Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao

Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity does not violate the Second Law

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, "excitable" systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems.Comment: 11 pages, 2 figures, as accepted to Scientific Reports on 2016/07/0

Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example

We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the ``taxis'', represented by nonlinear ``cross-diffusion'' terms in the mathematical formulation. We have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms, ``parabolic'' and ``linear''. Transition from one form to the other correlates with changes in the shape of the wave profile. Dependence of the propagation velocity on diffusion in this system differs from the square-root dependence typical of reaction-diffusion waves. We demonstrate also that, for systems with negative and positive taxis, for example, pursuit and evasion, there typically exists a large region in the parameter space, where the waves demonstrate quasisoliton interaction: colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries.Comment: 15 pages, 18 figures, submitted to Physica

Envelope quasisolitons in dissipative systems with cross-diffusion

Copyright © 2011 American Physical SocietyJournal ArticleWe consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasisoliton" pulses, which have a fixed stable structure but can reflect from boundaries and penetrate each other. Herein we demonstrate a different type of quasisolitons, with a phenomenology resembling that of the envelope solitons in the nonlinear Schrödinger equation: spatiotemporal oscillations with a smooth envelope, with the velocity of the oscillations different from the velocity of the envelope

Classification of wave regimes in excitable systems with linear cross diffusion

Copyright © 2014 American Physical SocietyWe consider principal properties of various wave regimes in two selected excitable systems with linear cross diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope waves, multienvelope waves, and intermediate regimes appearing as waves propagating at a fixed shape most of the time but undergoing restructuring from time to time. Depending on parameters, most of these regimes can be with and without the "quasisoliton" property of reflection of boundaries and penetration through each other. We also present some examples of the behavior of envelope quasisolitons in two spatial dimensions.Russian Foundation for Basic Research (RFBR

DESIGN AND TECHNOLOGICAL PROPOSALS FOR IMPROVING A SINGLE-PHASE TRANSFORMER WITH LAMINATED MAGNETIC CORE

Goal. The purpose of the work is to analyze the features and substantiate the advantages of the spatial radial electromagnetic system of a single-phase transformer with rectangular sections of the rods of a charged magnetic circuit. Methodology. Improvement of single-phase transformers is possible by structural-geometric transformations of active elements. The justification of the advantages of such transformations is achieved by the method of invariant objective functions with dimensionless optimization components and universal relative controlled variables. Results. Replacing the rectangular contours of the variants of a planar magnetic circuit with a hexagonal circuit leads to a decrease in the volume of steel and the loss of three angular zones of changes in the direction of the magnetic flux relative to the texture compared to planar counterparts. The separation of the windings into sections with an arrangement on three rods leads to a decrease in the average length of the coil. Originality. A three-core magnetic core can consist of rod and jugular-angular parallelogram plates of anisotropic and isotropic electrical steel. It is advisable to combine a combination of steels by integral welding of billets with subsequent separation into chevron jugular-rod elements. The method called on has developed mathematical models of the mass, cost, and active power losses of variants of a single-phase electromagnetic system of a transformer with rod and armor planar and spatial radial three-core magnetic cores. Practical significance. It was found that the decrease in the extrema of the mass and cost indicators, as well as the calculated decrease, under the condition that the coefficients of additional losses are identical, the extrema of the losses of the single-phase radial three-rod system of the transformer relative to the planar analogue with a bar stocked magnetic wire from anisotropic steel, respectively 13,0-12,3 %, 15,3-10,1 % and 15,1-18,1 % with copper windings and 10,8-10,2 %, 12,8-13,7 % and 12,6-12,3 % with aluminum windings. The main indicators of traditional single-phase systems with rod and armored magnetic circuits differ insignificantly, which is consistent with early known optimization and calculation data of transformers

Target and (Astro-)WISE technologies - Data federations and its applications

After its first implementation in 2003 the Astro-WISE technology has been rolled out in several European countries and is used for the production of the KiDS survey data. In the multi-disciplinary Target initiative this technology, nicknamed WISE technology, has been further applied to a large number of projects. Here, we highlight the data handling of other astronomical applications, such as VLT-MUSE and LOFAR, together with some non-astronomical applications such as the medical projects Lifelines and GLIMPS, the MONK handwritten text recognition system, and business applications, by amongst others, the Target Holding. We describe some of the most important lessons learned and describe the application of the data-centric WISE type of approach to the Science Ground Segment of the Euclid satellite.Comment: 9 pages, 5 figures, Proceedngs IAU Symposium No 325 Astroinformatics 201