Related papers: Dimensionality effects in Turing pattern formation
In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
The Thirring model and various generalizations of it are analyzed in detail. The four-Fermi interaction modifies the equation of state. Chemical potentials and twisted boundary conditions both result in complex fermionic determinants which…
We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…
We discuss different approaches for studying the influence of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalisation group calculations provide quite accurate results. Experiments carried out on…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
We propose here a geometric and topological setting for the study of branching effects arising in various fields of research, e.g. in statistical mechanics and turbulence theory. We describe various aspects that appear key points to us, and…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics…
We study both analytically and numerically how the electronic structure and the transport properties of a two-dimensional disordered system are modified in the presence of resonances. The energy dependence of the density of states and the…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
Traditionally the effects of MHD instabilities and micro-instabilities on plasma confinement are investigated separately. However, these two instabilities often occur simultaneously, with the overlap of the dynamics on a broad range of…
A class of peridynamic material models known as constitutive correspondence models provide a bridge between classical continuum mechanics and peridynamics. These models are useful because they allow well-established local constitutive…