Related papers: Effect of randomness and anisotropy on Turing patt…

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks.…

Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…

Latent diffusion models achieve state-of-the-art performance on a variety of generative tasks, such as image synthesis and image editing. However, the robustness of latent diffusion models is not well studied. Previous works only focus on…

We study the effect of anisotropy (strain) on dynamical gap generation in graphene. We work with a low energy effective theory obtained from a tight-binding Hamiltonian expanded around the Dirac points in momentum space. We use a…

Patterns are ubiquitous in nature, but how they form is often unclear. Turing developed a seminal theory to explain patterns based on reactions that counteract the equalizing tendency of diffusion. These reactions require continuous energy…

We study the stability of patterns arising in rotating convection in weakly anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy, either an endogenous characteristic of the system or induced by external forcing, can…

The effect of anisotropy on the statistics of a passive tracer transported by a turbulent flow is investigated. We show that under broad conditions an arbitrarily small amount of anisotropy propagates to the large scales where it eventually…

Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…

Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…

A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…

Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and…

A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection. The effects of asymmetric…

Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…

We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to…

We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…

A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…

Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the…

Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…

We explore the influence of density fluctuations on isotropic and anisotropic configurations, extending the concept of cracking for general relativistic fluid spheres. This concept, conceived to describe the behaviour of anisotropic matter…