On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page

Enhanced Preconditioner for JOREK MHD Solver

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation code for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. Due to the large scale-separation intrinsic to these phenomena both in space and time, the computational costs for simulations in realistic geometry and with realistic parameters can be very high, motivating the investment of considerable effort for optimization. In this article, a set of developments regarding the JOREK solver and preconditioner is described, which lead to overall significant benefits for large production simulations. This comprises in particular enhanced convergence in highly non-linear scenarios and a general reduction of memory consumption and computational costs. The developments include faster construction of preconditioner matrices, a domain decomposition of preconditioning matrices for solver libraries that can handle distributed matrices, interfaces for additional solver libraries, an option to use matrix compression methods, and the implementation of a complex solver interface for the preconditioner. The most significant development presented consists in a generalization of the physics based preconditioner to "mode groups", which allows to account for the dominant interactions between toroidal Fourier modes in highly non-linear simulations. At the cost of a moderate increase of memory consumption, the technique can strongly enhance convergence in suitable cases allowing to use significantly larger time steps. For all developments, benchmarks based on typical simulation cases demonstrate the resulting improvements

The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation

Topological excitations in 2D spin system with high spin s>=1s>= 1

We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the continuous classical analogue) that is based on a Landau-Lifshitz like equation, and describes large-scale fluctuations of the mean field. On the other hand, the classical model is a Hamiltonian system on a coadjoint orbit of the unitary group SU($2s {+} 1$) in the case of spin $s$. We have found a class of mean field configurations that can be interpreted as topological excitations, because they have fixed topological charges. Such excitations change their shapes and grow preserving an energy.Comment: 10 pages, 1 figur

OPPORTUNITY TO OPTIMIZE THE PARAMETERS OF AERODYNAMIC CHARACTERISTICS BY THE METHOD OF MATHEMATICAL MODELING

В данной работе получены оптимальные значения параметров для проектируемой вентиляционной сети шахты ГОКа Уральского региона. С целью эффективного использования вентиляторной установки в системе проветривания шахты решена оптимизационная задача с использованием данных полной аэродинамической характеристики. Представлены рекомендации для проектирования вентиляторной установки.In this work, the optimal values of the parameters for the designed ventilation network of the mine of the GOK of the Ural region are obtained. In order to efficiently use the fan unit in the mine ventilation system, the optimization problem has been solved using the data of the full aerodynamic characteristic. Recommendations for designing a fan unit are presented

The Vacuum Structure, Special Relativity and Quantum Mechanics Revisited: a Field Theory No-Geometry Approach within the Lagrangian and Hamiltonian Formalisms. Part 2

The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is devoted to studying the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of \cite{BPT,BRT1}. Based on the vacuum field theory no-geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. Within an approach developed a possibility of the combined description both of electrodynamics and gravity is analyzed.Comment: 11 page

OPTIMIZATION OF TECHNOLOGICAL PARAMETERS OF METALLURGICAL PROCESSES BY THE METHOD OF SIMULATION

In this work, statistical indicators are obtained that characterize the optimal values of the parameters of the concentrate smelting process in the Vanyukov furnaces. Recommendations for the analysis of the technological process are presented.работе получены статистические показатели, характеризующие оптимальные значения параметров процесса плавки концентрата в печах Ванюкова. Представлены рекомендации для анализа технологического процесса

Теорія та практика менеджменту безпеки

У збірнику подано тези доповідей та виступів учасників Міжнародної науково-практичної конференції, присвяченої питанням теорії менеджменту безпеки, безпеки особистості, прикладним аспектам забезпечення соціальної, екологічної, економічної безпеки підприємств, питанням механізму забезпечення соціоекологоекономічної безпеки регіону, проблемам забезпечення національної безпеки

Islamic pottery from Jerba (7th-10th century). Aspects of contiuity?

The aim of this paper is to discuss some aspects of the ceramic evidence discovered during the Jerba Survey Project (1995-2000). The project, directed by Ali Drine of the \u201cInstitut National du Patrimoine\u201d, Elizabeth Fentress of the American Academy of Rome and Renata Holod of the University of Pennsylvania, was aimed not only at the understanding of the history of settlement on the island, but also at recuperating the archaeological evidence that has been disappearing steadily under the impact of increased tourism and urban development over the last twenty-five years. Through this project, Jerba\u2019s archaeological past has thus been recorded, at least in part. The pottery described here derives both from the field survey and from limited test trenches conducted at Roman, late antique and early medieval period sites identified on the island . In this paper we will review the data concerning the periods from the Vandal occupation of the island beginning in the middle of the sixth century through what we have called the early medieval period (also known as the early Islamic period), ending in the first half of the eleventh century