Lotka--Volterra Type Equations and their Explicit Integration

In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar $A_n$ case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of $A_r$, $B_r$, $C_r$, and $G_2$ on the same footing.Comment: 3 pages LATEX fil

Ultra-relativistic electrostatic Bernstein waves

A new general form of the dispersion relation for electrostatic Bernstein waves in ultra-relativistic pair plasmas, characterized by a−1 = kBT/(mec2)  1, is derived in this paper. The parameter Sp = aΩ0/ωp, where Ω0 is the rest cyclotron frequency for electrons or positrons and ωp is the electron (or positron) plasma frequency, plays a crucial role in characterizing these waves. In particular, Sp has a restricted range for permitted wave solutions; this range is effectively unlimited for classical plasmas, but is significant for the ultra-relativistic case. The characterization of these waves is applied in particular to the presence of such plasmas in pulsar atmospheres

Novel kinetic consistent mhd algorithm for high performance computing

The impressive progress of the kinetic schemes in the solution of gas dy- namics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods for the solution of the magnetohydrodynamics problem in the important area of plasma physics. The novel feature of the method is the formulation of the complex Boltzmann- like distribution function of kinetic method with the implementation of electromagnetic interaction terms. The numerical method is based on the explicit schemes. Due to logical simplicity and its efficiency, the algorithm is easily adapted to modern high performance parallel computer systems including hybrid computing systems with graphic processors

Statistical distribution function of charged particles in magnetic field

The statistical distribution function introduced by Boltzmann and his ki- netic equation are the fundamental basis of the kinetic theory of gases and of the basic methods of solution of problems in the gas dynamics. At present time one of the areas of high interest in modern physics is the plasma in fusion processes and astrophysics which requires an extension of the kinetic processes to charged particles, in particular regard- ing the electromagnetic interactions. We propose a unified distribution function which includes the electromagnetic interactions for charged particles and is suitable for the solu- tion of problems of charged particle dynamics with Boltzmann type equations and kinetic consistent magneto gas dynamic equations

Novel kinetic consistent algorithm for the modeling of incompressible conducting flows

In this study we aim at demonstrating that kinetic consistent magneto gas dynamic algorithms are a valid for the computation of the dynamics of incompressible conductive flows. We obtain numerical solutions for the test problems, namely the laminar flow inside a wall-driven cavity and a magnetic driven pump. We show that kinetic consistent algorithms have a high stability in the solution of convection-dominated flows, due to a correct physical modeling of the fluid viscosity and to the possibility of tuning appropriate regularization terms on the basis of the physical properties of the fluid. We show that the kinetic consistent approach offers a stable basis for a correct physical description of the shear viscosity, thermal conduction and electric resistivity effects in incompressible magneto hydrodynamics flows

WW--geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Pl\"ucker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding K\"ahler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Pl\"ucker embedding. These conditions are automatically fulfiled when Toda equations hold.Comment: 30 pages, no figur

Topological gravity on plumbed V-cobordisms

An ensemble of cosmological models based on generalized BF-theory is constructed where the role of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed V-cobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460Comment: 29 page

Multidimensional Toda type systems

On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.Comment: 29 pages, LaTeX fil

Use of Vanadium for Low-alloy Steel Manufacturing at JSC “EVRAZ NTMK”

Joint Stock Company “EVRAZ Nizhniy Tagil Metallurgical Plant” ( JSC “EVRAZ NTMK”) is the World’s largest processor of vanadium-rich titanium magnetite ores. This work describes the results of the research performed to test various combinations of vanadium and nitrogen microalloying targeted at repeatable quality and strength properties of the rolled steel products. In particular the benefits are described of using vanadium mass fractions in steel for manufacturing railway steel (rails, wheels, rings/tires), railcar body products (Z-beams, I-beams, etc.), API grades including large diameter X70 and X80 pipes. To optimize the analysis of different steel grades for the shaped sections manufacturing EVRAZ NTMK has taken efforts to identify the impact of the vanadium mass fraction in steel grade 09G2S on the mechanical properties of rolled steel with the elements of various thickness. During the effort, the mechanical tests were performed, the extent of vanadium reduction in the form of carbonitrides during the rolling and cooling process and its impact on the mechanical properties, the macrostructuring of rolled products was also studied. Recommendations were given on the chemical composition of steel 09G2S for manufacturing rolled steel of strength classes 375 and 390. Keywords: EVRAZ NTMK, vanadium, I-beams, mechanical properties, impact strengt

Frameworks for Formation and Stability of Kurgan Regional Arboretum Phytocenosis

The article is devoted to solving the problem of biodiversity conservation in the framework of increasing sustainability of natural plant communities in arboretum being an artificial protected area. Research and application have accumulated significant knowledge on various aspects of the above problem, specifically, preserving biodiversity including vegetation, monitoring biodiversity and preserving phytocenosis, plant interaction in phytocenosis, causes of disturbed biodiversity and reducing phytocenosis stability, etc. The research objective is to theorize the frameworks for phytocenosis formation, identify the factors influencing phytocenosis stability, conduct observations and experimental research on the factors affecting the formation and stability of the Kurgan regional arboretum phytocenosis. The models of the way different factors influence the resistance mechanisms of the Kurgan regional arboretum phytocenosis are built as a result of studying research materials and differ from the theoretical model in the fact that the proven distinctions were found in the ratio of limiting and background factors reflecting their regional character