Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model

Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton interaction I show that the train propagation of N well separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalised (non-integrable) complex Toda chain is derived for description of the train propagation of well separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.Comment: RevTex, 23 pages, no figures. Submitted to Physical Review

Этапы управления малым предприятием

Proceeding from practical experience of management complemented by study of foreign and domestic experience, the authors offer to improve a control system, having allocated three basic stages of management of the small enterprise. The offered model of management will help to formalize process of management of the small enterprise, and, hence to raise(increase) efficiency of activity of the enterprise.Исходя из зарубежного и отечественного практического опыта управления авторы предлагают совершенствовать систему управления, выделив три этапа управления малым предприятием. Предлагаемая модель управления поможет формализовать процесс управления малым предприятием, а следовательно, повысить эффективность деятельности предприятия

Особенности стратегического управления малым предприятием

The feature of strategic management at the small enterprise consists in the contents of business strategy. From set of possible (probable) business strategy the small enterprises for the essence successfully can adhere only to adaptive strategy. The adaptive strategy should develop on the basis of association of industrial operations in uniform business-processes. Though in modern researches such concepts are widely used, as the reorganization and re-structuring, but, in opinion of the authors, orientation of processes of transformations to structures of the enterprise separate operations and tasks, instead of on business-process is traditional, most widespread mistake.Особенность стратегического управления на малом предприятии заключается в содержании самих деловых стратегий. Из множества возможных деловых стратегий малые предприятия по своей сущности успешно могут придерживаться только адаптивных стратегий. Адаптивные стратегии должны развиваться на основе объединения производственных операций в единые бизнес-процессы. Хотя в современных исследованиях широко используются такие понятия, как реорганизация и реструктуризация, но, по мнению авторов, ориентация процессов преобразований на структуры предприятия, отдельные операции и задачи, а не на бизнес-процесс является традиционной, наиболее распространенной ошибкой

Early Stages of Homopolymer Collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this Paper a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages respectively scale as the zeroth, 1/5 and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure

Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map : Mechanisms and their characterizations

A simple quasiperiodically forced one-dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors (SNAs) with reference to a two-parameter $(A-f)$ space. The routes include transitions to chaos via SNAs from both one frequency torus and period doubled torus. In the former case, we identify the fractalization and type I intermittency routes. In the latter case, we point out that atleast four distinct routes through which the truncation of torus doubling bifurcation and the birth of SNAs take place in this model. In particular, the formation of SNAs through Heagy-Hammel, fractalization and type--III intermittent mechanisms are described. In addition, it has been found that in this system there are some regions in the parameter space where a novel dynamics involving a sudden expansion of the attractor which tames the growth of period-doubling bifurcation takes place, giving birth to SNA. The SNAs created through different mechanisms are characterized by the behaviour of the Lyapunov exponents and their variance, by the estimation of phase sensitivity exponent as well as through the distribution of finite-time Lyapunov exponents.Comment: 27 pages, RevTeX 4, 16 EPS figures. Phys. Rev. E (2001) to appea

Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure

Many heads but one brain: FusionBrain – a single multimodal multitask architecture and a competition

Supporting the current trend in the AI community, we present the AI Journey 2021 Challenge called FusionBrain, the first competition which is targeted to make a universal architecture which could process different modalities (in this case, images, texts, and code) and solve multiple tasks for vision and language. The FusionBrain Challenge combines the following specific tasks: Code2code Translation, Handwritten Text recognition, Zero-shot Object Detection, and Visual Question Answering. We have created datasets for each task to test the participants’ submissions on it. Moreover, we have collected and made publicly available a new handwritten dataset in both English and Russian, which consists of 94,128 pairs of images and texts. We also propose a multimodal and multitask architecture – a baseline solution, in the centre of which is a frozen foundation model and which has been trained in Fusion mode along with Single-task mode. The proposed Fusion approach proves to be competitive and more energy-efficient compared to the task-specific one.We would like to thank Sber and SberCloud for granting the GPU-resources to us to experiment with different architectures and also to the participants to train their models, and for supporting the FusionBrain Challenge in general

Plasma heating and confinementat the GOL-3-II facility

Results of experiments on plasma heating and confinement in multimirror open trap GOL-3-II are presented. This facility is intended for heating and confinement of a relatively dense (10¹⁵-10¹⁷ cm⁻³) plasma in axially-symmetrical magnetic system. The plasma heating is provided by a high-power electron beam (1 MeV, 30 kA, 8 µs, 200 kJ). Results of the experiments with multimirror configuration of the device indicate that the confinement time of the plasma with ne ~ (0,5÷5).10¹⁵ cm⁻³ and Te ~1 keV increases more than order of magnitude in comparison with single mirror device

Spiral anchoring in anisotropic media with multiple inhomogeneities: a dynamical system approach

Various PDE models have been suggested in order to explain and predict the dynamics of spiral waves in excitable media. In two landmark papers, Barkley noticed that some of the behaviour could be explained by the inherent Euclidean symmetry of these models. LeBlanc and Wulff then introduced forced Euclidean symmetry-breaking (FESB) to the analysis, in the form of individual translational symmetry-breaking (TSB) perturbations and rotational symmetry-breaking (RSB) perturbations; in either case, it is shown that spiral anchoring is a direct consequence of the FESB. In this article, we provide a characterization of spiral anchoring when two perturbations, a TSB term and a RSB term, are combined, where the TSB term is centered at the origin and the RSB term preserves rotations by multiples of $\frac{2\pi}{\jmath^*}$, where $\jmath^*\geq 1$ is an integer. When $\jmath^*>1$ (such as in a modified bidomain model), it is shown that spirals anchor at the origin, but when $\jmath^* =1$ (such as in a planar reaction-diffusion-advection system), spirals generically anchor away from the origin.Comment: Revised versio

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure