Related papers: Field Patterns: A New Mathematical Object
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
A supersymmetric theory with several scalar superfields generically has several domain wall type classical configurations which interpolate between various supersymmetric vacua of the scalar fields. Depending on the couplings, some of these…
Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical and biological media and to macro-scale vegetation and cloud patterns. Their…
The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…
The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…
Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
Field theories compactified on non-simply connected spaces, which in general allow to impose twisted boundary conditions, are found to unexpectedly have a rich phase structure. One of characteristic features of such theories is the…
We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Speckle patterns are inherent features of coherent light propagation through complex media. As a result of interference, they are sensitive to multiple experimental parameters such as the configuration of disorder or the propagating…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the…
We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…