In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration proles of passive tracers in a two-dimensional shear ow. It is shown that a time-periodic concentration pro le exists for time-periodic external source, while for random source, the distribution functions of all concentration pro les weakly converge to a unique ...

Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer-resource interactions, localized disturbance-recovery processes and scale-dependent feedback. Despite abundant theoretical literature, studies revealing spatial self-organization in real ecosystems are limited. Rec...

In our previous work, we have studied the pattern formation during the electropolishing of both isotropic and anisotropic materials. Both models predict stable hexagonal and striped patterns and are in qualitative agreement with experiments. In this paper, we study the smallscale pattern size control during electropolishing. Our study shows that applied voltage, surface diffusion and surface de...

1 Introduction Diffusion-controlled growth of metal nanostructures and thin films on metallic and insulating substrates is important from both theoretical and practical points of view, including many technological applications, such as catalysis and microelectronics. Theory is challenged to describe two modes of thin film growth: monolayer-by-monolayer regime or 3D metal cluster formation [1]. ...

u(x, /) is an n vector which defines the state of the system at a given point x at time /. The nonlinear function F describes the "kinetics" of the medium while the diffusion effects enter via the term AAu. A is a diagonal matrix with nonnegative entries and A is the Laplace operator in the appropriate number of space dimensions, in this paper one or two. In a spatially homogeneous configuratio...

The vertebrate skull is anatomically complex and phylogenetically diverse; it presents unique opportunities to examine the role of developmental processes in evolutionary change. Previous studies have largely examined phylogenetic trends in tissue composition or change in the timing of developmental events (heterochrony). Additional important insights may be gained if skull evolution and develo...

The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable env...

In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a u...

In the preface we present a short overview of articles included in the issue “Bifurcations and pattern formation in biological applications” of the journal Mathematical Modelling of Natural Phenomena.