Bounds and exact theories for the transport properties of inhomogeneous media

We investigate the bounds of Milton on the transport coefficient of a two-component composite, in their application to the square and hexagonal arrays of cylinders, and the three cubic lattices of spheres. We show that, in all five cases, as more information is supplied about the geometry of the composite, the bounds converge to the precise point obtained from an exact theory specific to the geometry in question. We illustrate the use of the bounds in determining whether a set of known values of the transport coefficient adequately specifies the general behaviour of that quantity. We determine the values of two structure-dependent parameters for cell materials with spheroidal cells and the value of one parameter for hexagonal and square arrays of cylinders with missing array elements. These parameters determine bounds both on the transport and on the elastic properties of the respective materials.     

Concerning bounds on the transport and mechanical properties of multicomponent composite materials

The Hashin-Shtrikman and Walpole bounds for the transport properties and bulk modulus of multicomponent composite materials are shown to be attained in a wide range of cases. Thus in these cases the bounds are the best possible bounds that can be given in terms of the properties of the components and the volume fractions. For three-component materials new bounds are conjectured. The conjectured bounds are presumed to apply in the cases where the Hashin-Shtrikman and Walpole bounds are not attained.     

Correlation between morphology and transport properties of composite films: Charge transport in composites

Metal/dielectric composite films consisting of metal objects located in dielectric matrix are investigated by computer simulation. The complete computer experiment is devoted to the study of correlation between structural properties and electrical characteristics of composite films. In the present analysis transport properties of films are calculated near the metal-dielectric transition when the basic mechanism of charge transport is the tunnel effect. The conductivity of composite film is disseminated into individual percolation paths influenced by object arrangements in the composite film.     

Quantum-mechanical versus semiclassical capture and transport properties in quantum well laser structures

We have studied experimentally and modelled theoretically the capture properties and transport mechanisms of electrons and holes in laser structures. We describe first the extreme case where the barrier thickness is very large: then semiclassical drift-diffusion equations may be applied and quantum-mechanical effects at the edge of the well are negligible. A second extreme case occurs when the barrier is narrow enough for quantum mechanics to apply fully. There, strong variations of the capture time with the well width are expected and observed. In real laser structures, dimensions are such that we are in an intermediate case and both aspects have to be taken into account. We give some typical values for diffusion/capture mechanism induced delay times in such a case.     

Existence of Néel Order in the S=1 Bilinear-Biquadratic Heisenberg Model via Random Loops

We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of the attenuated ray transform on tensor fields with values in a Hermitian bundle (i.e., vector valued case). We also show that a connection and Higgs field on a Hermitian bundle are determined up to gauge by the knowledge of the parallel transport between boundary points along all possible geodesics. The main tools are an energy identity, the Pestov identity with a unitary connection, which is presented in a general form, and a precise analysis of the singularities of solutions of transport equations when there are trapped geodesics. In the case of closed manifolds, we obtain similar results modulo the obstruction given by twisted conformal Killing tensors, and we also study this obstruction.     

Thermal resistance of GaAs/AlAs superlattices used in modern light-emitting diodes

Superlattices are used in modern light-emitting diodes to modify intentionally electron, phonon and/or photon transport within their volumes, which leads to their expected performance characteristics. In particular, superlattices may have a dramatic impact on device thermal properties. Superlattice thermal resistance is anisotropic and usually distinctly higher than its values in constituent bulk materials, which results from phonon reflections and/or phonon scatterings at numerous layer interfaces. In the present paper, thermal resistance of a typical superlattice of layer thicknesses neither much higher nor much lower than the phonon free path is discussed. Besides, as an important example, thermal resistance of the typical GaAs/AlAs superlattice is determined theoretically and compared with its measured values known from literature.     

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999     

Combined meso-scale modeling and experimental investigation of the effect of mechanical damage on the transport properties of cementitious composites

The transport properties of cementitious composites such as concrete are important indicators of their durability, and are known to be heavily influenced by mechanical loading. In the current work, we use meso-scale hygro-mechanical modeling with a morphological 3D two phase mortar-aggregate model, in conjunction with experimentally obtained properties, to investigate the coupling between mechanical loading and damage and the permeability of the composite. The increase in permeability of a cylindrical test specimen at 28% aggregate fraction during a uniaxial displacement-controlled compression test at 85% of the peak load was measured using a gas permeameter. The mortar's mechanical behavior is assumed to follow the well-known compression damaged plasticity (CDP) model with isotropic damage, at varying thresholds, and obtained from different envelope curves. The damaged intrinsic permeability of the mortar evolves according to a logarithmic matching law with progressive loading. We fit the matching law parameters to the experimental result for the test specimen by inverse identification using our meso-scale model. We then subject a series of virtual composite specimens to quasi-static uniaxial compressive loading with varying boundary conditions to obtain the simulated damage and strain evolutions, and use the damage data and the previously identified parameters to determine the evolution of the macroscopic permeability tensor for the specimens, using a network model. We conduct a full parameter study by varying aggregate volume fraction, granulometric distribution, loading/boundary conditions and “matching law” parameters, as well as for different strain–damage thresholds and uniaxial loading envelope curves. Based on this study, we propose Avrami equation-based upper and lower bounds for the evolution of the damaged permeability of the composite.     

Thermal Rectification Effect of an Interacting Quantum Dot

We investigate the nonlinear thermal transport properties of a single interacting quantum dot with two energy levels tunnel-coupled to two electrodes using nonequilibrium Green function method and Hartree-Fock decoupling approximation. In the case of asymmetric tunnel-couplings to two electrodes, for example, when the upper level of the quantum dot is open for transport, whereas the lower level is blocked, our calculations predict a strong asymmetry for the heat （energy） current, which shows that the quantum dot system may act as a thermal rectifier in this specific situation.     

New integrable cases of a Cremona transformation: a finite-order orbits analysis

We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters ( and ), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping originates from the analysis of birational transformations obtained from very simple algebraic calculations, namely taking the inverse of q × q matrices and permuting some of the entries of these matrices. It has been seen to yield weak chaos and integrability. We have found new integrable cases of this Cremona transformation, corresponding to the values of = 0 when , besides the already known values = 0 and = −1, and also arbitrary when = 0. For these cases, one has a foliation of the parameter space in elliptic curves. We give the equations of these elliptic curves. Based on this very example we show how one can find these integrability cases of the Cremona transformation and actually integrate it using a method based on the systematic study of the finite-order conditions of the Cremona transformation. The method is shown to be efficient and straightforward. The various integrability cases are revisited using many different representations of this very mapping (birational transformations, recursion in one variable, …).     

Analysis of ultrasonic attenuation in particle-reinforced plastics by a differential scheme

Attenuation of ultrasonic longitudinal waves in some particle-reinforced polymer composites is studied theoretically by a micromechanical model based on a differential (incremental) scheme. A set of differential equations is established by which the attenuation spectrum of the composite can be computed from the known properties of viscoelastic matrix and elastic particles. For a composite reinforced with glass particles with radius 0.15 mm, the proposed scheme is shown to predict the attenuation in better agreement with the foregoing experimental results than the previous simplistic independent scattering model. Based on this scheme, the dependence of the longitudinal attenuation spectrum of a particulate polymer composite on the wavelength-to-particle radius ratio and the particle volume fraction is examined in detail. It is then shown theoretically that the attenuation of the composite decreases monotonically with the particle volume fraction when the particle radius is sufficiently small compared to the incident wavelength, while it shows non-monotonic particle-fraction dependence when the ratio of the particle radius to the wavelength is larger. To examine this theoretical finding from an experimental point of view, the longitudinal attenuation in a glass-particle-reinforced polyester composite with particle radius 0.0225 mm is measured for different particle volume fractions. The measured attenuation characteristics are shown to support the qualitative features of the theoretical prediction.     

Analysis of ultrasonic attenuation in particle-reinforced plastics by a differential scheme

Attenuation of ultrasonic longitudinal waves in some particle-reinforced polymer composites is studied theoretically by a micromechanical model based on a differential (incremental) scheme. A set of differential equations is established by which the attenuation spectrum of the composite can be computed from the known properties of viscoelastic matrix and elastic particles. For a composite reinforced with glass particles with radius 0.15 mm, the proposed scheme is shown to predict the attenuation in better agreement with the foregoing experimental results than the previous simplistic independent scattering model. Based on this scheme, the dependence of the longitudinal attenuation spectrum of a particulate polymer composite on the wavelength-to-particle radius ratio and the particle volume fraction is examined in detail. It is then shown theoretically that the attenuation of the composite decreases monotonically with the particle volume fraction when the particle radius is sufficiently small compared to the incident wavelength, while it shows non-monotonic particle-fraction dependence when the ratio of the particle radius to the wavelength is larger. To examine this theoretical finding from an experimental point of view, the longitudinal attenuation in a glass-particle-reinforced polyester composite with particle radius 0.0225 mm is measured for different particle volume fractions. The measured attenuation characteristics are shown to support the qualitative features of the theoretical prediction.     

Numerical simulation of micro-scratch tests for coating/substrate composites

In this paper the micro-scratch test is simulated by ANSYS finite element code for thin hard coating on substrate composite material system. Coulomb friction between indenter and material surface is considered. The material elastic-plastic properties are taken into account. Contact elements are used to simulate the frictional contact between indenter and material surfaces, as well as the frictional contact after the detachment of coating/substrate interfaces has taken place. In the case of coating/substrate interfaces being perfectly bonded, the distributions of interfacial normal stress and shear stress are obtained for the material system subjected to normal and tangential loading. In the case of considering the detachment of interfaces, the length of interfacial detachment and the redistribution of stresses because of interfacial detachments are obtained. The influences of different frictional coefficients and different indenter moving distances on the distributions of stresses and displacements are studied. In the simulation, the interfacial adhesion shear strength is considered as a main adhesion parameter of coating/substrate interfaces. The critical normal loading from scratch tests are directly related to interfacial adhesion shear strengths. Using the critical normal loading known from experiments, the interfacial adhesion shear strength is obtained from the calculation. When the interfacial adhesion shear strength is known, the critical normal loading is obtained for different coating thicknesses. The numerical results are compared with the experimental values for composite materials of thin TiN coating on stainless steel substrate.     

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.     

Transport between multiple users in complex networks

We study the transport properties of model networks such as scale-free and Erd?s-Rényi networks as well as a real network. We consider few possibilities for the trnasport problem. We start by studying the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution $\Phi_{\rm SF}(G)\sim G^{-g_G}$ , where g_G=2λ-1, and λ is the decay exponent for the scale-free network degree distribution. The power-law tail in Φ_SF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erd?s-Rényi networks where the tail of the conductivity distribution decays exponentially. We develop a simple physical picture of the transport to account for the results. The other model for transport is the max-flow model, where conductance is defined as the number of link-independent paths between the two nodes, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. We then extend our study to the case of multiple sources ans sinks, where the transport is defined between two groups of nodes. We find a fundamental difference between the two forms of flow when considering the quality of the transport with respect to the number of sources, and find an optimal number of sources, or users, for the max-flow case. A qualitative (and partially quantitative) explanation is also given.     

人工神经网络作为打印机色空间转换工具的问题

通过分析大量实测的打印机输入(R,G,B)与输出(L ,a ,b )数据之间的对应关系,发现在一些颜色区域存在着RGB与L a b 之间的二对一甚至多对一的关系。另一方面,一个已知的事实是,当一个神经网络已经建立后,任一个(或一组)输入只能产生一个(或一组)输出。结合以上两个事实得出的结论是,在要求打印机的输出颜色能准确地复现指定颜色的情况下,神经网络不适合作为由指定颜色的L a b 值来寻求打印机的相应输入RGB的工具。     

Shot noise in magnetic field modulated graphene superlattice

We investigate the shot noise properties in a monolayer graphene superlattice modulated by N parallel ferromagnets deposited on a dielectric layer. It is found that for the antiparallel magnetization configuration or when magnetic field is zero the new Dirac-like point appears in graphene superlattice. The transport is almost forbidden at this new Dirac-like point, and the Fano factor reaches its maximum value 1/3. In the parallel magnetization configuration as the number of magnetic barriers increases, the shot noise increases. In this case, the transmission can be blocked by the magnetic–electric barrier and the Fano factor approaches 1, which is dramatically distinguishable from that in antiparallel alignment. The results may be helpful to control the electron transport in graphene-based electronic devices.     

Approximation of the erosion zone profile in planar magnetrons with a disk cathode

We have proposed a universal approximation of the normalized erosion zone profile of planar magnetrons with a disk cathode by a composite function that includes the probability density function for the minimal distribution of extremal values for the region from the center of the disk cathode to the maximum of the erosion zone and the survival Weibull distribution function (from the maximum to the outer boundary of the sputtering zone). The accuracy of the approximation has been verified for six magnetrons differing in the cathode size or in the design of the magnetic systems. In all cases, good agreement has been observed between the approximation and experimentally measured values. The results reported here can be used to analyze processes that occur on the cathode during sputtering and to refine the calculations of coating profiles.