Waves in the Skyrme--Faddeev model and integrable reductions

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation of periodic wave states, leading to a quasi-linear system. The reduction to general hydrodynamic systems have been considered and it is compared with other integrable reductions of the system.Comment: 16 pages, 5 figure

Wave Instabilities in Excitable Media with Fast Inhibitor Diffusion

An excitable activator-inhibitor system with relatively fast inhibitor diffusion is considered. Numerical simulations of wave propagation inside long channels show transitions from stable flat traveling waves to folded waves and further to spreading spiral turbulence as the inhibitor diffusivity is increased. For sufficiently narrow channels the suppression of turbulence and the development of regular steadily propagating patterns is observed. The curvature dependence of the wave propagation velocity is derived and used to interpret the observed phenomena

Controlling Spiral Waves in Confined Geometries by Global Feedback

The evolution of spiral waves on a circular domain and on a spherical surface is studied by numerical integration of a reaction-diffusion system with a global feedback. It is shown that depending on intensity, sign, and/or time delay in the feedback loop a global coupling can be effectively used either to stabilize the rigid rotation of a spiral wave or to completely destroy spiral waves and to suppress self-sustained activity in a confined domain of an excitable medium. An explanation of the numerically observed effects is produced by a kinematical model of spiral wave propagation

A normal form for excitable media

We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao

Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2

Research of Wheat Drying in a Microwave and Combined Filter-microwave Dryer

The aim of the conducted study is to determine kinetics of the complex effect of microwave energy supply and filter drying of the process of water release from the wheat layer. There is offered a combination of MW and filter drying. A special feature of this combination must be its more effectiveness and high speed of water elimination from surface layers of wet seeds and, as a result, the productivity increase of the drying way, decrease of specific energy consumption.There was determined the influence of the specific load of the material, radiator power on processes of microwave and filter-microwave drying of wheat seeds. There were compared microwave, filter-microwave and convective drying of seeds by parameters of specific energy consumption, drying speed.The specific energy consumption at microwave drying of seeds was 4 MJ/kg, at filter-microwave drying 3.8 MJ/kg that is lower than existent convective dryers. The speed of microwave drying changes from 0,5 to 3 %/min, filter-microwave – from 0.3 to 0.7 %/min. The speed is at the level of standard convective dryers.The conducted studies allow to recommend a new combined way of FMW drying of seeds with low energy consumption.Revealed features of heating and drying are possible to be used at developing industrial dryers.The base of experimental data is possible to be used for optimizing and determining effective conditions of MW and FMW drying

Existence of a rotating wave pattern in a disk for a wave front interaction model

[[abstract]]We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front and wave back respectively. Using a delicate shooting argument with the help of the comparison principle, we derive the existence and uniqueness of rotating wave patterns for any admissible angular speed with convex front in a given disk.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

Studying laser radiation effect on steel structure and properties

There was studied the effect of laser radiation on the structure and properties of annealed and tempered steel with different content of carbon. For surface hardening there was used a laser complex equipped with Nd: YAG pulse laser with power density up to 30 kW/сm2. As a result of the carried-out studies there were calculated characteristics of laser, steel microstructure and properties