Delocalization transition in one dimension

Singular extended states among random system localized states are proved to be a general rule. When a Fermi energy coincides with the extended state energy, a residual resistance becomes proportional to the square of the system length.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.     

Reentrant wetting transition of a rough wall

A 2D model describing depinning of an interface from a rough, self-affine substrate, is studied by transfer matrix methods. The phase diagram is determined for several values of the roughness exponent, ζs, of the attractive wall. For all ζs > 0 the following scenario is observed. In first place, in contrast to the case of a flat wall (ζs = 0), for wall attraction energies between zero and a ζs-dependent positive value, the substrate is always wet. Furthermore, in a small range of attraction energies, a dewetting transition first occurs as T increases, followed by a wetting one. This unusual reentrance phenomenon seems to be a peculiar feature of self-affine roughness, and does not occur, e.g., for periodically corrugated substrates.     

Excitation of lateral waves on a rough interface

Institute of Oceanography, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 7, pp. 823–831, July, 1989.     

Pinning of a rough interface by an external potential

An analysis is given of the behavior of an interface between two phases in the presence of an external pinning potential in the solid-on-solid limit of the two-dimensional Ising model. It is found that the potential turns a rough interface into a smooth one, except in the case of a boundary potential, where a minimum potential strength is required. The connection with the roughening transition found by Abraham is discussed. The interface width is calculated as a function of the potential parameters in the limit of a weak pining potential.     

Magnetic phase diagram of a ferromagnet-antiferromagnet bilayer with a rough interface

The thickness-roughness phase diagram of a thin ferromagnetic film on an antiferromagnetic substrate is studied in the case where the roughness of the interface between the layers causes frustration of the exchange interaction between them. It is shown that the inclusion of single-ion anisotropy makes the phase diagram significantly more complicated in comparison with that calculated within the exchange approximation. The evolution of a new type of domain walls caused by frustrations is traced with an increase in the film thickness and the width of the atomic steps on the film-substrate interface.     

Damping of the magnetoplasmon propagating along a rough dielectric-semiconductor interface

The damping of a surface magnetoplasmon propagating along a rough dielectric-semiconductor interface is considered. The interaction between charge carriers in the semiconductor and the boundary has been taken into account both in the “specularity parameter” and a microscopic model of the boundary. The effective surface relaxation frequency has been analyzed as a function of the boundary parameters and the magnetic field.     

Electromagnetic wave diffraction by a rough interface of homogeneous isotropic media

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 4, pp. 451–460, April, 1989.     

固体粗糙界面与超声的非线性相互作用研究

本文提出了一种随机弹性接触界面与超声的非线性相互作用理论. 首先建立了描述随机弹性接触界面的模型, 然后分别研究了界面间应力-应变关系在线性简化模型、指数模型、高斯模型下与超声的非线性相互作用. 数值仿真和实验研究结果均表明高斯模型更适合描述固体接触界面. 本文在介观结构上解释了固体界面与超声的相互作用, 对工业超声无损检测裂缝、缺陷及损伤有指导意义. 关键词： 超声无损检测 固体粗糙界面 非线性效应     

Ultrasonic backward radiation profile on painted rough interface

Generalized Lamb surface waves are generated in a surface region when ultrasonic waves are incident to the layered substrates such as painted specimen in liquid. Then, backward radiated waves are returned to the direction of incidence by scattering and energy radiation of the surface waves. Hence, the backward radiation could be used in assessing the interracial state between layer and substrate because the surface wave is sensitive to the change of physical properties in a surface region. Painting surface treatment of commercial products and articles occasionally hide the surface region trouble such as roughness and crack. The evaluation of interfacial state under painting layer is very important in the prevention of great accidence, hence the evaluation technique should be nondestructive, fast and easy applicable to the fields. The backward radiations were measured for the painted glass with periodic interfacial roughness immersed in water tank. The effect of interfacial roughness on the angular pattern and frequency spectrum of the ultrasonic backward radiation was investigated to develop the nondestructive technique for interfacial roughness evaluation.     

Explicit results for wave scattering and transmission through a rough fluid-fluid interface

This paper describes an analysis of reflection and transmission of acoustic waves from an imperfectly reflecting, rough fluid-fluid interface within the Kirchhoff approximation. It presents the results of calculations of the coherent and diffuse field. This work is motivated by the fact that few explicit results of the characteristics of the scattered and transmitted wave field exist in the literature for this problem. For the problem of interest, the surface reflection coefficient depends at each point upon the local angle between the incident wave and the rough surface. For surfaces with statistically independent local surface position and gradient, coherent field calculations show that the correction to constant reflection coefficient analyses is simply a multiplicative factor that depends upon the statistical characteristics of the surface gradient, sound speed and density ratio across the surface. This multiplicative factor is interpreted as an average reflection or transmission coefficient, <R> and <T>, respectively. The principle differences between these results and constant reflection coefficient analyses occur when waves impinge upon regions with higher sound speeds, where total internal reflection may occur. While the wave characteristics of smooth or constant reflection coefficient surfaces change abruptly in the vicinity of the angle of total internal reflection, the average reflection coefficient exhibits a much smoother dependence upon angle of incidence or sound speed ratio for rough surfaces. It is also shown that the direction of maximum diffuse scattering moves relative to its value were the reflection coefficient constant.     

Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

Boundary conditions for an electromagnetic field in the presence of a rough interface

Kharkov State University. Translated from Izvestiya Vysshikh Uchebykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1091–1096, September, 1989.     

On the interface pinning transition

Using the continuous form of the solid-on-solid model with an additional gaussian pinning potential an increase of the width of the potential is found near the roughening transition. The power-law behaviour of the width is given by application of the renormalization-group approach.     

A finite element approach for scattering from inhomogeneous media with a rough interface

Electromagnetic scattering from an inhomogeneous medium with a one-dimensional rough interface is analysed. The proposed procedure combines the finite element method (FEM), to model the electromagnetic field in the inhomogeneous region, with a perturbative technique to account for the contributions due to the rough interface. Backscattering and bistatic scattering coefficients are computed and plotted for both plane wave and Gaussian beam incident fields in the case of TM_z polarization.     

Laplacian transfer across a rough interface: numerical resolution in the conformal plane

We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can be efficiently treated in the conformal plane. We show in particular that an expansion of the potential on a basis of evanescent waves in the conformal plane allows to write a well-conditioned 1D linear system. These general principle are illustrated by numerical results on rough interfaces.     

亲水性微观粗糙表面润湿状态转变性能研究

以亲水性微观粗糙表面上不同几何形貌及分布的微柱阵列为对象, 讨论了液滴在亲水性粗糙表面上的润湿过程以及润湿状态的转变阶段. 从能量角度分别考察了微观粗糙结构几何形貌及分布、微柱几何参数、固体表面亲水性、接触角滞后作用等因素对液滴润湿状态转变的影响规律. 研究发现: 在亲水粗糙表面, 正方形微柱呈正六边形阵列分布时, 液滴更容易形成稳定的Cassie状态, 或者液滴仅发生Cassie状态向中间浸润状态的转变; 与此同时, 减小微柱间距、增大方柱宽度或圆柱直径、增大微柱高度、增强固体表面的亲水性将有利于液滴处于稳定的Cassie状态, 或阻止润湿状态向伪-Wenzel或Wenzel状态转变; 然而, 当液滴处于Cassie状态时, 较小的固-液界面面积分数或减弱固体表面亲水性能均有利于增大液滴的表观接触角, 因此在亲水表面设计粗糙结构时应综合考虑润湿状态稳定性和较大表观接触角两方面因素; 此外, 接触角滞后作用对于液滴状态的稳定性以及疏水性能的实现具有相反作用的影响. 研究结果为液滴在亲水表面获得稳定Cassie状态的粗糙结构设计方法提供了理论依据. 关键词： 亲水表面 微观粗糙结构 表面自由能 润湿状态转变