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

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

Conjugacy of two types of phenotypic variability of small-leaved linden

The properties of five bilaterally symmetrical features of the leaf blades of the small-leaved linden (Tilia cordata Mill.) in four populations of the Moscow Region in 2014–2017 were studied. The angle trait was excluded, because it possessed the property of directional asymmetry. Instead, a new linear trait was used: the distance between the base of the second vein of the first order and the base of the first vein of the second order on the first vein of the first order. The population difference in fluctuating asymmetry (FA) was found only in the first two traits (leaf width and distance between the bases of the first vein of the first order and the second vein of the second order). The largest value of FA was in the urban environment, the smallest was in the rural areas. A weak negative correlation was obtained between the magnitude of linear characteristics and the value of FA, as well as a weak positive correlation relationship between the values of FA in five traits. The first trait had the highest fluctuation variability, and the second one had the highest plastic variability. The regression dependence of the fluctuation variability on the plastic variability (b1 = 0.25, p <0.05) and the dependence of these two types of variability on the interaction of the factors “year” and “site of sampling” were revealed. Thus, the conclusion was made about the conjugacy of two types of variability: fluctuation and plastic. According to the authors, asynchronous growth, competition for light in conditions of high solar activity in 2014–2016 compared to the abnormal wet summer of 2017 led to an increase in FA due to destabilization of mechanisms of growth and regulation of gene expression, which contributed to a decrease in the stability of development. The increase in FA and the decrease in the developmental stability in urban ambient in 2016 could be due to: a)an intensive flow of vehicles in spring and summer, b) a high level of groundwater in this part of the city and c) increased hydrolytic acidity of the soil

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.Comment: 22 pages, 3 figures, 2 table

Diffusion-induced vortex filament instability in 3-dimensional excitable media

We studied the stability of linear vortex filaments in 3-dimensional (3D) excitable media, using both analytical and numerical methods. We found an intrinsic 3D instability of vortex filaments that is diffusion-induced, and is due to the slower diffusion of the inhibitor. This instability can result either in a single helical filament or in chaotic scroll breakup, depending on the specific kinetic model. When the 2-dimensional dynamics were in the chaotic regime, filament instability occurred via on-off intermittency, a failure of chaos synchronization in the third dimension.Comment: 5 pages, 5 figures, to appear in PRL (September, 1999

Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure

Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wavefront slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including: (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three-dimensions, and spatial or/and time-dependent variation of excitability), and (iv) the dynamics of multi-armed spiral waves with the new prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHug-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semi-quantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models

Investigation the impact of a laser on the chernov-luders lines in the 40X9C2 steel

The study presents investigation results of the hardening points impact, created on the model surface by means of a laser complex. The authors investigated the change in the steel microhardness in the area which is treated with laser processing and presented the model of stress-strain diagram. The article reveals a change in the yield point and the plasticity of the models as a result. The authors made a number of speckle photos showing the Chernov-Luders lines behavior