Lateral transport in quasiperiodically ordered layered media with isotropic randomness

We investigate the lateral wave transport in quasiperiodically ordered layer media with isotropic randomness. As an example, we consider the case of the Fibonacci sequence and study the ergodic properties in such systems. From the results of the channel occupation number of nine generations, we find that the wave transport in such systems falls between the transport of anisotropic hopping systems and that of randomly layered media and can be associated with a fractal dimension that can be tuned according to the strength of the layer coupling. The origin of this fractal dimensionality is attributed to the interplay between the quasiperiodic ordering in the layer direction and the presence of isotropic randomness in the system.     

The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

Quasi elasto-electromagnetic surface waves on a piezo-plasma-like layer

Considering a piezo-plasma-like layer with finite thickness and hexagonal symmetry whose main symmetry axis is parallel to the z axis and approximating it by an isotropic medium, we study the coupling of the elastic wave with plasma properties of the medium with and without spatial dispersion and collisions. In this case we investigate the coupled surface quasi elasto-electromagnetic wave propagating on the interface of piezoelectric layer with vacuum. Furthermore, the coupling of elasticity and ion-acoustic waves is investigated.     

Elastic–plastic transition in three-dimensional random materials: massively parallel simulations,fractal morphogenesis and scaling functions

Elastic–plastic transitions were investigated in three-dimensional (3D) macroscopically homogeneous materials, with microscale randomness in constitutive properties, subjected to monotonically increasing, macroscopically uniform loadings. The materials are cubic-shaped domains (of up to 100?×?100?×?100 grains), each grain being cubic-shaped, homogeneous, isotropic and exhibiting elastic–plastic hardening with a J ₂ flow rule. The spatial assignment of the grains’ elastic moduli and/or plastic properties is a strict-white-noise random field. Using massively parallel simulations, we find the set of plastic grains to grow in a partially space-filling fractal pattern with the fractal dimension reaching 3, whereby the sharp kink in the stress–strain curve of individual grains is replaced by a smooth transition in the macroscopically effective stress–strain curve. The randomness in material yield limits is found to have a stronger effect than that in elastic moduli. The elastic–plastic transitions in 3D simulations are observed to progress faster than those in 2D models. By analogy to the scaling analysis of phase transitions in condensed matter physics, we recognize the fully plastic state as a critical point and, upon defining three order parameters (the ‘reduced von-Mises stress’, ‘reduced plastic volume fraction’ and ‘reduced fractal dimension’), three scaling functions are introduced to unify the responses of different materials. The critical exponents are universal regardless of the randomness in various constitutive properties and their random noise levels.     

The exact response of a two-dimensional flat-layered medium to a probing pulse: An application to a layer stripping reconstruction procedure

Abstract

We consider a simple model problem that can be found in many fields of application such as, for example, reflection seismology. That is we consider an initial boundary value problem on a half-plane for a class of two-dimensional wave equations with a piecewise-constant coefficient. This coefficient describes the flat layered medium under consideration. An initial pulse located on the boundary of the half-plane is used to probe the medium. An integral representation of the solution of this problem is obtained by studying the spectral measures of some differential operators in one variable. This integral representation is exploited to obtain an ‘explicit’ formula for the solution of the problem considered evaluated at the location of the probing pulse. This ‘explicit’ formula is exploited to reconstruct the structure of the medium from its response to a probing pulse via a layer stripping procedure. Some numerical results obtained with this procedure on test problems are shown. The ‘explicit’ formula obtained can be used in several other contexts such as, for example, the study of perturbed flat layered media or the study of random flat layered media.     

Numerical solutions of matrix Riccati equations for radiative transfer in a plane-parallel geometry

Abstract

In this paper, we conduct numerical experiments with matrix Riccati equations (MREs) which describe the reflection (R) and transmission (T) matrices of the specific intensities in a layer containing randomly distributed scattering particles. The theoretical formulation of MREs is discussed in our previous paper where we show that R and T for a thick layer can be efficiently computed by successively doubling R and T matrices for a thin layer (with small optical thickness τ_Δ). We can compute R(τ_Δ) and T(τ_Δ) very accurately using either a fourth-order Runge–Kutta scheme or the fourth-order iterative solution. The differences between these results and those computed by the eigenmode expansion technique (EMET) are very small (<0.1%). Although the MRE formulation cannot be extended to handle the inhomogeneous term (source term) in the differential equation, we show that the force term can be reformulated as an equivalent boundary condition which is consistent with MRE methods. MRE methods offer an alternative way of solving plane-parallel radiative transport problems. For large problems that do not fit into computer memory, the MRE method provides a significant reduction in computer memory and computational time.     

Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles

An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal’s and Catalan’s triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems.     

Nonlinear waves in elastic media

We ask about the possible existence of solitary waves in infinite, homogeneous, isotropic, elastic media. Namely, can a nonlinear localized wave packet propagate without altering its shape in such materials? We consider one- dimensional propagation both of body and surface waves. In the first case we show, under rather general assumptions, that if a wave packet propagates without altering its shape it must, of necessity, be a solution of a linear wave equation and in this sense, (body) solitary waves do not exist. Surface solitary waves may however exist: a model equation is derived in which nonlinear and dispersive effects balance each other to allow for waves-both periodic and solitary-of constant shape. It is conceivable they are of some relevance in seismology.     

关于波导管的格林张量函数

本文以本征函数展开的方法,研究了波导管中格林函数的一般性质和形式。为了得到波导管的本征函数(简正波)和格林张量函数的一些关系,我们首先对格林函数作富氏变换,它的象函数在各向同性介质波导中以并矢形式作为最简单的表达方法,而在充有各向异性介质波导中可以表为ABA⁺e^-ikz₀的形式,这里A是坐标矩阵。用这种方法详细推导了均匀各向同性介质波导中的并矢格林函数。 关键词：     

The scattering of electromagnetic waves in fractal media

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

Statistical inversion from reflections of spherical waves by a randomly layered medium

Abstract

We show that the asymptotic theory developed for the analysis of reflected wave pulses from randomly layered media can be used to solve statistical inverse problems. In particular, we recover the large scale behavior of medium properties from a single realization of reflected wave pulses observed at different points on the surface.     

Parametric wave interaction in one-dimensional nonlinear photonic crystal with randomized distribution of second-order nonlinearity

We theoretically study the parametric wave interaction in nonlinear optical media with randomized distribution of the quadratic nonlinearity $\chi ^{(2)}$ . In particular, we discuss the properties of second and cascaded third harmonic generation. We derive analytical formulas describing emission properties of such harmonics in the presence of $\chi ^{(2)}$ disorder and show that the latter process is governed by the characteristics of the constituent processes, i.e. second harmonic generation and sum frequency mixing. We demonstrate the role of randomness on various second and third harmonic generation regimes such as Raman?CNath and ?erenkov nonlinear diffraction. We show that the randomness-induced incoherence in the wave interaction leads to deterioration of conversion efficiency and angular spreading of harmonic generated in the processes relying on transverse phase matching such as Raman?CNath interaction. On the other hand, the ?erenkov frequency generation is basically insensitive to the domain randomness.     

A multi agent model for the limit order book dynamics

By means of the Howard-Busse method of the optimum theory of turbulence we investigate numerically the effect of strong rotation on the upper bound on the convective heat transport in a horizontal fluid layer of infinite Prandtl number Pr. We discuss the case of fields with one wave number for regions of Rayleigh and Taylor numbers R and Ta where no analytical asymptotic bounds on the Nusselt number Nu can be derived by the Howard-Busse method. Nevertheless we observe that when R > 10⁸ and Ta is large enough the wave number of the optimum fields comes close to the analytical asymptotic result α₁ = (R/5)^1/4. We detect formation of a nonlinear structure similar to the nonlinear vortex discussed by Bassom and Chang [Geophys. Astrophys. Fluid Dyn. 76, 223 (1994)]. In addition we obtain evidence for a reshaping of the horizontal structure of the optimum fields for large values of Rayleigh and Taylor numbers.     

Enhancement of the backscattered intensity from fractal aggregates

Abstract

Comparative measurements were conducted for the backscattered intensities of light from uniform random and fractal aggregated media. Different features are found for the backscattered intensity peak shapes. A crossover between the θ^1?D and θ^?2 dependences of the backscattered intensity occurs in the case of fractal aggregated medium, where D indicates the fractal dimension.     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.     

含单负特异材料一维无序扰动周期结构中的光子局域特性研究

采用传输矩阵法研究了电磁波在由单负特异材料组成的一维无序扰动周期结构中的Anderson局域(Anderson Localization)行为,分别讨论了色散和非色散两种模型.结果发现,在对应周期结构的通带位置,无序的引入对局域长度的影响较大,而在带隙位置,影响较小,几乎可以忽略.该性质与我们曾讨论的随机结构有较明显不同.导致这种局域性质的主要原因应为,光在单负材料组成的系统中的传输主要依赖于两种单负材料间的界面.在无序扰动结构中,该界面数相对于周期结构并没有减少,因此对光的传输性质影响较小,而随机结构中     

Fractal structures in turbulence

We present a qualitative overview of our work on the issue of fractal structures in turbulence. We explain why fully developed turbulence is not space filling and describe how its fractal dimension can be estimated theoretically. The implications of the fractal nature of turbulence on transport processes like turbulent diffusion and on fluctuations in passive scalars are discussed. The latter affect wave propagation in turbulent media and these effects are examined. In addition we consider clouds in the atmosphere which are claimed to have fractal perimeters (or surfaces) and outline the physical reasons for this phenomenon. The fractal dimension of clouds is tied to the theory of turbulent diffusion and is computed theoretically. Indications of the road ahead are given.     

A coordinate–spectral method for rough surface scattering

Abstract

In this paper, we deal with the time-harmonic scattering by one-dimensional rough surfaces separating two homogeneous and isotropic media. The method is based on a rigorous integral formalism. The unknown of the integral equation is projected onto a Fourier basis while the equation itself is sampled as in a classical method of moments. The accuracy is tested against both other methods and experimental results. One of the main interests in choosing a Fourier basis lies in the ability to solve rigorously the scattering of a p polarized incident beam by a shallow metallic rough surface. The role of the surface waves is accurately taken into account and phenomena such as enhanced backscattering are well described. With this method, one can consider that the gap between the domain of validity of perturbation theories and the domain of practical use of rigorous methods is filled.     

New Trends in Magnetic Exchange Bias

The study of layered magnetic structures is one of the hottest topics in magnetism due to the growing attraction of applications in magnetic sensors and magnetic storage media, such as random access memory. For almost half a century, new discoveries have driven researchers to re-investigate magnetism in thin film structures. Phenomena such as giant magnetoresistance, tunneling magnetoresistance, exchange bias and interlayer exchange coupling led to new ideas to construct devices, based not only on semiconductors but on a variety of magnetic materials Upon cooling fine cobalt particles in a magnetic field through the Néel temperature of their outer antiferromagnetic oxide layer, Meiklejohn and Bean discovered exchange bias in 1956. The exchange bias effect through which an antiferromagnetic AF layer can cause an adjacent ferromagnetic F layer to develop a preferred direction of magnetization, is widely used in magnetoelectronics technology to pin the magnetization of a device reference layer in a desired direction. However, the origin and effects due to exchange interaction across the interface between antiferromagneic and ferromagnetic layers are still debated after about fifty years of research, due to the extreme difficulty associated with the determination of the magnetic interfacial structure in F/AF bilayers. Indeed, in an AF/F bilayer system, the AF layer acts as “the invisible man” during conventional magnetic measurements and the presence of the exchange coupling is evidenced indirectly through the unusual behavior of the adjacent F layer. Basically, the coercive field of the F layer increases in contact with the AF and, in some cases, its hysteresis loop is shifted by an amount called exchange bias field. Thus, AF/F exchange coupling generates a new source of anisotropy in the F layer. This induced anisotropy strongly depends on basic features such as the magnetocrystalline anisotropy, crystallographic and spin structures, defects, domain patterns etc of the constituant layers. The spirit of this topical issue is, for the first time, to gather and survey recent and original developments, both experimental and theoretical, which bring new insights into the physics of exchange bias. It has been planned in relation with an international workshop exclusively devoted to exchange bias, namely IWEBMN’04 (International Workshop on Exchange Bias in Magnetic Nanostructures) that took place in Anglet, in the south west of France, from 16th to 18th September 2004. The conference gathered worldwide researchers in the area, both experimentalists and theoreticians. Several research paths are particularly active in the field of magnetic exchange coupling. The conference, as well as this topical issue, which was also open to contributions from scientists not participating in the conference, has been organized according to the following principles: 1. Epitaxial systems: Since the essential behavior of exchange bias critically depends on the atomic-level chemical and spin structure at the interface between the ferromagnetic and antiferromagnetic components, epitaxial AF/F systems in which the quality of the interface and the crystalline coherence are optimized and well known are ideal candidates for a better understanding of the underlying physics of exchange bias. The dependence of exchange bias on the spin configurations at the interfaces can be accomplished by selecting different crystallographic orientations. The role of interface roughness can also be understood from thin-film systems by changing the growth parameters, and correlations between the interface structure and exchange bias can be made, as reported in this issue. 2. Out-of-plane magnetized systems: While much important work has been devoted to the study of structures with in-plane magnetization, little has been done on the study of exchange bias and exchange coupling in samples with out-of-plane magnetization. Some systems can exhibit either in-plane or out-of-plane exchange bias, depending on the field cooling direction. This is of particular interest since it allows probing of the three-dimensional spin structure of the AF layer. The interface magnetic configuration is extremely important in the perpendicular geometry, as the short-range exchange coupling competes with a long-range dipolar interaction; the induced uniaxial anisotropy must overcome the demagnetization energy to establish perpendicular anisotropy films. Those new studies are of primary importance for the magnetic media industry as perpendicular recording exhibits potential for strongly increased storage densities. 3. Parameters tuning exchange bias in polycrystalline samples and magnetic configurations: Different parameters can be used to tune the exchange bias coupling in polycrystalline samples similar to those used in devices. Particularly fascinating aspects are the questions of the appearance of exchange bias or coercivity in ferromagnet/antiferromagnet heterostructures, and its relation to magnetic configurations formed on either side of the interface. Several papers report on either growth choices or post preparation treatments that enable tuning of the exchange bias in bilayers. The additional complexity and novel features of the exchange coupled interface make the problem particularly rich. 4. Dynamics and magnetization reversal: Linear response experiments, such as ferromagnetic resonance, have been used with great success to identify interface, surface anisotropies and interlayer exchange in multilayer systems. The exchange bias structure is particularly well suited to study because interface driven changes in the spin wave frequencies in the ferromagnet can be readily related to interlayer exchange and anisotropy parameters associated with the antiferromagnet. Because the exchange bias is intimately connected with details of the magnetization process during reversal and the subsequent formation of hysteresis, considerations of time dependence and irreversible processes are also relevant. Thermal processes like the training effect manifesting itself in changes in the hysteretic characteristics depending on magnetic history can lead to changes in the magnetic configurations. This section contains an increasing number of investigations of dynamics in exchange bias coupled bilayers, and in particular those of the intriguing asymmetric magnetization reversal in both branches of a hysteresis loop. The Editors of the topical issue: Alexandra Mougin Laboratoire de Physique des Solides, UMR CNRS 8502, Université Paris Sud, F-91405 Orsay, France Stéphane Mangin Laboratoire de Physique des Matériaux, UMR CNRS 7556, Université Henri Poincaré, F-54506 Nancy, France Jean-Francois Bobo Laboratoire de Physique de la Matière Condensée - NMH, FRE 2686 CNRS ONERA, 2 avenue Edouard Belin, F-31400 Toulouse, France Alois Loidl Experimentalphysik V, EKM, Institut für Physik, Universität Augsburg, Universitätsstrasse 1, D-86135, Augsburg, Germany