Academic literature on the topic 'Wave scattering coefficient'

By considering a simple one-dimensional Gross–Pitaevskii equation with variable coefficient, we study various rogue waves by the choice of different trapping potential coefficient. The trapping potential coefficient is used as an independent parameter function; a simple procedure is established to obtain different chasses of the scattering length and rogue wave solutions by using similarity transformation. A few properties of rogue wave solutions are also discussed. Our results demonstrate that the rogue waves can be controlled by selecting appropriate trapping potential coefficients.

The momentum-space diffusion equation and the kinetic wave equation for resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma are derived from the relativistic Vlasov–Maxwell equations by perturbation theory. The p-dependent diffusion coefficient and the nonlinear wave—wave coupling coefficient are given in terms of third-order tensors which are amenable to analysis. The transport equations describing energy and momentum transfer between waves and particles are obtained by momentum-space integration of the momentum-space diffusion equation, and are expressed in terms of the nonlinear wave—wave coupling coefficient in the kinetic wave equation. The conservation laws for the total energy and momentum densities of waves and particles are verified from the kinetic wave equation and the transport equations. These equations are very useful for the theoretical analysis of transport phenomena or the acceleration and generation of high-energy or relativistic particles caused by quasi-linear and resonant wave—wave scattering processes.

Scattering of oblique surface gravity waves by a finite, floating porous-elastic plate is investigated, with assumptions of linear water wave theory and plate response. A boundary value problem is set up, wherein the thin plate equation together with a porosity parameter is used to formulate the condition on the floating plate. A matched eigenfunction approach is adopted for the solution of this problem, with roots of the dispersion relation being located with the aid of contour plots, and various hydrodynamic scattering quantities are computed. Energy dissipation due to plate porosity is seen to have a significant impact on both reflection and transmission of waves, while flexibility of plate only alters the extent of wave reflection by porous elastic plates. An oscillatory trend is shown by reflection coefficient for smaller values of relative plate width, and there is no variation in reflection or transmission coefficients when the plate width is increased beyond a certain cut-off value. Comparison of scattering properties of four different types of plates highlights the effects of porosity and flexibility and establishes the superiority of a flexible porous plate as a wave attenuating device, with moderate reflection, high energy dissipation and low transmission.

Bragg scattering of surface gravity waves by an array of submerged bottom-standing non-smooth breakwaters is studied under the assumption of linearized long wave theory. The closed-form long-wave analytical solutions are derived and validated by comparing them with the results available in the literature. The role of various physical parameters such as breakwaters friction coefficient, depth, width and gap between the adjacent breakwaters are investigated by analyzing the reflection and transmission coefficients. Further, the time-domain simulation for the scattering of long gravity waves over multiple breakwaters is analysed for different values of parameters of breakwaters. The results reveal that the rough surface of the breakwater plays a vital role in reducing wave reflection and transmission. Moreover, it is observed that the transmitted wave dissipates completely for larger values of friction parameters. For certain critical angles, change in wave dissipation becomes maximum due to the variation of phase of the incident wave. Various findings can be considered as benchmark results for the design of the non-smooth structures to attenuate the waves based on the Bragg reflection.

Elastic waves cause energy loss during the transmission of coal measures. These losses include propagation loss, dielectric absorption loss, scattering loss, and frequency migration loss. The absorption loss is mainly caused by the inelastic absorption. The scattering loss is caused by the uneven heat absorption in the formation. The frequency shift loss is caused by the piezoelectric effect of coal-bearing formations and the intermodulation of different frequency signals. After considering the influence factors of the coal seam structure, this paper presents a model of low-frequency elastic waves loss coefficient. The paper proposed the loss coefficient of the elastic wave in the coal measure strata by considering two main attenuation mechanisms: intrinsic absorption and scattering. This paper theoretically studied the effects of the model parameters such as density, porosity, particle size, and wave frequency on the loss of wave energy using COMSOL simulation. Besides, the comparison of MATLAB simulation results shows that the simulation results produced by the model proposed in this paper are similar to the models embedded in COMSOL. This work can be applied to coal, oil, and gas exploration and is also helpful to study the mechanisms of wave attention on the low-frequency band.

In order to analyze the scattering characteristics of sea surface under high sea state, a complete scattering model of sea surface considering breaking wave is established in this study based on the refined facet scattering field model (RFSFM) and the scattering theory of breaking wave. On the basis of this model, the influence of breaking waves on the mono/bistatic SAR imaging of sea surface at HH and VV polarization is studied. The results show that with the increase in wind speed, the coverage of breaking wave increases obviously and the consideration of breaking wave has a good correction for the scattering coefficient at HH polarization under grazing incidence; however, for VV polarization, the effect of breaking wave is very small.

Acoustic wave scattering from a randomly rough surface is studied using a multiple scattering analysis. Assuming the surface asperities to be small, approximate boundary conditions are used to derive a pair of coupled integral equations for the velocity potentials. The Dyson equation is next derived on introducing symbolic operators. Using the bilocal approximation the Dyson equation is solved, thereby obtaining explicit expressions for the coherent reflection and transmission coefficients. The analysis is similarly carried on further to compute the incoherent intensity by using the ladder approximation, and hence an expression for the scattering coefficient is obtained.

The interaction of Love waves with a surface-breaking crack normal to the free surface is investigated. By the use of Fourier transform techniques, the mixed-boundary value problem is reduced to a singular integral equation which is solved numerically. It is shown that the reflected and transmitted displacement fields at some distance from the crack are the superposition of a finite number of Love-wave modes. The reflection coefficients for the first three modes and the transmission coefficient are plotted versus the frequency. Several sharp resonances are observed. Each resonance corresponds to the vanishing of the amplitude of a particular Love-wave mode.

AbstractWave attenuation in a diffuse marginal ice zone (MIZ) is thought to be mainly a result of wave scattering. In a compact MIZ, additional physical factors are thought to be relevant. In this paper, we propose that viscous drag, form drag and energy lost to internal waves under the ice play a role in attenuating wave energy. We derive a relation for the wave attenuation due to drag. We combine the drag attenuation coefficient with the scattering attenuation coefficient and compare the result to experimental results for compact MIZs. We find that the combined scatter and drag (CSD) model improves the rate of decay of wave attenuation in compact ice fields, but fails to predict the ‘rollover’ seen at short periods.

SUMMARY The isotropic scattering model is a simple mathematical model of the radiative transfer theory (RTT) for the propagation of the wave energy density in random media. There have been many measurements of the isotropic scattering coefficient of the heterogeneous solid earth medium, where the target region varies from the lower and upper mantle, the crust, sediments, volcanoes, mines, rock samples and also the crust and the upper mantle of the moon. Reported isotropic scattering coefficients increase according to some power of frequency with some scatter. We know that the RTT is well approximated by the diffusion equation in the multiple scattering regime, where the equipartition is established. Then, the transport scattering coefficient effectively functions as an isotropic scattering coefficient even if the scattering coefficient derived by the Born approximation for the random velocity fluctuation is anisotropic. Recent review of the power spectral density functions of random velocity fluctuations in the solid earth revealed from various kinds of measurements shows that their spectral envelope is well approximated by the inverse cube of wavenumber for a wide range of wavenumbers (Sato, 2019). The transport scattering coefficient derived from the spectral envelope linearly increases with frequency, which well explains the observed isotropic scattering coefficients for a wide range of frequencies. However, some reported isotropic scattering coefficients show unusual behaviour: the isotropic scattering coefficient increases as depth decreases in the crust and the upper mantle of the earth and the moon, those beneath volcanoes are larger than those in the lithosphere, and that in a sandstone sample with a large porosity is larger than that in a gabbro sample with little porosity. Those differences may suggest possible scattering contribution of pores and cracks widely distributed in addition to the scattering by random velocity fluctuations.

Viele Problemstellungen der Naturwissenschaften führen zur Betrachtung von nichtlinearen Wellengleichungen. Dabei ist von großem Interesse, ob zu vorgegebenen kleinen Daten Lösungen eindeutig existieren und ob diese stetig von den Daten abhängen. Hilfsmittel für diese Probleme sind Aussagen über lineare Wellengleichungen. In der vorliegenden Arbeit werden lineare Klein-Gordon Gleichungen, also Wellengleichungen mit Potentialterm, mit zeitabhängiger Masse bzgl. des Verhaltens ihrer Lösungen untersucht. Von speziellem Interesse sind Resultate mit Bezug auf verallgemeinerte Energieerhaltung und sogenannte Lp – Lq decay-Abschätzungen. Aus der Arbeit geht hervor, dass man eine Klassifizierung für Gleichungen mit fallendem Masseterm finden kann. Für Gleichungen vom Wellentyp ist der Einfluss des Potentialterms gering und die Lösungen verhalten sich wie Lösungen der Wellengleichung. Dem gegenüber stehen Gleichungen vom Klein-Gordon-Typ mit erkennbarem Einfluss des Masseterms. Ausgangspunkt für die Klassifizierung ist das kritische Verhalten der Lösungen einer skaleninvarianten Gleichung mit speziellem Masseterm.

Mesure des coefficients d'attenuation des elements de numero atomique 46 a 54 dans le domaine 15 a 45 kev. Determination des parametres de la loi de variation empirique du coefficient d'attenuation en fonction de la longueur d'onde du rayonnement. Determination des facteurs de diffusion anomale vers l'avant, en utilisant la relation de dispersion

Using the method of matched asymptotic expansions the reflection and transmission coefficients are calculated for scattering of oblique water waves by a vertical barrier. Here an assumption is made that the barrier is small compared to the wavelength and the depth of water. A number of sloshing problems are considered. The eigenfrequencies are calculated when a body is placed in a rectangular tank. Here the bodies considered are a vertical surface-piercing or bottom-mounted barrier, and circular and elliptic cylinders. When the body is a vertical barrier, the eigenfunction expansion method is applied. When the body is either a circular or elliptic cylinder, and the motion is two-dimensional, the boundary element method is applied to calculate the eigenfrequencies. For comparison, two approximations, "a wide-spacing", and "a small-body" are used for a vertical barrier and circular cylinder. In the wide-spacing approximation, the assumption is made that the wavelength is small compared with the distance between the body and walls. The small-body approximation means that a typical dimension of the body is much larger than the cross-sectional length scale of the fluid motion. For an elliptic cylinder, the method of matched asymptotic expansions is used and compared with the result of the boundary- element method. Also a higher-order solution is obtained using the method of matched asymptotic expansions, and it is compared with the exact solution for a surface-piercing barrier. Again the assumption is made that the length scale of the motion is much larger than a typical body dimension. Finally, the drift force on multiple bodies is considered the ratio of horizontal drift force in the direction of wave advance on two cylinders to that on an isolated cylinder is calculated. The method of matched asymptotic expansions is used under the assumption that the wavelength is much greater than the cylinder spacing.

Thesis (M.S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2005.
Laurence J. Jacobs, Committee Chair ; Reginald DesRoches, Committee Member ; Jianmin Qu, Committee Member. Includes bibliographical references.

The estimation of radar cross section (RCS) of randomly rough surfaces is essential for designing terrain and sea surface remote sensing systems. The particular problem of wave scattering at low grazing angles is of great interest because of its importance for the low-altitude/long-range radar surveillance, target tracking, communication and navigation systems operating at low grazing conditions above the rough surface. The radar cross section from a rough surface becomes very small at grazing incidence, since most part of the incident power is scattered around the specular direction (depending on the degree of surface roughness). Moreover, the dominant scattering mechanisms at low and high grazing angles are different e. G. , the effects of multiple scattering (or higher order scattering), shadowing, fading and mechanisms attributable to wave breaking are particularly marked in the low grazing angle regime. Therefore, in this context the research has been conducted in this thesis. A second order two-scale model (TSM2) has been developed to study the bistatic scattering enhancement at grazing angles and the accurate depolarization estimation in a radar return. The applications of TSM2 are presented for sea and bare soil surfaces. The results obtained from newly developed model are compared with the available experimental data and other models to demonstrate the validity and efficiency of TSM2
L’estimation de la surface équivalente radar (SER) des fouillis de mer et terrestre est essentielle pour la conception et l’amélioration des performances des systèmes de télédétection et d’observation de la planète. Le problème particulier de la diffusion des ondes en configuration à angle rasant est de grand intérêt à cause de son importance pour la surveillance, suivi de cible, la communication et les systèmes de navigation fonctionnant au-dessus de surfaces rugueuses, terrestre ou maritime. La surface équivalente radar d’une surface rugueuse devient très faible en incidence rasante puisque la plus grande partie de la puissance incidente est diffusée dans la direction spéculaire (selon le degré de rugosité de k surface). De plus, les mécanismes principaux de diffusion sont différents aux angles rasants, par exemple, les effets de diffusion multiple (ou de diffusion d’ordre supérieur), l’ombrage, fading et les mécanismes liés au déferlement des vagues sont particulièrement présents dans une telle configuration. Par conséquent, c’est dans ce contexte que s’intègre les travaux de recherche développés dans cette thèse. Ceci en développant le modèle deux échelles à l’ordre 2 (TSM2) permettant ainsi de contribuer à l’estimation des coefficients de diffusion bistatique par les surfaces rugueuses avec l’application de ce modèle aux surfaces maritime et terrestre. L’évaluation du modèle développé est réalisée en effectuant des comparaisons par rapport aux résultats obtenus avec d’autres modèles et aussi aux données issues de la littérature ouverte

Le travail réalisé dans cette thèse s'intègre globalement dans le cadre de I'observation et la surveillance maritime.Afin d'améliorer la reconnaissance et I'identification automatique de cibles noyées dans un environnement perturbé, nous avons opté à la fusion de différentes connaissances et informations concernant une scène observée à distance par des capteurs micro-ondes. En effet, plusieurs phénomènes physiques co-existent et perturbent la propagation des ondes électromagnétiques au-dessus d'une surface et notamment au-dessus d'une surface maritime hétérogène (la réfraction due aux gradients d'indice, la rugosité de la surface de mer, les effets hydrodynamiques non linéaires du type vagues déferlantes, la présence d'objets, les polluants, sillage de navires, zones côtières, ...). Dans ce contexte, le travail présenté dans cette thèse porte sur l'étude de la signature électromagnétique (coefficients de diffusion) d'une surface maritime hétérogène avec la prise en compte des phénomènes hydrodynamiques (linéaires : vagues de capillarité et de gravité, non linéaires : vagues déferlantes). Cette estimation de la signature électromagnétique est effectuée en configuration bistatique (monostatique et propagation avant) et en bande X. L'étude complète de cette problématique est difficile. En effet, le déferlement est un processus dissipatif de l'énergie qui correspond à la dernière étape de la vie d'une vague et qui a donc le plus souvent lieu à I'approche du rivage. Ce phénomène non linéaire produit un pic de mer qui est une augmentation rapide des coefficients de diffusion et qui peut dépasser 10 dB dans une période de 100 ms. Ce pic peut conduire à des échos parasites, qui peuvent être identifiés comme des cibles virtuelles, et par la suite elles peuvent perturber le système de détection radar (fausses alarmes). Par conséquent, pour améliorer le processus de détection et pour réduire le taux de fausses alarmes, il est important de distinguer entre les cibles et les pics de mer générés par des vagues déferlantes. Ceci constitue I’une des motivations et aussi I'intérêt d'étudier la signature électromagnétique des vagues déferlantes dans différentes configurations d'observation de sorte que nous puissions facilement indiquer la présence voir I'identification des pics de mer. Pour contribuer à cette problématique, nous avons proposé une méthodologie basée sur un modèle électromagnétique hybride basé sur une combinaison d'une part de méthodes asymptotiques(SPMI utilisée dans le cadre de ce travail) pour simuler la réponse radar des vagues linéaire (vagues de capillarité et de gravité décrites via le spectre de mer d'Elfouhaily), et d'autre part de méthodes exactes (MoM, FB < Forward-Backward ) retenue dans le travail présenté dans ce manuscrit) pour calculer la réponse électromagnétique des vagues non-linéaires (profils considérés sont issus des résultats du code LONGTANK). Afìn de compléter l'étude théorique et les simulations réalisées, nous avons effectué une phase d'évaluation et de validation par des mesures de signature radar réalisées dans la chambre anéchoïque de I'Ensta Bretagne
The work done in this thesis fits generally under the observation and maritime surveillance. To improve the detection and automatic identification of targets embedded in a noisy environment targets, we opted for the fusion of different knowledge and information regarding a remotely observed scene by microwave sensors. Indeed, several physical phenomena co-exist and interfere with the propagation of electromagnetic waves over a heterogeneous sea surface (the refraction due to the index gradients, the roughness of the sea surface, nonlinear hydrodynamic effects like waves breaking, the presence of objects, pollutants, ship wake, coastal areas,..). In this context, the work presented in this thesis focuses on the study of electromagnetic signature (diffusion coefficients) of a heterogeneous sea surface with consideration of hydrodynamic phenomena (linear: capillary and gravity waves, nonlinear: breaking waves). The electromagnetic signature is performed in bistatic configuration (monostatic and forward propagating) and in X-band. The complete study of this problem is difficult.Indeed, the breaking wave is a dissipative process of energy that corresponds to the last stage of the life of a wave and therefore has most often held in the shore. This nonlinear phenomenon produces a sea peak which is a rapid increase of the diffusion coefficients and can exceed l0 dB in a 100 ms period. This peak can lead to clutter, which can be identified as virtual targets, and then they can disrupt the detection radar system (false alarms). Therefore, to improve the detection process and reduce the false alarm rate, it is important to distinguish between targets and sea peaks generated by breaking waves. This represents one of the motivations and also the interest to study the electromagnetic signature of breaking waves in different observation configurations so that we can easily detect and identify the sea peaks. To solve this problem, we proposed a methodology based on a hybrid electromagnetic model which is on a combination of asymptotic methods (SPMI used in this work) to simulate the radar response of linear waves (capillary and gravity waves described via the Elfouhaily sea spectrum) and an exact methods, the method of moment (the FB "Forward-Backward" method is used in this work), to calculate the electromagnetic response of nonlinear waves (profiles are produced by the LONGTANK code). To complement the theoretical study and simulations, we carried out an evaluation and validation phase by measuring the radar signature of breaking wave profiles in the ENSTA Bretagne anechoic chamber

Ultrasonic guided wave-based detection of structural defects or damages is one of the promising methods for structural health monitoring (SHM). A significant proportion of structural elements in an aircraft structure and other civil and marine structures are thin structures and those components can be monitored using ultrasonic guided wave. Piezoelectric transducers have been extensively applied to ultrasonic wave based non-destructive inspection (NDI). SHM is considered an extension of NDI adding a new dimension to the way future structures will be designed. In recent years, research on the behavior of guided wave in structures, especially targeted for aerospace application, received enormous significance. Guided wave interaction with structural features and defects/damages creates complicated wave field patterns. Experimental observation is limited to the availability of sophisticated instrumentation and tomography techniques to visualize the wave pattern even on the surface of a structure and simulation is the only way various details regarding internal patterns of the waves in a complex geometry can be analyzed. Analytical approach to deal with the wave propagation in a structure is limited to simple geometries and simple forms of damage. Guided wave in a simple geometry like beam/plate is modeled using analytical as well as semi-analytical methods. But when it comes to complicated problems like structures with actual damage/fracture or geometrical complexity which includes curvature and components with joints etc., one requires efficient computational schemes to simulate the behavior. Contents x There are various numerical tools developed in last few decades, such as finite difference, finite element, boundary element methods etc. In high frequency guided wave propagation problems, higher-order modes participate. Moreover, to detect a small damage, a high-frequency wave is needed. To deal with such kind of problems incorporating standard polynomial incorporation based finite element schemes need very fine mesh, which makes the computations of such problem enormously expensive, sometimes prohibitive. Time domain spectral element (TSFE) method is an efficient numerical method that can capture higher order field and therefore can deal with wave propagation problems efficiently and with better accuracy. TSFE uses higher order highly convergent interpolation functions based on the Chebyshev or Lobatto nodal distributions. TSFE based on the Lobatto nodal distribution and Legendre-Lobatto quadrature rule makes the mass matrix diagonal, which reduces the computer memory requirement to a great extent. As the number of nodes increases, accuracy increases exponentially and hence the term spectral finite element. The present thesis incorporates this idea and formulates a TSFE scheme to simulate guided wave propagation in laminated composite materials with damages such as material uncertainty/degradation, micro-cracks, and delaminations. Various benchmark problems are solved to validate the simulated results and establish superior convergence properties. Because of anisotropy of composite laminate and direction dependent properties of its constituent, composite laminate has various damage modes including matrix crack, fiber break, delamination etc. Among those damage modes, in this thesis, a special focus is given on delamination detection problem as it grows in the interfacial plane under repeated loading and reduces load-carrying capability to a great extent. Those damage modes are internal hence invisible. In wave propagation based detection methods, delamination can be identified and localized from the wave scattering from it. But it is of great interest to quantify the damage in terms of various parameters such as delamination length as well as the thickness and position of the laminate. Delamination scatters an incident wave and the strength of the reflection depends on the frequency/wavelength, length and thickness position of the delamination for a given structure. Simulation results show that the near-field effect of the damaged region provides crucial information about the scattering and reflected wave characteristics. Delamination in a laminate divides the damaged region into sub-laminates which are thinner compared to the base laminate. Each sub-laminate behaves like a separate waveguide. The vibration of the sub-laminates during the propagation of the wave through the damaged region Contents xi is of great interest. The energy of scattered waves and dissipation/conversion of energy due to the damage depends on the resonance characteristics of the sub-laminates. Therefore, the resonance phenomenon is correlated to the damage quantification problem with the help of simulation. Detection of damage near the structural boundary is one of the most challenging tasks as the scattering from the damage is overlapped by the strong reflection from the boundary. Effect of incident wave frequency/wavelength on the delamination near a structural boundary is studied. Damaged region behaves like the material degradation and in some frequency range the energy is trapped inside the damaged region and slow dissipation/conversion of the trapped energy into other forms of vibration creates a significant difference in the reflected wave and the simulated results help to identify the presence of damage. Impact-induced damage in composite has a great influence on the integrity and life of a composite structure. In most cases, initially, it develops material degradation in terms of matrix cracks at micro-scale. Although in composite structural design, micro-scale matrix cracks are not considered, however, as these micro-cracks coalesce, it gives initiate delamination. Under a severe dynamic impact loading, such small size delamination can grow and can lead to catastrophic failure of the structure. Ultrasonic wave propagation in composite with matrix crack is one of the major subjects of study which can predict the delamination onset in the composite. In the present thesis, wave scattering due to matrix cracks is studied and behavior of wave reflection from matrix cracking zone is investigated for various damage severity, which is expressed in terms of matrix crack density. Moreover, the matrix cracks along with delamination initiated from the zone, which is a kind of mixed-mode damage zone, appears more commonly in a composite structure than an ideal single-mode damage like a sharp crack or delamination. A mixed-mode damage complicates the modeling problem to be dealt with considering complex nature of near-field scattering of the incident wave. In the present thesis, this aspect is studied in details and damage severity effects are correlated to the scattered wave packet properties. Guided wave has a special characteristic that it is guided by the material media geometrically even when the structure is curved. This advantage can be exploited in developing damage detection scheme, for example, by bringing the scattered wave field located behind the curvature in a structural component without direct access to the surface where inspection cannot be carried out using local methods. Another important aspect of Contents xii guided wave is that propagation through a curved region not only produces reflection, it also generates mode converted waves which appear in both the reflected and transmitted waves. In the present thesis, wave transmissibility and signal loss at various frequencies and the effect of the radius of curvature is studied in detail. The simulation results provide a new insight regarding the wave mode and frequency for inspection for a given curved structure. Delamination near the curved region and T-joint is modeled and simulation shows correlation where the wave scattering due to delamination is possible to discriminate from that due to curved junctions. In composite, material uncertainty is inherent because of limited control over the fabrication processes, which in turn affects the proportion of the constituent materials or the fiber orientation. Significant material property variation can take place due to the variability in fiber volume fraction or the distortion in the stacking angle. The location of a damage and various other parameters are directly influenced by the material property variations. Therefore, the deterministic study is not sufficient to deal with these problems. In the present thesis, a Monte-Carlo method based simulation of wave scattering is carried out. The study primarily focuses on the problem of quantification of uncertainty in various damage detection parameters such as wave scattering coefficient and variation in the time of flight of the scattered packet, wave velocity etc. Detailed analysis is carried out regarding how the simulation based inspection method can be developed that gives better insight on the probabilistic distribution of the detection parameters of interests.

Wave scattering by arrays of cylinders has received special attention by many authors and analytical solutions have been derived. The investigation of optical and acoustical analogies to the problem of interaction of water waves with rigid and flexible cylinder arrays is the main focus of this thesis. In acoustics, a sound may be attenuated while it propagates through a layer of bubbly liquid. In fact, if the natural frequency of the bubbles is in the range of the wave periods, the attenuation becomes more evident. The ultimate objective of the research described herein is to determine if this phenomenon may also be found in the interaction between water waves and arrays of flexible cylinders. In a first approach, arrays of rigid cylinders are studied in shallow water. The array is treated as an effective medium, which allows for the definition of reflection and transmission coefficients for the array, and theories from Hu and Chan (2005) associated with the Fabry-Perot interferometer are compared against direct computations of wave scattering using the commercial code WAMIT. Reflection and transmission coefficients from WAMIT are evaluated by applying a Maximum Likelihood Method. The results from WAMIT were found to be in good agreement with those obtained from the effective medium theory. Due to observed inconsistencies for short wave periods and small incident angles, the effective width of the medium is defined and corrected. For the case of a flexible cylinder, generalized modes corresponding to deformations of the cylinder's surface are formulated and added to WAMIT's subroutine. Equations of motion are derived from the theory of vibration for thin shells and mass and stiffness matrices are defined. The objective is to maximize wave attenuation from the array of flexible cylinders. Therefore, the natural periods of the "breathing" mode for these cylinders is set in the range of the studied wave periods. Then, material properties, as well as mass and stiffness matrices, are chosen to achieve this effect.

In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic beam falling on the plate from a surrounding or contacting fluid will be strongly influenced by the RC or TC of the plate material. The scattering coefficients are in turn dependent on the plate elastic properties and structural composition: fiber and matrix properties, fiber volume fraction, layup geometry, and perhaps other factors. These elements are not, however, the only ones to determine the amplitude and spatial distribution of energy in the scattered ultrasonic field. Extrinsic factors such as the finite transmitting and receiving transducers, their focal lengths, and their placement with respect to the sample under study can make contributions to the signal as important as the SC itself. Therefore, a systematic study of the role of the transducer is essential for a complete understanding and correct interpretation of acoustic signals in the scattered field. The interpretation of these signals leads ultimately to the inference of composite elastic properties. As we pointed out in Chapter 5, the near coincidence under some conditions of guided plate wave modes with the zeroes of the reflection coefficient (or peaks in the transmission coefficient) has been exploited many times to reveal the plate’s guided wave mode spectrum.

The formal theory developed in Chapter 2 assumed the Stokes parameters to be additive. The sufficient condition for additivity is that the radiation fluxes in the atmosphere shall have no phase coherence. Thermal emission from independently excited molecules is necessarily incoherent with respect to phase. Atmospheric scattering centers are widely and randomly spaced, and they can be treated as independent and incoherent scatterers. The situation differs, however, when we consider details of the scattering process within a single particle, and in order to derive the extinction coefficient and the scattering matrix (see § 2.1.3) we must make use of a theoretical framework that involves the phase explicitly. The problem of the interaction between an electromagnetic wave and a dielectric particle can be precisely formulated using Maxwell’s equations. For a plane wave and a spherical particle, Mie’s theory provides a complete solution (see §7.6). But the general problem is complicated and our understanding is rendered more difficult by preconceptions based on the approximations of elementary optics. This chapter provides a brief survey of the important results and the underlying concepts. The geometry of the problem is illustrated in Fig. 7.1. An isolated particle is irradiated by an incident, plane electromagnetic wave. The plane wave preserves its character only if it propagates through a homogeneous medium; the presence of the scattering particle, with electric and magnetic properties differing from those of the surrounding medium, distorts the wave front. The disturbance has two aspects: first, the plane wave is diminished in amplitude; second, at distances from the particle that are large compared with the wavelength and particle size, there is an additional, outward-traveling spherical wave. The energy carried by this spherical wave is the scattered energy; the total energy lost by the plane wave corresponds to extinction; the difference is the absorption. The properties of the spherical wave in one particular direction (the line of sight) will be considered. This direction can be specified by the scattering angle 6 (see Fig. 7.1) in a plane containing both the incident and scattered wave normals (the plane of reference), and the azimuth angle ϕ) between the plane of reference and a plane fixed in space.

The description of neutron optical phenomena within the framework of dynamical diffraction theory is described. The coherent wave and optical potential are introduced, and an expression for the complex neutron refractive index in terms of the scattering length density and attenuation coefficient is obtained. The extension to magnetic media and polarized neutrons is covered. Neutron reflectivity is defined, and the wavevector dependence of the reflectivity profile is derived by a transfer matrix method and an optical method. Exact results are compared with the Born approximation. The technique of neutron imaging is described, including neutron radiography and computed tomography. Several optical phenomena that occur in Bragg diffraction from near-perfect crystals, including Pendellösung oscillations, and primary and secondary extinction.

This chapter examines the properties of one-dimensional Jost solutions for S-matrix problems. It first considers how the left–right transmission and reflections coefficients can be expressed in terms of the elements of the S-matrix for one-dimensional scattering problems on, focusing on poles of the transmission coefficient. It then uses the radial equation to revisit the problem of the square-well potential from the perspective of the Jost solution, with Jost boundary conditions at r = 0 and as r approaches infinity. It also presents the notations for the Jost functions and the S-matrix before discussing the problem of scattering from a constant spherical inhomogeneity.

This chapter deals with the WKB(J) approximation, commonly used in applied mathematics and mathematical physics to find approximate solutions of linear ordinary differential equations (of any order in principle) with spatially varying coefficients. The WKB(J) approximation is closely related to the semiclassical approach in quantum mechanics in which the wavefunction is characterized by a slowly varying amplitude and/or phase. The chapter first introduces an inhomogeneous differential equation, from which the first derivative term is eliminated, before discussing the Liouville transformation and the one-dimensional Schrödinger equation. It then presents a physical interpretation of the WKB(J) approximation and its application to a potential well. It also considers the “patching region” in which the Airy function solution (the local turning point) is valid, the relation between Airy functions and Bessel functions, Airy integral and related topics, and related integrals.

The scattering of a plane transverse-electric electromagnetic wave with a nonlinear dielectric thin film, which is embedded between two semi­infinite linear media, is theoretically studied. We assume that the nonlinear film can be characterized by an intensity-dependent dielectric constant with a negative Kerr coefficient, and the wave is monochromatic. Exact analytical solutions to Maxwell’s equations for the fields are derived in terms of the Jacobian elliptic sine function. The solutions contain four integration constants, and they are determined by imposing the necessary boundary conditions on the fields. We also find that the reflection and transmission coefficients can exhibit optical bistable and multistable behaviors as a function of the intensity of the incident wave. For a given film thickness and at particular values of the incident intensity, induced transparency and induced resonances can also exist. (12 min)

In a series of papers, the first in 1994, Sánchez-Gil et al [1] and in 1997 Madrazo and Maradudin [2] studied the scattering of electromagnetic waves from a wave guide film on a perfect conductor with a random rough surface. They found the enhanced backscattering and satellite peaks in the incoherent part of the mean differential reflection coefficient (DRC) as a function of the scattering angle when the system supports several guided waves modes.

One of the most dominant nonlinear effects in single-mode fibers is stimulated Brillouin scattering (SBS). The generation of SBS in a ring resonator can be considered as a lasing action, with the Stokes output downshifted in frequency by an amount equal to the Brillouin frequency. In the stationary case stimulated Brillouin scattering in a length of optical fiber can be described by the following partial differential equations for the slowly varying complex amplitudes of the pump wave E p and the backscattered first order Stokes wave E B1 , with the wave amplitudes E i related to the intensities I i by I i = |E i |2 (i=p,B1) [1]: (1) In a ring resonator geometry as depicted in Fig. 1 the wave amplitudes at the ports of the directional coupler obey the relations [2] (2) where V k 2 is the coupler intensity radiation loss, K is the field coupling coefficient, and T is the field transmission coefficient.

The paper considers the theory of stimulated Mandelshtam-Brillouin scattering (SMBS) in running conditions, i.e., with the length of the scattering medium significantly exceeding the spatial length of the pump pulse. In such conditions the pump pulse runs through the medium, and stimulated scattering of the pump wave into the Stokes wave takes place from different layers of the medium.1 An investigation of the process is carried out for both homogeneous and inhomogeneous media. The strict expressions are obtained from the Green function and the Stokes wave field. The spectrum and the coefficient of increment of the Stokes irradiation are analyzed. It has been shown that the effect of modulation of the Stokes irradiation frequency takes place due to stationary periodic inhomogeneities of the refractive index in a medium. This effect occurs also from periodic alterations of the value of light fiber cross-section. A computer simulation of the process of running SMBS confirms the theory. Practical possibilities are discussed concerning the usage of running SMBS for remote probing of a medium’s inhomogeneities and for some other applications.

This paper concerns the estimation of wave run-ups on a fixed surface-piercing square column. Experiments and numerical simulations were carried out under waves of different scattering parameters and steepnesses. The results of the run-up height ratio, force coefficient, velocity field, and scattered wave profile were shown and discussed. The reasonable agreement with the experimental results indicates the capability and reliability of the numerical model in the wave run-up prediction. The nonlinearity under short waves is mainly due to the interaction between the scattered waves and the next incident wave crest, while the wave-induced flow around the column becomes more influential under long waves. These nonlinearities are further intensified under steeper waves, and the run-up height ratio increases consequently. A correction factor of 1.2–1.3 can be applied to estimate the run-up height based on the linear potential prediction, but a higher factor of 1.3–1.4 is necessary under long and steep incident waves.

This paper describes the experimental results of microwave backscattering at water surfaces. Active microwave remote sensing is one of the useful techniques for sea surface measurement. For example, it enables us to know the wind vector on global scale. A principle of measurement is that the microwave backscattering depends on the wind speed. Therefore understanding of the phenomena of microwave scattering at sea surface in detail is indispensable for improvement of measuring accuracy. The purpose of the research is to investigate the characteristics of microwave scattering at various water surface conditions. Water surface was generated by wind and currents, microwave backscattering at that surface was measured by X and C-band microwave scatterometer. The experimental results were summarized in scattering coefficients and Doppler spectra. X-band microwave was more sensitive at wind wave surface than C-band. The mean frequency of Doppler spectrum of backscattering microwave was corresponded to the phase velocity of the mean water surface wave and the bandwidth of Doppler spectrum had close relation to the orbital velocity of the mean wave. A current had no effect on the scattering coefficient, but the Doppler spectrum was shifted to the side corresponding to current direction.

Abstract The yttria-stabilized zirconia (YSZ) top coat provides a thermal resistance function in the thermal barrier coatings used in gas turbines and Diesel engines. Besides the thermal conductivity, the thermal radiative properties, especially their dependence on the coating microstructure, under the high temperature combustion temperature are critically needed to the design and operation of the thermal barrier coating (TBC) systems. In this study ceramic oxide films made of thermally sprayed YSZ powder are prepared with three average porosities 5.9%, 14.5%, and 23.3% at film thickness from 283 to 955 μm. These films are fabricated with the air plasma spray (APS) deposition on the aluminum surface. The porosity changes are accomplished by varying the spraying parameters or ceramic oxide powder particle size. The room-temperature, spectral directional-hemispherical transmittance and reflectance are measured over the wavelength range from 1.35 to 2.5 μm. The radiative properties of absorption and scattering coefficients are reduced by using a hybrid method of the discrete ordinate method and the Kubelka-Munk four-flux method, depending on the film’s optical thickness. The films are then mounted, sectioned, and polished for SEM imaging. Using the image processing tools developed in-house, the porosity and pore size distribution (PSD) are obtained for each film. A numerical algorithm is used to convert the two-dimensional PSD into a three-dimensional PSD assuming all pores are spheriod. The absorption and scattering coefficients can be computed directly by the Mie theory based on the electromagnetic wave scattering from a distribution of sphere sizes. The new approach provides a predictive model of radiative properties based on the pore size distribution and pore number density, which are dependent on the APS spraying parameters, powder size and morphology. Comparison of radiative properties obtain by direct Mie theory computation and those obtained by reduction from spectral measurement is made and discrepancy is discussed.