Related papers: Stability of hexagonal solidification patterns
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic…
We use the Dynamic Density-Functional Formalism and the Fundamental Measure Theory as applied to a fluid of parallel hard squares to study the dynamics of heterogeneous growth of non-uniform phases with columnar and crystalline symmetries.…
Mathematical models for physiological processes aid qualitative understanding of the impact of various parameters on the underlying process. We analyse two such models for human physiological processes: the Mackey-Glass and the Lasota…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This class of models…
The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's…
Beginning from a relatively simple set of dynamical equations for a fluid permeated by a radiative field strong enough to produce significant forces, we find the structure of plane-parallel equilibria and study their stability to small…
We study the robustness and stability of the yeast cell regulatory network by using a general inhomogeneous discrete model. We find that inhomogeneity, on average, enhances the stability of the biggest attractor of the dynamics and that the…
We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case has been treated comprehensively by Amari 30 years ago, two-dimensional neural…
A combination of analytical and numerical techniques are used to efficiently determine the qualitative and quantitative behaviour of a one-basin zonally averaged thermohaline circulation ocean model. In contrast to earlier studies which use…
We consider a cellular monolayer, described using a vertex-based model, for which cells form a spatially disordered array of convex polygons that tile the plane. Equilibrium cell configurations are assumed to minimize a global energy…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…
We discuss the geometric phases and flux densities for the metastable states of hydrogen with principal quantum number n=2 being subjected to adiabatically varying external electric and magnetic fields. Convenient representations of the…
We analyse metastable states in the East model, using a recently-proposed patch-repetition analysis based on time-averaged density profiles. The results reveal a hierarchy of states of varying lifetimes, consistent with previous studies in…
Solid-solid phase transitions are ubiquitous in nature, but the kinetic pathway of anisotropic particle systems remains elusive, where the coupling between translational and rotational motions plays a critical role in various kinetic…
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that…
This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…