"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

A generalised Landau-Lifshitz equation for isotropic SU(3) magnet

In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We use the generalized Heisenberg Hamiltonian with biquadratic exchange as a quantum model. A quantum thermodynamical averaging gives classical effective models, which are interpreted as Hamiltonian systems on coadjoint orbits of Lie group SU(3).Comment: 15 pages, 1 figur

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

Modeling of Metallurgical Process of Copper Fire Refining

The refining of blister copper is based on the partial removal of impurities that have an increased affinity for oxygen. The most interesting is the process of centralized copper refining at one plant. This is because blister copper from the producer plants has a different chemical composition. Obviously, the batch of each loading also has a variable chemical composition. Therefore, for a constantly changing averageweighted composition of a liquid metal, a different amount of oxygen is required to oxidize and slag the impurities. The aim of the work is the method of creating a mathematical model for solving the single-criterion and multicriteria task of firerefining of copper. Algorithms of the model based on the passive experiment are presented, with the chosen assumptions and limitations. Mathematical models are developed using correlation regression analysis. The resultant variable in the models is the concentration of oxygen in the melt. The objective function is determined by the main variables of the refining process. The results of mathematical modeling allow us to quickly calculate the concentration of oxygen supplied in the air composition into the melt of a batch of different chemical composition for the oxidation of impurities. The models are consistent with the general theory of anode melting, and can be used to control and predict the process. Keywords: fire refining, blister copper, impurity oxidation, mathematical model, linear regressio

Дослідження шляхів зниження професійного ризику серед механізаторів в АПК

The problem of reducing occupational risk in agriculture is extremely complex and at present not found a universal way to solve it. Reduction of occupational risk should be considered as a major component part of occupational safety as one of the most important functions of state authorities and business entities. Current trends in the growth of professional (production) risks in agriculture necessitated the development of an industry-wide system assessment and the introduction of modern methods of management of labour safety. One of the priority areas reducing the number of accidents at production is increased attention to the prevention of accidents and occupational diseases on the basis of existing production of dangerous and harmful factors, there are certain risks of injury and health loss. Modern scientific and methodological approaches and experiences of developed countries show that an effective model of protecting workers from negative (threat) impact the production environment should be based on occupational risk management. Implementation of quantitative methods for the assessment of occupational risks is one of the strategic directions achievements in the state acceptable level of safety, environmental and industrial objects. In the conditions of modern agricultural production is a complex probabilistic system, in which, as a rule, there is an unresolved danger that is inherent through participation in the process of a man with his emotional, physiological and psychological weakness, there is always the risk of an accident. In the traditional tasks of labour protection are investigating the actions of the employee as a potential source of danger because of his wrong actions, ignorance of safe methods of work. However, the technical security will play a critical role in solving problems of complex reduce the risk of injury to the mechanized processes of agriculture, that allows to consider this problem as a new and up to date.Проблема зниження професійного ризику в сільському господарстві є надзвичайно складною, і в даний час не знайдено універсального способу її вирішення. Зниження професійного ризику потрібно розглядати як основну складову частину охорони праці, як одну з найважливіших функцій органів державної влади та суб`єктів господарювання. Сучасні тенденції зростання професійних (виробничих) ризиків у сільському господарстві обумовлюють необхідність розвитку єдиної галузевої системи їх оцінки  і впровадження сучасних методів управління безпекою праці. Одним із пріоритетних напрямів зниження кількості нещасних випадків на виробництві є посилення уваги до профілактики нещасних випадків та професійних захворювань на основі врахування наявних виробничих небезпечних та шкідливих чинників, тобто визначених ризиків травмування та втрати здоров’я. Сучасні науково-методологічні підходи та досвід розвинених країн свідчать, що ефективна модель захисту працівників від несприятливої (небезпечної) дії виробничого довкілля має спиратися на управління професійними ризиками. Запровадження кількісних методів оцінки професійних ризиків є одним із стратегічних напрямів досягнення у державі прийнятного рівня безпеки праці, природного довкілля та виробничих об`єктів. За умов сучасного аграрного виробництва – складної ймовірнісної системи, в якій, зазвичай, присутня потенційна небезпека, що закладена через участь у технологічному процесі людини з її емоційною, фізіологічною і психологічною слабкістю, завжди існує ризик нещасного випадку. У традиційних завданнях охорони праці досліджують дії працівника, як потенційного джерела небезпеки через його помилкові дії, незнання ним безпечних способів виконання робіт. Разом з тим, технічні засоби безпеки праці мають відігравати вирішальну роль у розв’язанні проблеми комплексного зниження ризику травмування на механізованих процесах АПК, що  дозволяє розглядати дане завдання як нове і актуальне

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

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

Dressing Technique for Intermediate Hierarchies

A generalized AKNS systems introduced and discussed recently in \cite{dGHM} are considered. It was shown that the dressing technique both in matrix pseudo-differential operators and formal series with respect to the spectral parameter can be developed for these hierarchies.Comment: 16 pages, LaTeX Report/no: DFTUZ/94/2