Interface response theory of electromagnetism in composite dielectric materials

It is shown how a recent interface theory can be used for solving the Maxwell equations in any composite dielectric material. General expressions for the corresponding response functions are given. These new results are illustrated by a general application to layered isotropic dielectrics and a simple derivation of the response function of two different isotropic dielectrics separated by a planar interface.     

Interface response theory of continuous composite materials

The interface response theory was recently established by the author for any composite material in d-dimensional discrete spaces. The macroscopic approach is the limit in which the properties of a discrete (e.g. microscopic) material, can be studied in d-dimensional continuous spaces. This continuum limit of the main equations of the interface responce theory of discrete composite systems is given here for the first time for any composite material.     

金属超晶格中的电子输运过程

本文借助文献[1]的方法解出在存在温度梯度和外磁场时金属超晶格的电子系统Boltz-mann方程,并以Nb-Ti超晶格系统为例计算出其电子热导率、热电功率、Thomson系数和Hall系数随调制周期变化的曲线,以此说明这种人造材料的电子输运性质与其微观结构的关系的基本物理特性。 关键词：     

超晶格和层状结构传热特性的连续模型及其在能源材料设计中的应用

层状材料和超晶格结构为提高热电材料和隔热涂层提供了新的设计思路, 并成为最近的研究热点. 应用连续波动方程和线性阻尼理论, 本文研究了此类材料中的声子输运特性. 给出了在整个相空间里的界面调制和声子局域化效应, 得出了超晶格材料热导率的上极限和下极限; 同时, 分析表明界面锐化加强了声子带隙, 使得部分模态的声子局域化加强. 最后, 通过对石墨烯/氮化硼超晶格(G/hBN)和硅/锗超晶格的分子模拟(Si/Ge), 验证了该理论模型. 该方法适用于所有的层状材料和超晶格结构, 对此类新能源材料的设计提供了普适的设计思路.     

A higher order dynamic theory for viscoelastic plates and layered composites

By using a new technique proposed by the first author [1] approximate theories are developed for the dynamic response of viscoelastic plates and layered composites. The originality of the new technique lies in the fact that it permits the approximate theory to satisfy correctly the lateral boundary conditions of a plate, or the interface (continuity) conditions of a layered composite. This, in turn, enables the approximate theory to describe accurately the geometric dispersion of waves propagating in a plate or layered composite. The approximate equations of a single viscoelastic plate are first derived by making use of the new technique. To develop the approximate theory for viscoelastic layered composites made of two alternating layers it is noted that the approximate equations of a single plate already established also hold in each layer of the composite. The theory is completed by adding the continuity conditions to these equations and using a smoothing operation. The equations thus obtained constitute a continuum (homogeneous) model (CM) which simplifies the determination of the dynamic response of viscoelastic layered composites when the number of layers in the composite is large. The proposed approximate theories are open to improvement in the sense that their region of validity in the wave number-frequency plane can be enlarged as much as one wishes by increasing the orders of the theories and continuity conditions.     

一维有限超晶格的电子态与透射问题的转移矩阵方法研究

采用转移矩阵方法,研究了一维有限超晶格的电子态与透射问题.计算了一维有限超晶格含单个缺陷层或少量缺陷层的透射谱和波函数,以及当电子被束缚在一维有限超晶格中电子的本征值和相应的定态本征函数.给出的方法对于研究电子通过任意排列的一维有限超晶格的输运具有普适性.     

Dynamical behavior of coupled magnetic bilayers

We obtain the magnetic susceptibility of systems constituted of two coupled magnetic layers. We consider that the coupling of the films is well described by a Heisenberg like interaction to write the equation of motion for the magnetization of each part of the system. The dynamical response of each constituent material is calculated taking into account the presence of an interacting magnetic media (a magnetic layer) in its border. The susceptibility obtained incorporates the effects of a different magnetic film in the neighborhood (via the interfilm interaction), as well as the properties of the interface. We use a procedure similar to the effective medium approach developed for superlattices to obtain an effective magnetic permeability for the whole system. We show that the knowledge of this property allows one to have information on the interface of the magnetic bilayer through the analysis of its optical properties. We illustrate this point by calculating the dispersion relation of magnetic polaritons propagating in a system consisting of an antiferromagnetic (MnF₂) layer grown in direct contact with a ferromagnetic film (Fe). We also simulate numerically an optical experiment where ATR (Attenuated Total Reflection) spectra are obtained.     

Study of Phase Transition Properties in Epitaxial Ferroelectric Film

Based on the transverse Ising model and using decoupling approximation to the Fermi-type Green's function, we study the phase transition properties of the epitaxial ferroelectric film with one substrate. A general recursive equation of the ferroelectric thin film with two n-layer materials is obtained, which enables us to study the phase transition properties for any number layers forepitaxial ferroelectric thin film. With the help of this equation, we analyze the effect of the exchange interaction and the transverse field in the phase diagram, the influence to the polarizations and Curie temperature numerically. The results show that epitaxial ferroelectric film are able to induce a strong increase or decrease of Curie temperature to different exchange interactions and transverse fields within the epitaxial film layers. The theoreticalresults are in reasonable accordance with experimental data of different ferroelectric thin film.     

Bandstructure matching at a heterojunction interface

An analytic theory for the matching of the bandstructure of different crystals at the interface of a heterojunction is presented. The Generalized Wannier functions serve as a basis. For a simple uniform band, the Hamiltonian matrix elements then reduce to the k-space Fourier coefficients of the bandstructure along the superlattice direction. The technique therefore accounts for non-effective mass effects, and the lower and upper valleys, and enables us to invoke both the quasi-k-space periodicity together with the spatial variations of the bandstructure. The superlattice Hamiltonian is a system of difference equations taking the form of a band matrix. A new definition of current not based on the effective-mass is introduced for this higher-order Schroedinger equation. The enforcement of the continuity of the elemental currents leads to analytic connection rules for the overlap Hamiltonian matrix elements. A maximum transparency for all energies is achieved only for geometrically related bandstructures. Non-effective-mass effects are demonstrated in resonant-tunneling structures. The technique presented offers new theoretical insights together with efficient numerical tools for the study of non-effective-mass superlattices.     

Structural response of cylindrically curved laminated composite shells subjected to blast loading

This paper is concerned with the theoretical analysis and correlation with the numerical results of the displacement time histories of the cylindrically curved laminated composite shells exposed to normal blast shock waves. The laminated composite shell is clamped at its all edges. The dynamic equation of the cylindrical shell used in this study is valid under the assumptions made in Love's theory of thin elastic shells. The constitutive equations of laminated composite shells are given in the frame of effective modulus theory. The governing equation of the cylindrical shell is solved by the Runge-Kutta method. In addition, a finite element modeling and analysis are presented and compared with the theoretical results. The peak deflections and response frequencies obtained from theoretical and numerical analyses are in agreement. The effects of material properties and geometrical properties are examined on the dynamic behaviour.     

Interfaces in metal matrix composites

The interface region in a given composite has a great deal of importance in determining the ultimate properties of the composite. An interface is, by definition, a bidimensional region through which there occurs a discontinuity in one or more material parameters. In practice, there is always some volume associated with the interface region over which a gradual transition in material parameter(s) occurs. The importance of the interface region in composites stems from two main reasons: (i) the interface occupies a very large area in composites, and (ii) in general, the reinforcement and the metal matrix will form a system that is not in thermodynamic equilibrium. One can discuss the interface in a composite at various levels. An optimum one should be neither so simple that it covers only a few special cases nor so complex that it is not useful in designing composites from processing and applications points of view. In this paper, my objective is to give examples of interface microstructure in different metal matrix composite systems and suggest some ways of controlling the interface characteristics in order to control the properties of the composite. I shall give examples of the interface microstructure in different metal matrix composites (particle and fiber reinforced as well as laminates) and discuss some of the important implications on various aspects of metal matrix composites, from the processing stage to ultimate performance of the composite.     

Strongly interacting particles with strongly singular potentials

A statistical system of particles is considered for which interaction potentials are strongly singular so that the standard perturbation theory cannot be used. A regular procedure for constructing a mass operator is suggested, having no ultraviolet divergences and giving the possibility of finding corrections for any approximation chosen. In this procedure, the divergences connected with the potential singularity are eliminated with the help of a smoothing function, for which a simple equation is given and whose properties are analyzed both analytically and numerically. Two effective regularization methods are formulated, eliminating divergences occurring while iterating propagator equations. A continuous iterative procedure is invented for calculating observable quantities and the fast convergence conditions for this procedure are shown to be equivalent to the fixed-point conditions.     

Tunneling in quantum superlattices with variable lacunarity

Fractal superlattices are composite, aperiodic structures comprised of alternating layers of two semiconductors following the rules of a fractal set. The scattering properties of polyadic Cantor fractal superlattices with variable lacunarity are determined. The reflection coefficient as a function of the particle energy and the lacunarity parameter present tunneling curves, which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for such curves are derived using the transfer matrix method. Comparison with numerical results shows good accuracy. The new results may be useful in the development of band-pass energy filters for electrons, semiconductor solar cells, and solid-state radiation sources up to THz frequencies.     

Localization in the model of contacting media with specific nonlinearity and interface interaction

In this paper, we consider the new model of nonlinear contacting media based on nonlinear Schrodinger equation with point potential and term, which is depended stepwise on field amplitude. Such a model theoretically describes a change in properties of the boundary regions along the interface between a Kerr-type crystal with cubic nonlinearity and a nonlinear medium characterized by abruptly change in dielectric constant depending on field amplitude. The short-range local interaction between wave and interface is taken into account by point potential in nonlinear Schrodinger equation. We obtain two new types of localized states characterized by composite structure consisting of three parts of the field distributions. We find exact and approximate solutions of dispersion equations. We described new properties of the spectrum of localized states arising as a result of the interaction of the wave with the interface and the presence of threshold field of the switching between the medium constants. All results are obtained in an analytical form. The proposed theory can be used to describe the propagation features of intense light beams localized along media interfaces in nonlinear optics, and to describe Bose-Einstein condensates with cubic nonlinearity.     

Effect of exchange interaction in ferromagnetic superlattices:A Monte Carlo study

The Monte Carlo simulation is used to investigate the magnetic properties of ferromagnetic superlattices through the Ising model. The reduced critical temperatures of the ferromagnetic superlattices are studied each as a function of layer thickness for different values of exchange interaction. The exchange interaction in each layer within the interface and the crystal field in the unit cell are studied. The magnetic coercive fields and magnetization remnants are obtained for different values of exchange interaction, different values of temperature and crystal field with fixed values of physical parameters.     

The effects of photoexcitation on excitons in semiconductor doping superlattices

Calculations of the properties of excitons in doping superlattices have been made as a function of doping density using a variational approach. Interesting new features are obtained when the exciton energy becomes comparable to the superlattice potential energy. These results are compared to recent experimental data on GaAs doping superlattices.     

Transport studies of MBE-grown InAs/GaSb superlattices

We report on the results of transport studies of MBE-grown InAs/GaSb superlattices. We demonstrate that the in-plane mobility is limited by interface roughness scattering by showing that, as a function of InAs layer width L, the in-plane mobility behaves as μ ∝ L^5.3, which closely follows the classic sixth power dependence expected from theory for interface-roughness-limited mobility. Fits to the mobility data indicate that, for one monolayer surface roughness, the roughness correlation length is about 35 Å. Next, we show that the in-plane carrier mobility in InAs/GaSb superlattices is inversely proportional to carrier density in n- and p-type samples, the result of screened interface roughness scattering.     

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic(hyperchaotic) maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features:(i) it enables synchronization to be achieved for both cases of n m and n m;(ii) it is rigorous,being based on theorems;(iii) it can be readily applied to any chaotic(hyperchaotic) maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map(as the drive system) and the three-dimensional hyperchaotic Wang map(as the response system),and the three-dimensional H′enon-like map(as the drive system) and the two-dimensional Lorenz discrete-time system(as the response system).     

A generalized RPA theory of the nuclear response function

A new method of calculating the response function is proposed. The new method gives the response which is explicitly a generalization of the RPA response in a perturbative sense.When we calculate the transition amplitude of a one-body operator from the ground state to a particle-hole (p-h) state, the new response function provides all the second-order effects in addition to the first-order ones which can be obtained in the RPA theory. The new response function is obtained by the following procedure. Firstly, we consider the second RPA theory which is a generalization of the usual RPA theory. It is found that the second RPA misses some of the second-order effects. Secondly, we formulate a modified second RPA equation from the equation of motion of the operators, and then derive the p-h response function from it. It is found that the newly derived p-h response function is obtained by adding new terms to the self-energy of the p-h response function derived from the second RPA theory. Lastly, we introducd vertex functions which take into account the transitions from a particle (hole) state to a particle (hole) state. Note that the p-h response function deals with only the transition amplitudes from a particle (hole) state to a hole (particle) state.