332 research outputs found
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 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 -residually free towers and NTQ-groups). It follows
that acts freely, essentially freely and co-specially on a real cubing if
and only if 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 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
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