52 research outputs found
Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
A hydrodynamic description for an -component mixture of inelastic, smooth
hard disks (two dimensions) or spheres (three dimensions) is derived based on
the revised Enskog theory for the single-particle velocity distribution
functions. In this first portion of the two-part series, the macroscopic
balance equations for mass, momentum, and energy are derived. Constitutive
equations are calculated from exact expressions for the fluxes by a
Chapman-Enskog expansion carried out to first order in spatial gradients,
thereby resulting in a Navier-Stokes order theory. Within this context of small
gradients, the theory is applicable to a wide range of restitution coefficients
and densities. The resulting integral-differential equations for the zeroth-
and first-order approximations of the distribution functions are given in exact
form. An approximate solution to these equations is required for practical
purposes in order to cast the constitutive quantities as algebraic functions of
the macroscopic variables; this task is described in the companion paper.Comment: 36 pages, to be published in Phys. Rev.
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Diffusion in a Granular Fluid - Theory
Many important properties of granular fluids can be represented by a system
of hard spheres with inelastic collisions. Traditional methods of
nonequilibrium statistical mechanics are effective for analysis and description
of the inelastic case as well. This is illustrated here for diffusion of an
impurity particle in a fluid undergoing homogeneous cooling. An appropriate
scaling of the Liouville equation is described such that the homogeneous
cooling ensemble and associated time correlation functions map to those of a
stationary state. In this form the familiar methods of linear response can be
applied, leading to Green - Kubo and Einstein representations of diffusion in
terms of the velocity and mean square displacement correlation functions. These
correlation functions are evaluated approximately using a cumulant expansion
and from kinetic theory, providing the diffusion coefficient as a function of
the density and the restitution coefficients. Comparisons with results from
molecular dynamics simulation are given in the following companion paper
Особенности процесса лазерной сварки разнородных материалов на железной и медно-никелевой основе
The paper presents investigations on influence of laser welding parameters with fiber lasers on formation of a welding joint, its geometrical and physical and mechanical properties while welding spring steel and Fe–Cu–Ni system.Исследовано влияние параметров процесса лазерной сварки с применением волоконных лазеров на процесс формирования сварного соединения, его геометрические и физико-механические свойства при сварке рессорно-пружинной стали и системы «железо – медь – никель»
First normal stress difference and crystallization in a dense sheared granular fluid
The first normal stress difference () and the microstructure
in a dense sheared granular fluid of smooth inelastic hard-disks are probed
using event-driven simulations. While the anisotropy in the second moment of
fluctuation velocity, which is a Burnett-order effect, is known to be the
progenitor of normal stress differences in {\it dilute} granular fluids, we
show here that the collisional anisotropies are responsible for the normal
stress behaviour in the {\it dense} limit. As in the elastic hard-sphere
fluids, remains {\it positive} (if the stress is defined in
the {\it compressive} sense) for dilute and moderately dense flows, but becomes
{\it negative} above a critical density, depending on the restitution
coefficient. This sign-reversal of occurs due to the {\it
microstructural} reorganization of the particles, which can be correlated with
a preferred value of the {\it average} collision angle in the direction opposing the shear. We also report on the shear-induced
{\it crystal}-formation, signalling the onset of fluid-solid coexistence in
dense granular fluids. Different approaches to take into account the normal
stress differences are discussed in the framework of the relaxation-type
rheological models.Comment: 21 pages, 13 figure
Data Sets Formation on the Physical Properties of Oxide Scale Components for Theoretical Assessment of Efficiency Parameters of Laser Cleaning of Carbon Steels and Related Processes
There is a need in machine-building industries nowadays to automate technologies, in particular, laser ones, to remove surface oxide layers – mill scale, rust – from steel products/pieces in order to improve the energy effectiveness of processing. Herewith, a theoretical assessment method for the intensity of heating of the oxide layer and the phase transition in it can be used to optimize laser cleaning (LC) of the steel surface. To realize this, it is possible to use some calculation and modeling procedures that require, as a first step, the data collection and verification on the temperature-dependent properties of iron-containing condensed phases, as possible components contained, in particular, in scale, which is typically widespread into various metal products. In this regard, the formation of database for characteristics of oxide scale components by the way of selection of information on thermophysical (including optical) properties of the components mentioned and of steel base, which are required for a reliable calculation of the thermal efficiency parameters of the technology for laser cleaning of carbon steels, as well as such actively developed related technologies as laser cutting, drilling, coating remelting, etc., was chosen as the task of our research. An analytical overview of published experimental data made it possible to systematize information on a number of transport and other physical properties of iron-containing components at ambient pressure, including thermal conductivity (k) and diffusivity (a), density ρ, irradiation absorptance and integral emissivity in the temperature range from T ≈ 298 K to the melting temperatures of oxide and metal phases and above them. At the same time, a preliminary thermochemical estimation shows (on the calculated data) the existence of such thermodynamically stable forms of the condensed phase in the heating spot of scale layers during its LC at the melting point and above it, as Fe3O4, FeO, and Fe, which is consistent with known experimental data. Comparison of the values of a calculated by us (using the published values of k, ρ and molar heat capacity and using extrapolation in the high-temperature region) for the types of scale components under consideration with a set of experimental values of this parameter in current literature revealed the presence of differences for both oxide and metal phases. These new values make it possible to fill in a gap in the temperature range T = 1600–1800 K that existed in the data on the thermal diffusivity. The value of a = (0.83–0.92)·10–6 m2/s was also calculated for liquid iron oxide for the T ≈ 1800 K, which was not measured experimentally, that, obviously, prevented modeling of not only laser surface processing, melting and cleaning of steels, but also calculations in the field of metallurgical and other technologies, which are characterized by the presence of iron oxide melts during heating
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.
Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime
The Landau-Lifshitz fluctuating hydrodynamics is used to study the
statistical properties of the linearized Kolmogorov flow. The relative
simplicity of this flow allows a detailed analysis of the fluctuation spectrum
from near equilibrium regime up to the vicinity of the first convective
instability threshold. It is shown that in the long time limit the flow behaves
as an incompressible fluid, regardless of the value of the Reynolds number.
This is not the case for the short time behavior where the incompressibility
assumption leads in general to a wrong form of the static correlation
functions, except near the instability threshold. The theoretical predictions
are confirmed by numerical simulations of the full nonlinear fluctuating
hydrodynamic equations.Comment: 20 pages, 4 figure
The imprints of superstatistics in multiparticle production processes
We provide an update of the overview of imprints of Tsallis nonextensive
statistics seen in a multiparticle production processes. They reveal an
ubiquitous presence of power law distributions of different variables
characterized by the nonextensivity parameter q > 1. In nuclear collisions one
additionally observes a q-dependence of the multiplicity fluctuations
reflecting the finiteness of the hadronizing source. We present sum rules
connecting parameters q obtained from an analysis of different observables,
which allows us to combine different kinds of fluctuations seen in the data and
analyze an ensemble in which the energy (E), temperature (T) and multiplicity
(N) can all fluctuate. This results in a generalization of the so called
Lindhard's thermodynamic uncertainty relation. Finally, based on the example of
nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon
collisions) we demonstrate that, for the standard Tsallis entropy with degree
of nonextensivity q < 1, the corresponding standard Tsallis distribution is
described by q' = 2 - q > 1.Comment: 12 pages, 3 figures. Based on invited talk given by Z.Wlodarczyk at
SigmaPhi2011 conference, Larnaka, Cyprus, 11-15 July 2011. To be published in
Cent. Eur. J. Phys. (2011
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