Non-stationary conjugate heat exchange and phase transition at the high-energy surface processing. Part 1. Computational approach and its realization

The paper presents the developed physical and mathematical models, calculation procedure based on finite-element method, and also the software for the numerical studying the processes of the non-stationary conjugate heat exchange and phase transition during the surface processing with high-concentrated energy fluxes with stationary, pulse, and movable heat sources (fusing of coatings, surface layer quenching, surface cleaning, etc.). The proposed and realized method permits to study the processes within a wide range of the power density of external heat fluxes q∈[10⁷; 10¹⁴] W/m² with significantly different spatial and temporal scales. The results presented are of interest for understanding and simulation of the processes occurring at the surface processing of the coatings and materials with high-concentrated energy fluxes. The project has been financially supported by the Russian Foundation for Basic Research (Grant No. 07-08-00209).     

Conservation laws for classes of nonlinear evolution equations solvable by the spectral transform

The existence of conservation laws for novel classes of nonlinear evolution equations (with linearlyx-dependent coefficients) solvable by the spectral transform is investigated. A remarkably explicit representation is moreover obtained for the conserved quantities of the old classes of nonlinear evolution equations (withx-independent coefficients; including the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the nonlinear Schrödinger equation, etc.).     

Computer simulations of critical phenomena and phase behaviour of fluids

Computer simulation techniques such as Monte Carlo (MC) and Molecular Dynamics (MD) methods yield numerically exact information (apart from statistical errors) on model systems of classical statistical mechanics. However, a systematic limitation is the restriction to a finite (and often rather small) particle number N (or box linear dimension L, respectively). This limitation is particularly restrictive near critical points (due to the divergence of the correlation length of the order parameter) and for the study of phase equilibria (possibly involving interfaces, droplets, etc.). Starting out with simple lattice gas (Ising) models, finite size scaling analyses have been developed to overcome this limitation. These techniques work for both simple Lennard-Jones fluids and their mixtures, including generalizations to approximate models for quadrupolar fluids such as carbon dioxide, benzene etc. and various mixtures, whose phase behaviour can be predicted. A combination of MC and MD allows the study of dynamic critical phenomena, and specialised techniques (umbrella sampling plus thermodynamic integration) yield the surface free energy of droplets as function of droplet size. Thus, computer simulation has become a versatile and widely applicable tool for the study of fluids.     

The influence of cysteamine and counterion concentrations on the properties of CdSe/ZnS quantum dots

The influence of the cysteamine surfactant concentration on the stability of CdSe/ZnS nanoparticles (NPs) solubilized by this compound at the phase interface between two immiscible liquids is considered. The steady-state and time-resolved fluorescence spectroscopy data show that the fluorescence quantum yield of cysteamine-coated NPs and their stability to aggregation in a potassium phosphate buffer are determined by the balance between the concentrations of surfactant in the aqueous phase and hydrophobic NPs in the nonpolar phase (chloroform, toluene, etc.). It is found that the brightest and most stable hydrophilic NPs can be obtained by completely coating them by cysteamine molecules without a surfactant deficit or excess in the reaction at the phase interface.     

Condensed Phase Isotope Effects

It is well known that the condensed phase physical properties of molecular isotopic isomers are not the same. These differences in the vapor pressure, molar volume, surface tension, etc., are purely quantal phenomena. The effects are most exterme for isotopic substitution at hydrogen isotopes. Of the various physical properties which have been investigated the isotope effect on vapour pressure (VPIE) shows the largest ralative effects. In face, for hydrogen-deuterium substitution they range all the way from about inverse 2% per deuterium atom for nonpolar hydrocarbons (by inverse we mean that the molecule substituted with the heavier isotope has the higher vapor pressure) to as much as 20% normal (P_H > P_D ) per deuterium atom for molecules which are strongle associated in the condensed phase. Such effects are about one order of magnitude larger than isotope effects which are observed in most systems on molar volumes, surface tension, etc. (Thus, for example, benxene at 20°C shows a rather small VPIE of 0.4% per atom D 3 but the molar volume effect is only 0.05% per D and the surface tension effect 0.03% [4].) This it would appear is the reason a majority of recent studies have been directed toward the VPIE. The emphasis in this paper reflects that trend and the balance of the discussion will deal almost exclusively with the vapor pressure isotope effect.     

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.     

Model of discontinuity surface in continuum physics

In this paper we adopt the division of the discontinuity surfaces into autonomous, nonautonomous and surfaces of jump. A uniform, general integral form of balance equations (conservation laws) is derived for all three types and its localisation to the point on the discontinuity surface is carried out. In the case of the surfaces of jump the local balance equation takes the form of the Kotchine condition. Local form of the balance equations is specified for the mass, momentum, energy (total, kinetic and internal) and entropy. The equation which expresses the hypothesis of local equilibrium for a discontinuity surface is derived. This equation reflects also the phase transitions that take place in equilibrium. The relations of the derived results to other theories are discussed.     

Axisymmetric stationary solutions as harmonic maps

We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commuting Killing vectors. This method consists of writing the axisymmetric stationary Einstein equations in vacuum as a harmonic map which belongs to the groupSL(2,), and decomposing it into its harmonic submaps. This method provides a natural classification of the solutions in classes (Weyl's class, Lewis' class etc.).On leave of absence from Warsaw University, Warsaw, Poland     

Inverse method for determining the depth of nonhomogeneous surface layers in elastic solids from the measurements of the dispersion curves of group velocity of surface SH Waves

In this paper, the variational inverse method for determining the depth of nonhomogeneous surface layers in elastic materials, from the measurements of the group velocity of surface shear horizontal (SH) waves, is developed. The direct problem for a given a priori type of profile of the coefficientc44in(x) (e.g. linear, Gaussian, etc.) is solved. The dispersion curves of phase and group velocity of surface SH waves in nonhomogeneous solids are calculated. Experimental verification of the inverse method has been performed for step profiles (structure of Cu on steel). It is stated that the inverse method based on the measurements of group velocity (for step profile) gives a smaller error in the unknown depth of the surface layer than that resulting from the inverse method based on the measurements of phase velocity of surface SH waves.     

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

ABSTRACT

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H²-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.     

An In situ Experimental Study on Solidification Kinetics of Polyolefins: Effect of Cooling Conditions

The solidification kinetics of polyolefins (PO) under three cooling conditions were investigated using an in situ measurement of the temperature decay within the PO resins. The phase-change temperature range of high-density polyethylene (HDPE) was located between 110 and 120°C, and those of low-density polyethylene (LDPE) and polypropylene (PP) were 90–110°C and 100–120°C, respectively. The cooling rate of the liquid-state stage is larger than that of the crystallization stage, primarily owing to the release of the latent heat of crystallization as well as the reduced temperature difference between the sample and cooling medium; they jointly slow down the cooling rate to an extent. The time with respect to phase transformation and its lasting period have close relations to the materials' molecular characteristics (e.g., Mw, MWD, LCB, etc.). Three empirical equations were proposed, and found to be applicable for the cooling analysis of the PO molten materials at relatively low cooling rates prior to crystallization.     

A molecular theory of smectic C liquid crystals made of rod-like molecules

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form U _C ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. Received 3 August 2002 RID="a" ID="a"Present address: Department of Physics, Vijaya College, R. V. Road, Bangalore - 560 004, India. RID="b" ID="b"e-mail: nvmadhu@rri.res.in     

Effects of Schwarzschild black hole horizon on isothermal plasma wave dispersion

The 3 + 1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates with isothermal state of plasma are formulated. We consider the cases of non-rotating and rotating backgrounds with non-magnetized and magnetized plasmas. For these cases, the perturbed form of these equations are linearized and Fourier analyzed by introducing plane wave type solutions. The determinant of these equations in each case leads to two dispersion relations which give value of the wave number k. Using the wave number, we obtain information like phase and group velocities etc. which help to discuss the nature of the waves and their characteristics. These provide interesting information about the black hole magnetosphere near the horizon. There are cases of normal and anomalous dispersion. We find a case of normal dispersion of waves when the plasma admits the properties of Veselago medium. Our results agree with those of Mackay et al. according to which rotation of a black hole is required for negative phase velocity propagation.     

Barnett kinetic coefficients in dense charged and neutral media

An approach based on the nonlinear response theory is proposed for determining nonlinear transport properties of nonideal multielement charged and neutral media. A version of this theory developed for describing these properties involves the comparison of phenomenological conservation equations for dense media in the Barnett approximation and microscopic equations for operators of dynamic variables. The Mori algorithm used for formulating the microscopic equations makes it possible to obtain these equations for non-ideal media in the form of generalized nonlinear Langevin equations. As a result, macroscopic expressions are derived for nonlinear kinetic coefficients in the second order in thermal perturbations (of temperature, mass velocity, etc.). The expressions for nonlinear and linearized Barnett kinetic coefficients are compared.     

Formulation of rough-surface scattering theory in terms of phase factors and approximate solutions based on this formulation

Abstract

This paper presents the formulation of rough-surface scattering theory in which the bounded phase shift factors, ζ(r, α) ζ exp[iαζ(r)], replace the elevation, ζ(r). Both the Dirichlet and the Neumann problems are considered. The integral equations for secondary surface sources are obtained that contain only this phase function in their kernels.

The Neumann (iterative) series for the solutions of the integral equations thus derived are functional Taylor series in powers of L(r, α), not in powers of ζ. If we expand L(r, α) in these series in powers of ζ(r), we obtain the standard perturbation theory series. Thus, the new formulation corresponds to the partial summation of the perturbation series.

Using the Neumann series, we obtain several uniform (with respect to αζ) approximate solutions that contain, as limiting cases, Bragg scattering, the Kirchhoff approximation, and most known advanced approximations.

In the case of random surface z = ζ(r), these new expansions contain the function ζ(r) only in the exponents, and, therefore, the result of averaging can be expressed only in terms of the characteristic functions of the multivariate probability distribution of elevations.     

Energy-momentum description of electrostatic waves in magnetoactive plasmas

The physical mechanism of the energy-momentum transfer governing the propagation of electrostatic waves in collisionsless plasmas is presented. Plasma is supposed to be immersed in external uniform crossed magnetic and electric field. The equilibrium plasma, determined by a stationary distribution of charged particles, is assummed to be generally anisotropic and weakly nonuniform. The changes in macroscopic quantities (in the kinetic energy of perpendicular and parallel motion, etc.) due to the self-consistent wave-particle interaction are derived. It is shown, that the corresponding dispersion equation is identical with the energy-momentum balance equations expressed in the wave frame. A new expression of the energy of waves (plasmons) is given, which ensures the energy-momentum balance equations to be mutually independent equations. This differs from the usual expression of the wave energy leading to energy-momentum balance equations which are not mutually independent.     

Nonisomorphic nucleation pathways arising from morphological transitions of liquid channels

Motivated by unexpected morphologies of the emerging liquid phase (channels, bulges, droplets) at the edge of thin, melting alkane terraces, we propose a new heterogeneous nucleation pathway. The competition between bulk and interfacial energies and the boundary conditions determine the growth and shape of the liquid phase at the edge of the solid alkane terraces. Calculations and experiments reveal a "precritical" shape transition (channel-to-bulges) of the liquid before reaching its critical volume along a putative shape-conserving path. Bulk liquid emerges from the new shape, and, depending on the degree of supersaturation, the new pathway may have two, one, or zero energy barriers. The findings are broadly relevant for many heterogeneous nucleation processes because the novel pathway is induced by common, widespread surface topologies (scratches, steps, etc.).     

Surface Acoustoelectric Waves in a Piezoelectric–High-Temperature Granular Superconductor Layered Structure

Interactions of surface acoustoelectric waves with a granular high-temperature superconducting medium are studied. Dispersion equations describing the characteristics of surface acoustoelectric waves are derived for piezoelectrics of 4 and 6mm and 3m symmetry. It is shown that at a temperature above the critical point an attenuation jump and a sudden change in the phase velocity of surface acoustoelectric waves are observed. This effect increases with increase in the electromechanical coupling coefficient and decrease in the thickness of the high-temperature superconducting film. The results obtained can be used in designing frequency selectors and transient photodetectors.