Computer simulations of three-dimensional Turing patterns in the Lengyel-Epstein model

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction-diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reaction†"diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system's diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants.

Reaction-Diffusion Pathways for a Programmable Nanoscale Texture of the Diamond-SiC Composite

The diamond-SiC composite has a low density and the highest possible speed of sound among existing materials except for diamond. The composite is synthesized by a complex exothermic chemical reaction between diamond powder and liquid Si. This makes it an ideal material for protection against impact loading. Experiments show that a system of patterns is formed at the diamond-SiC interface. Modeling of reaction-diffusion processes of composite synthesis proves a formation of ceramic materials with a regular (periodic) interconnected microstructure in a given system. The composite material with interconnected structures at the interface has very high mechanical properties and resistance to impact since its fractioning is intercrystallite.

Three-dimensional chimera patterns in networks of spiking neuron oscillators

We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.