Multicomponent composites,electrical networks and new types of continued fraction II

The outstanding problem of systematically developing rigorous bounds on the complex effective conductivity tensor * ofd-dimensional,n-component composites withn>2 is solved. The bounds incorporate information contained in successively higher order correlation functions which reflect the composite geometry. Explicit expressions are given for many of the bounds and some, but not all of them, are represented by nested sequences of circles in the complex plane that enclose, and in fact converge to, each diagonal element of *. They are derived from the fractional linear matrix transformations found in Part I that recursively link * with a hierarchy of complex effective tensors ^(j),j=0, 1, 2, ..., of increasing dimension,d(n–1) ^j . Elementary bounds on ^(j) confining the diagonal elements of ^(j) or its inverse to half-plane, wedge or open polygon regions of the complex plane, imply narrow bounds on * which converge to the exact value of * in the limit asj . When the component conductivities are real these bounds are more restrictive than the corresponding variational bounds. Besides applying to the effective conductivity *, the bounds extend to a wide class of matrix-valued multivariate functions called -functions, and thereby to conduction in polycrystalline media, viscoelasticity in composites, and conduction in multi-component, multiterminal, linear electrical networks. The analytic and invariance properties of -functions are explored and within this class of function most of the bounds are found to be optimal or at least attainable. The bounds obtained here are essentially a generalization to matrix-valued, multivariate functions of the nested sequence of lens-shaped bounds in the complex plane derived by Gragg and Baker for single variable Stieltjes functions.     

Multicomponent composites,electrical networks and new types of continued fraction I

The development of bounds on the complex effective conductivity tensor * (that relates the average current to the average electric field in a multicomponent composite) has been hindered by lack of a suitable continued-fraction representation for *. Here a new field equation recursion method is developed which gives an expression for * as a continued fraction of a novel form incorporating as coefficients the component conductivities and a set of fundamental geometric parameters reflecting the composite geometry. A hierarchy of field equations is set up such that the solutions of the (j+1)th-order equation generate the solutions of thejth-order equation. Consequently the effective tensor ^(j) associated with thejth-order field equation is expressible as a fractional linear matrix transformation of ^(j+1). These transformations combine to form the continued fraction expansion for *=⁽⁰⁾ which is exploited in the following paper, Part II, to obtain bounds: crude bounds on ^(j), forj1, give narrow bounds on *. The continued fraction is a generalization to multivariate functions of the continued fraction expansion of single variable Stieltjes functions that proved important in the development of the theory of Páde approximants, asymptotic analysis, and the theory of orthogonal polynomials in the last century. The results extend to other transport problems, including conduction in polycrystalline media, the viscoelasticity of composites, and the response of multicomponent, multiterminal linear electrical networks.     

Multicomponent Quantitative Analysis

Abstract

Reduction in the time required for performing chemical analyses is all-important a s long a s it is not attained by sacrificing required accuracy o r precision. The time for an analysis can be translated into productivity which, in the long run, means money. In analytical laboratories which perform hundreds or even thousands of analyses daily, a time savings of minutes per analysis can be financially rewarding.     

Multicomponent vacuum-arc ion beams

The paper generalizes the results of research on pulsed-periodic generation of multicomponent ion streams in sources based on vacuum arc discharge. Methods are considered for forming composition-and-energy controlled multicomponent beams for multielement ion implantation in Raduga sources. The features and laws governing the emission properties of wide-aperture ion sources with plasma generation by evaporation of a material in a cathode spot are discussed. A comparative analysis is made of the physical laws and possibilities of forming one-element or multielement ion beams during extraction from a free plasma boundary under conditions when a virtual anode exists and a positive voltage drop near the anode exists in the vacuum-arc-discharge plasma.Scientific-Research Institute of Nuclear Physics at the Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 34–52, March, 1994.     

Multicomponent periodic nanoparticle superlattices

In this article, we review the state-of-the-art in the preparation and characterization of multicomponent self-assembled superlattices of colloidal nanoparticles with core sizes in the range of 2–20 nm and interparticle spacing less than 2 nm down to intimate contact stemming from sintering. Several aspects of the field are discussed, including: structural organization, the role of particle size distribution, key interparticle forces at play, and methods of investigation of the structures. Contrary to the extensively studied colloidal crystals composed of microscale particles, the nanoparticles possess unique size-dependent properties, such as electronic, optical, or magnetic, which when combined into periodic structures can potentially lead to new collective states stemming from precise positioning of the nanocolloids. As such, we examine a number of emerging applications of this new class of metamaterials. Finally, we speculate on the potential impact of these materials, the new directions, and the challenges for the researchers.     

Multicomponent dipole-mode spatial solitons

We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics.     

多组分金属聚合体的光学纳米复合体系(英文)

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Wave Propagation in Multicomponent Plasmas

The well-known linearization technique has been used to derive the dielectric tensor for a multicomponent plasma in the presence of a static magnetic field. The equation of motion for various species of particles has been considered with Maxwell's field equations and the dispersion relation for different specific cases have been obtained.     

Multicomponent sonochemical synthesis of podands

An efficient sonochemical methodology is described for the synthesis of new podands containing substituted dihydropyrimidines.     

Rapid Infrared Multicomponent Control Analyses

Abstract

The present status of rapid IR multicomponent control analysis is that of a rapidly changing dynamic field of investigation in which the state-of-the-art is largely reflected in meeting abstracts, instrument manufacturer's seminars, brochures, private communications, and widely scattered articles in rather obscure journals. There are no definitive texts. These facts notwithstanding, the actual state of affairs is that several hundred investigators are very active in this field, partially in research but many in quality control laboratories. The dearth of information of the usual more formal sort reflects in part the very pragmatic and proprietary use to which the IR instruments capable of doing this work are being employed. The results do not always represent publishable material. However, when viewed from a suitable breadth of viewpoint, there is genuine merit in the multicomponent measurements.     

Multicomponent field theories and classical rotators

It is shown that aD-component Euclidean quantum field, =(¹,...,^D), with ||⁴+|²| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the caseD=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies forD=2 or 3 and that Griffiths' second inequality is valid forD=2; a complete proof is included of a Lee-Yang theorem for plane rotator and classical Heisenberg models. As an application of Griffiths' second inequality forD=2, an interesting relation between the parallel and transverse two-point correlations is obtained.Research supported in part by the National Science Foundation under grant NSF MPS 74-04870.     

Frequency Estimate for Multicomponent Crystalline Compounds

Among crystal structures of N-component metal alloys, far fewer examples are known with \(N\ge 4\) than with \(N=2\) or 3, in apparent contradiction to the exponentially growing number of possible combinations of elements. Two effects contribute to this shortfall. Since the N-component composition space resides within a d-dimensional simplex with \(d=N-1\), the vanishing volume in high dimensions reduces the distinct N-component compositions. Additionally, the increasing surface area makes it more probable that stable structures reside on the surface of the simplex (containing fewer than N components) as opposed to its interior. Specific estimates are developed through application of the empirical Miedema enthalpy model. Despite their rarity, we propose that the actual number of \(N=4\)- and 5-component alloys greatly exceeds the number that are currently known.     

Multicomponent lattice-Boltzmann model with interparticle interaction

A lattice Boltzmann model for simulating fluids with multiple components and interparticle forces proposed by Shan and Chen is described in detail. Macroscopic equations governing the motion of each component are derived by using the Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirment by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity, so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confiremoed numerically.     

Multicomponent two-dimensional solitons carrying topological charges

We propose multihump N-component two-dimensional vector solitons for which each constituent carries a different topological charge. These new structures exhibit a unique triple-point phase diagram that is completely absent in the two-component limit.     

Zero-Flux Plane Kinetics at Multicomponent Interfaces

Zero flux planes (ZFP's) are the locations in a diffusion couple where fluxes of individual components vanish. The conditions required for developing ZFP's between interdiffusing multicomponent alloys are now well understood through the works of Dayananda and Morral. In this paper we analyze the kinetics of multicomponent diffusion near ZFP's. In contrast to the usual mixing that occurs between end-member alloys in a diffusion couple, where the average component compositions are approached through “global” exchange of atoms, the presence of a stationary ZFP requires instead that mixing of the blocked component occurs through the release of a pair of coupled diffusion waves. In classical (thick) couples these waves spread symmetrically away from the Matano plane. The wave pair consists of a “depletion” wave that reduces the blocked component concentration in the component-rich alloy, and a conjugate “repletion” wave that increases the concentration in the adjacent component-poor alloy. Curiously, each of these waves establishes the average (equilibrium) concentration unilaterally on either side of the Matano plane. A stationary ZFP precludes net transport of one component across the Matano plane—a circumstance that has practical and theoretically interesting implications for the design of stable multicomponent films and coatings that must resist diffusive loss of a component.     

Multicomponent Thermal Plasma of Arc Discharges

This paper deals with investigations of thermal electric arc plasma in complex gas - metal vapour mixtures. Experimental techniques in the diagnostic were widely discussed. The study of non-steady-state discharges was performed with an appropriate temporal and spatial resolution. Spectroscopy investigations of plasma parameters in some modes of discharge operation were carried out. Spatial profiles of temperatures and electron densities were obtained. Plasma composition was calculated in an assumption of the local thermodynamic equilibrium. The influence of some mechanisms on plasma condition was analysed.     

Macroscopic Equations for a Multicomponent Plasma

From the balance equations for partial quantities we derive equations for lumped quantities, e.g. a generalized Ohm's law. They are especially useful for a three-component system (electrons, one species of ions and neutral particles). Certain conditions are derived and investigated to describe a plasma with more than three components by the lumped quantities.     

Phase Evolution in Multicomponent Ceramic Solid Solutions

Russian Physics Journal - The paper studies the phase evolution in multicomponent solid solutions (Hf, Zr, Ti)C and (Hf, Zr, Nb)C during hot pressing of equimolar powder mixtures of metal carbides....