R-matrix-valued Lax pairs and long-range spin chains

In this paper we discuss $R$-matrix-valued Lax pairs for ${\rm sl}_N$ Calogero-Moser model and their relation to integrable quantum long-range spin chains of the Haldane-Shastry-Inozemtsev type. First, we construct the $R$-matrix-valued Lax pairs for the third flow of the classical Calogero-Moser model. Then we notice that the scalar parts (in the auxiliary space) of the $M$-matrices corresponding to the second and third flows have form of special spin exchange operators. The freezing trick restricts them to quantum Hamiltonians of long-range spin chains. We show that for a special choice of the $R$-matrix these Hamiltonians reproduce those for the Inozemtsev chain. In the general case related to the Baxter's elliptic $R$-matrix we obtain a natural anisotropic extension of the Inozemtsev chain. Commutativity of the Hamiltonians is verified numerically. Trigonometric limits lead to the Haldane-Shastry chains and their anisotropic generalizations.Comment: 12 pages, Introduction added, minor correction

Method of comprehensive assessment of efficiency of decrease of fire and explosion risk of coal suspended particles

Methods and results of experimental study of explosive and wetting characteristics of coal dust are presented. Modified evaluation method of explosive characteristics of coal dust allows estimating critical concentrations of suspended dust at variation of temperature of ionizing ignition source corresponding to beginning of flame propagation by means of approximation method. Method of measuring the contact angle of particles of coal powder is based on visualization of the drop placed on the pressed coal

Development of a Calculation Methodology for the Ventilation on a Besis of a Mobile Unit

An algorithm for the analysis of safety and efficiency of the processes, which are located inside the mobile unit are developed. It follows from the calculations that the safe concentration of combustible material in the space of industrial premises is about 3.69%. Automation systems must be focused on this value. The time of occurrence of the maximum permissible concentration of pollutant was determined and amounted to 160 seconds. It is shown that the ventilation rate of 0.5 would be sufficient for functioning of the object

Carrying out thermodynamic calculations and definition of the main reactions of decomposition of vapours of ethyl alcohol

Thermodynamic opportunities of course of chemical reactions of decomposition of the vapors of ethyl alcohol necessary at development of devices where these reactions will take place are considered. The entalpiyny method of calculation of constants of balance of probable chemical reactions is given in the Excel editor. Independent reactions of process of oxidation are defined. By result of thermodynamic calculation of each reaction schedules of dependence of a constant of balance on environment temperature from which follows are constructed that one reactions proceed until the end of aside formation of the final products, and others are improbable or impossible. The analysis of the received results shows that reactions of oxidation will successfully proceed in the established directions, and for an intensification of process of decomposition it is necessary to provide a supply of some energy which quantity will be sufficient for oxidation of vapors of ethyl alcohol. Results of calculations showed good convergence with programs of thermodynamic calculations like "Aster-4" and "TERRA"

Definition of Time Induction of Self-Ignition of the Substance on the Prognostic Extrapolation Depending on the Basis of Indicators Fire and Explosion Hazard

In this article the research directed on development of a technique of definition of time of induction of the self-ignition of substances and materials which is an indicator of the beginning of development of an emergency is conducted. The experiment consisting in supervision over process of self-ignition of coal and oil deposits was the basis for research. On the basis of experimental data the curve expressing analytic - expected dependence of size of temperature of ignition on induction time was constructed. Proceeding from graphical representation of process, functional dependence of time of induction on a temperature indicator was received: y=16920•x{0.537}. By means of known indicators of such substances as bitumen oil oxidized (the combustible solid substance received by oxidation of residual product of oil refining) and tar oil (the combustible solid substance which is residual product of oil refining) and the received algorithm, verification of reliability of the received dependence and a technique of definition of time of induction of spontaneous ignition of deposits of oil in general was carried out. The practical importance of the conducted research is that having data on time of induction of process of self-ignition, by means of preventive measures becomes possible to avoid and prevent accidents in oil and oil processing branches, at the same time loss of property and loss of human life