Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk “poor conductors” in which Fermi energy E_F is located in the region of localized states not so far from the Anderson mobility edge E_c. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: ‘critical’ superconductive state formed at E_F = E_c, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E_F still deeper inside a localized band. The ‘critical’ superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap Δ, that is due to many-body correlations and a new “pseudo-gap” energy scale Δ_P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T_c. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to the presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T) ∼ 1/T.Based on these results we propose a new “pseudo-spin” scenario of superconductor-insulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.     

Reflection and transmission coefficients for diffuse photon density waves

Diffuse photon density waves are proposed for use in characterizing diffuse media, similar to the use of electromagnetic waves to characterize reflection from materials. To this end basic expressions for the reflection and transmission coefficients at interfaces are put forward. Effects such as the existence of modes analogous with Brewster modes are shown. Also, we illustrate through numerical simulations how the diffusion optical parameters are estimated both with and without noise in the data.     

Reflection and transmission of waves in pyroelectric and piezoelectric materials

The reflection and transmission theories of waves in pyroelectric and piezoelectric medium are studied in this paper. In general in an infinite homogeneous pyroelectric medium there are four bulk wave modes: quasi-longitudinal, two quasi-transversal and temperature waves. In an infinite homogeneous piezoelectric medium there are three bulk wave modes: quasi-longitudinal and two quasi-transversal waves. In the reflection and transmission problem there are five complex boundary conditions in the pyroelectric medium and four complex boundary conditions for the piezoelectric medium. In this paper, we find that the surface waves will be revealed in the reflection and transmission wave problem. The surface waves have the same wave vector component with the incident waves on the interface plane. The two dimensional reflection problem of waves at the interface between the semi-infinite pyroelectric medium and vacuum is researched in greater detail and a numerical example is given.     

Reflection and transmission of circularly polarized waves in nonlinear dielectrics

A time-sinusoidal circularly polarized plane standing wave solution is obtained for isotropic lossless dielectric media with arbitrary nonlinearity. The spatial variation of the standing wave depends on the nonlinearity and is found by solving a problem of centralforce motion in which the electric complementary energy density furnishes the potential and the spatial coordinate has the role of time. Two special nonlinear dielectric response laws-cubic and quintic-are treated, and explicit solutions for the spatial variation of the wave amplitude and phase are obtained in terms of elliptic functions and elliptic integrals, respectively. The standing-wave solution is applied to give steady state solutions of two reflection/transmission problems (a) reflection from, or resonance modes between, ideally conducting planes and (b) reflection and transmission at a plane interface between two nonlinear dielectric media.     

Reflection and transmission of acoustic waves on multilayered porous media

Based on the Boit theory of acoustic wave propagation in fluid-satu-rated porous medium we have studied in this paper the acoustic reflection andtransmission on multilayered porous media,in which the adequate boundaryconditions across the interfaces are taken into account.Numerical calculationsof the reflection and transmission coefficients at different incident angles andfrequencies of the fast compressional wave incident on porous media with threeor four layers are presented.The results indicate that the maximum or mini-mum reflection and transmission coefficients appear at certain ratios of thewavelength to the thickness.The acoustic incident angle and porous mediumproperties are shown to affect significantly these coefficients.As an example,the measured transmission coefficients in a water-saturated fused glass beadsample are in good agreement with theoretical prediction.     

Reflection and transmission of plane waves at the interface of pyroelectric bi-materials

A simple reflection and transmission theory of plane waves at the interface of pyroelectric media is studied in this paper. In an infinite homogeneous pyroelectric medium, there are four bulk wave modes: quasi-longitudinal (QL), two quasi-transversal (QT) and one temperature (T) waves, whose velocities depend on the frequency and incident angle. Simultaneously, a quasi-surface (QS) wave on each side of the interface of pyroelectric bi-materials will appear in the general reflection and transmission problem. The quasi-surface wave has the same wave vector component with the incident waves along the interface plane. So, the reflection and transmission problem is different with the propagation wave in the infinite homogeneous space, but it is still solvable. In the reflection and transmission problem, there are ten complex continuous conditions on the interface, which are satisfied by the bulk and quasi-surface waves together. Numerical calculations are performed for bi-material PZT-6B/BaTiO₃. Incidences of the quasi-longitudinal and quasi-transversal waves from the side of PZT-6B or BaTiO₃ medium are discussed. The reflection and transmission amplitude coefficients and energy flow ratios varying with the incident angle are examined.     

Behavior of reaction-diffusion waves with fast activator diffusion near propagation threshold

Numerical simulation is performed to analyze behavior of reaction-diffusion waves in a medium whose parameters are near both the propagation threshold and diffusive (oscillatory) instability boundary. The wave decays in the subthreshold parameter region and propagates at a constant velocity in the parameter region well above the threshold. Just above the threshold, the wave velocity exhibits alternate intervals of chaotic and constant-amplitude oscillations. The transition from steady to chaotic propagation is a sequence of period-doubling bifurcations that occupies a narrow interval of the bifurcation parameter. In the subthreshold region, the wave decay time is a random function of the bifurcation parameter increasing on average toward the threshold.     

Nonlinear growth rate of wind water waves and their excitation near the stability threshold

The amplitude dependences of the growth rate of water waves generated by turbulent wind are theoretically investigated within the framework of a quasilinear approximation.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 206–210, March–April, 1995.     

Reflection and transmission of plane electromagnetic waves in uniaxial bianisotropic materials

Electromagnetic waves in the most general linear reciprocal uniaxial media are considered. The theory is appropriate for novel reciprocal microwave materials which have properties of chiral composites and omega structures (or both) and can be modeled by uniaxial bianisotropic constitutive relations. Field coupling terms in the media equations are assumed to be the most general uniaxial dyadics with symmetric and antisymmetric components. Plane eigenwaves in unbounded media are studied and the theory of reflection and transmission in plane layers is constructed.     

单轴各向异性手征介质平板的反射和透射特性研究

研究了光轴平行于界面的单轴各向异性手征介质平板对平面电磁波的反射和透射特性, 推导出了反射和透射系数(功率)公式; 按介电常数的正负分4种情形给出了反射和透射功率曲线; 讨论了手征参数对反射和透射特性的影响, 特别是给出了伪布儒斯特角与手征参数的变化关系曲线. 关键词： 单轴各向异性手征介质 手征参数 伪布儒斯特角 反射和透射     

Reflection and transmission characteristics of ultrasonic guided waves in fractured long bone

Assessment of fractured long bone using ultrasonic guided wave（GW） has gained considerable attention.This paper focuses on using the hybrid boundary element method （HBEM） to analyze the propagation characteristics of ultrasonic GW in fractured long bones. The reflection coefficients（RC） and transmission coefficients（TC） for different depth-to-width ratio（d/w） cracks were numerically calculated and analyzed.It has been shown that the primary output modes,which include the transmission and reflection modes,are the same as the incidence modes.For some cracks,different TC curves always got the local maxima in adjacent frequencies.For different d/w cracks,most of the TC curves had local maxima which are not overlapped.These simulation results are helpful to optimize the modes and frequencies of the incidence GWs for quantitatively evaluating the bone quality and providing the numeral results of the cracks in long cortical bones.     

Reflection and transmission of electromagnetic plane waves from an uniaxial chiro-omega slab

Chiro-omega medium is a combination of the reciprocal chiral and omega media, and can be obtained by mixing helical and — shaped wire elements in the host medium. In this article the most general uniaxial chiro-omega medium is studied. The solutions for the dispersion equations and corresponding eigenwaves are derived. Transmission and reflection properties of a chiro-omega slab at a normal incidence are studied, and the polarization, direction of the polarization ellipse, and relative powers of transmitted and reflected waves are given. The results are applied to find suitable parameters for designing a polarization transformer. These results are compared with those obtained in earlier studies on wave propagation in a free uniaxial chiral space, where the effect of the boundaries of a proposed polarization transforming device have been neglected.     

Reflection and transmission of plane waves from a fluid-porous piezoelectric solid interface

The reflection and transmission of plane waves from a fluid-porous piezoelectric solid interface is studied. The porous piezoelectric solid, having 6 mm symmetry, is supposed to be filled with viscous fluid. The expressions for amplitude ratios and energy ratios corresponding to reflected wave and transmitted waves are derived analytically. The Christoffel equation of a leaky wave propagating along the surface of a porous piezoelectric solid is derived. The effects of the angle of incidence, frequency, porosity, piezoelectric interaction, and anisotropy on the reflected and transmitted energy ratios are studied numerically for a particular model BaTiO(3). The porous piezoelectric solid half space is assumed to be loaded with water. The effects of porosity and frequency on the leaky wave velocity are also studied.     

Reflection and transmission of plane waves at the interface between anisotropic random discrete media

The Maxwell equations are solved for a random discrete medium using the single-scattering approximation and the condition of immersion in a maximally packed medium. The reflection and transmission factors of plane waves at the interface between vacuum and a random discrete anisotropic medium are determined. The calculated and experimental results on reflection and transmission of plane waves near the edge of a forest as an example of natural anisotropy of a random discrete medium are compared.     

压电晶体-液体-各向同性固体分层结构中的声反射和声透射

本文给出由压电晶体－液体－各向同性固体组成的分层结构中声反射和声透射的一些理论结果，与不考虑介质压电性的情形相比，反射和秀射声场具有大的复杂性，与晶体取向，界面电边界条件等均有关。