An approach for modeling of multiphase flows as random processes

The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation equations for mass, momentum and energy are obtained under the assumption that parameters of the interacting phases are players of the statistical process. In parallel, dynamical system by the Kolmogorov's theorem for two states of a statistical system (phases of a two-phase mixture) is considered. Probability of phases in a flow is taken further for comparison with the probability and parameters of a two-phase flow from the equations of flow dynamics. Analysis of the parameters of a two-phase flow is performed as relating to available flow regimes from a statistical point of view on the basis of achievable parameter values and, first of all, on the condition that the probability is strictly in the range from 0 to 1. Correspondence of parameters by the equation array for flow dynamics and by solution of the dynamical system of two phases (two interacting statistical states) revealed the values of the coefficients for dynamical system, expressed in terms of the flow parameters. The results obtained are intended for further discussion, research, comparison with experimental data and with results of other researchers of the multiphase flows.Comment: 12 pages, 18 references. arXiv admin note: text overlap with arXiv:1510.0698

Controlled Film Flow in Granulation of Metals for the Development of Amorphous Superhard and Functionally Unique New Materials

The problem of granulation is very bright by the granulated materials, as well as by their application. In the paper, some history of the granulation problem during over century and modern applications of the metallic granulates and amorphous materials are given at the beginning. Then the specific own granulation problem is presented, which has concern to the controlled liquid metal jet and film flows for a production of the uniform by size and form particles (granules) cooled with a high rate, to be amorphous or close to the amorphous materials. Such granules of the given size and form are needed for the new material science. The basics of developed theory of the controlled jet and film flow disintegration with further rapid cooling of the drops obtained after flow disintegration are presented together with the new patented granulation devices. The developed methods and devices can be used for production of the amorphous or close to amorphous granules in a wide range of the given sizes, with very narrow (plus-minus 50% deviation of size from the average one).Comment: 19 pages, 11 figures, 57 reference

Particle cooling in Vaporizing Coolant

The approximate mathematical model for a cooling of the particle in a volatile liquid is developed and analyzed. Despite the precise model is complex and requires the solution of the nonstationary two-phase flow equations with the conjugated heat transfer boundary problem for the particle, vapor, and liquid cooling pool, the considered simple model may be of interest. Vapor is permanently produced and removed from the coolant pool. Analysis of the model obtained resulted in some correlations for the three main parameters of the cooling process, which may be used for estimation of the particle cooling.Comment: 9 pages, 4 figures, 19 reference

A combined space discrete algorithm with a Taylor series by time for CFD

The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a class of initial-boundary value problems for the PDEs using one of the known space discrete numerical schemes and a Taylor series expansion by time. Normally a second order discretization by space is applied while a first order by time is satisfactory. Nevertheless, in a number of different problems, discretization both by temporal and by spatial variables is needed of highest orders, which complicates numerical solution, in some cases dramatically. Therefore it is difficult to apply the same numerical methods for the solution of some PDE arrays if their parameters are varying in a wide range so that in some of them different numerical schemes by time fit the best for precise numerical solution. The Taylor series based solution strategy for the non-stationary PDEs in CFD simulations has been proposed here that attempts to optimise the computation time and fidelity of the numerical solution.Comment: 17 page

Investigation the Critical Levels in Development of the Complex Systems with Shifted Arguments for their Optimal Control

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels in a development of complex systems for various natures associated with diverse complicated factors, in particular with shifted arguments of the system. Intensive research in this direction and developed techniques may optimize management of the complex systems in financial-economic, natural and other fields. Construction of adequate mathematical models for development of complex systems, critical modes and their effective control are important tasks for a wide range of contemporary issues as shown in paper on examples. Critical levels in development of economic, banking, technical, political and other systems are necessary to determine and anticipate, to manage their system requirements and provide stable development, without being hit in a critical situations, leading to growing oscillations of the system settings.Comment: 14 pages, 5 figures, pape

The dynamics of thin gas layer moving between two fluids

The dynamics and stability of a thin gas layer moving between two fluid layers moving in the same or opposite direction is studied. The linear evolutionary equations describing the spatial-temporal dynamics of the interface perturbations between gas and two fluid layers are derived for the flat two-dimensional case. Integral correlations across the layer are obtained, and the various kinds of time dependent base states are found. A linear stability is considered for the system using non-stationary equation array derived. The equation array consists of the two one-dimensional non-stationary equations of a seventh and fourth order. The results of the numerical study of the governing evolution equations support the results of the analysis for more simple limit cases. It is found that the thin sheet gas flow in-between two liquid layers is unstable and the peculiarities are found and discussed together with some applications available.Comment: 15 pages, 1 figure, 10 reference

Algebraic Geometry over Lie Algebras

This is a survey paper on Alegbraic Geometry over Lie AlgebrasComment: 40 page

The Theory and Applications of Parametric Excitation and Suppression of Oscillations in Continua: State of the Art

The results by development of physical, mathematical and numerical models for parametric excitation and suppression of oscillations on the interfaces separating continuous media, for carrying out computing, physical and natural experiments by revealing the new phenomena and parametric effects, and for their use in improvement the existing and creation the perspective highly efficient technological processes are presented. Scientific novelty of this work consists in development of the theory and applications of parametric excitation and suppression of oscillations on the boundaries of continua on the samples of three tasks classes: flat and radial spreading film flows of viscous incompressible liquids, conductive as well as non-conductive ones; surfaces of phase transition from a liquid state into a solid one; and heterogeneous granular media. The external actions considered are: alternating electromagnetic, vibration, acoustic and thermal fields. Along with linear the non-linear parametric oscillations are investigated (including strongly non-linear) too and the results of theoretical studies are confirmed and supplemented with the corresponding experimental data. The general and specific peculiarities of parametrically excited oscillations and the new parametric effects revealed are discussed for technical and technological applications. First the general statement and substantiation of the problems studied is considered, and then the various parametric oscillations in continua are analyzed from common methodological base. Also the assessment of a current state of the problems, analysis of their features, prospects of further development and the main difficulties of the methodological, mathematical and applied character are presented.Comment: 25 pages, 233 reference

Group Actions on Real Cubings and Limit Groups over Partially Commutative Groups

We introduce a class of spaces, called real cubings, and study the stucture of groups acting nicely on these spaces. Just as cubings are a natural generalisation of simplicial trees, real cubings can be regarded as a natural generalisation of real trees. Our main result states that a finitely generated group $G$ acts nicely (essentially freely and co-specially) on a real cubing if and only if it is a subgroup of a graph tower (a higher dimensional generalisation of $\omega$-residually free towers and NTQ-groups). It follows that $G$ acts freely, essentially freely and co-specially on a real cubing if and only if $G$ is a subgroup of the graph product of cyclic and (non-exceptional) surface groups. In the particular case when the real cubing is a tree, it follows that $G$ acts freely, essentially freely and co-specially on the real cubing if and only if it is a subgroup of the free product of abelian and surface groups. Hence, our main result can be regarded as a generalisation of the Rips' theorem on free actions on real trees. We apply our results to obtain a characterisation of limit groups over partially commutative groups as subgroups of graph towers. This result generalises the work of Kharlampovich-Miasnikov, \cite{KhMNull}, Sela, \cite{Sela1} and Champetier-Guirardel, \cite{CG} on limit groups over free groups.Comment: 91 pages, 2 figure

Derivation and analysis of the nonlinear boundary conditions at the deformable interface between two fluids

The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the non-linear description is performed and analyzed in a wide range of physical situations. The differential equations of the interfacial motion thus obtained may be useful in research of the non-linear development of the classical hydrodynamic instabilities. They should play an important role in the understanding of the hydrodynamic phenomena associated with the flows involving complex interfacial evolution including parametric control of the boundaries in continua (for example, with electromagnetic field or/and vibration).Comment: 9 pages, 1 fugure, 20 reference