on the…

We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation towards its "frozen" state with quasi-stationary spiral structures. We study the transition kinetics from…

Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…

We perform bifurcation analysis of plane wave solutions in one-dimensional cubic-quintic Ginzburg-Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is…

Linearized complex Ginzburg-Landau equation models various physical phenomena and the stability controls of them are important. In this paper, we study the control of the LCGLE with a simultaneously space and time dependent coefficient by…

We investigate the stability of noncomposite fractional vortex states in a mesoscopic two-band superconductor within the two-component Ginzburg-Landau model. Our analysis explicitly takes into account the relationship between the model…