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Статті в журналах з теми "Non-Linear wave scattering":
1
Savotchenko, S. E. "THE LINEAR WAVE SCATTERING BY A NON-LINEAR DEFECT." Belgorod State University Scientific bulletin Mathematics Physics 50, no. 3 (September 30, 2018): 283–91. http://dx.doi.org/10.18413/2075-4639-2018-50-3-283-291.
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PETER, MALTE A., and MICHAEL H. MEYLAN. "Water-wave scattering by a semi-infinite periodic array of arbitrary bodies." Journal of Fluid Mechanics 575 (March 2007): 473–94. http://dx.doi.org/10.1017/s0022112006004319.
Анотація:
We consider the scattering by a semi-infinite array of bodies of arbitrary geometry excited by an incident wave in the linear water-wave formulation (which reduces to the simpler case of Helmholtz scattering if the depth dependence can be removed). The theory presented here is extremely general, and we present example calculations for an array of floating elastic plates (a highly non-trivial scatterer). The solution method follows closely from the solution for point scatterers in a medium governed by Helmholtz's equation. We have made several extensions to this theory, considering water-wave scattering, allowing for bodies of arbitrary scattering geometry and showing how to include the effects of bound waves (called Rayleigh–Bloch waves in the water-wave context) in the formulation. We present results for scattering by arrays of cylinders that show the convergence of our methods and also some results for the case of scattering by floating elastic plates and fixed docks.
3
Ghodake, Pravinkumar. "The complexity of harmonically scattered nonlinear waves from triangular, circular, and rectangular corners of the 2-D domain." Journal of the Acoustical Society of America 154, no. 4_supplement (October 1, 2023): A262. http://dx.doi.org/10.1121/10.0023468.
Анотація:
Considering recent advancements in the nonlinear pulse-echo technique, understanding reflected nonlinear waves from inaccessible edges and surfaces becomes important. A unique geometrical model solved numerically using the finite element method is proposed and studied via extensive numerical experiments to gain insight into harmonically scattered waves from different shapes of the 2-D spaced corners considering the challenges of theoretical solutions that can capture the interplay between multiple phenomena. Tang et al. (2012), Kube (2017-18), and Achenbach and Wang (2017-18) studied the harmonic scattering of waves from nonlinear inclusions using analytical techniques. Linear longitudinal waves scattered from the triangular, circular, and rectangular-shaped free and fixed edges of the 2-D spaced corner show mode conversion and energy transfer between bulk wave modes at fundamental frequencies. The interaction of nonlinear ultrasonic waves with the edges makes things complex due to an interplay between harmonic generation, linear scattering, harmonic scattering, bulk wave mode conversion, and harmonic energy redistribution between all harmonics of the scattered longitudinal and transverse waves. This results in non-intuitive interesting responses. These studies are extended to explore one-way and two-way two-wave mixing of longitudinal waves and their interesting nonlinear effects. Phase difference introduced during harmonic scattering distinguishes the sensitivity of fundamental harmonics.
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Belibassakis, Kostas, and Julien Touboul. "A Nonlinear Coupled-Mode Model for Waves Propagating in Vertically Sheared Currents in Variable Bathymetry—Collinear Waves and Currents." Fluids 4, no. 2 (March 30, 2019): 61. http://dx.doi.org/10.3390/fluids4020061.
Анотація:
A novel coupled-mode model is developed for the wave–current–seabed interaction problem, with application in wave scattering by non-homogeneous, sheared currents over general bottom topography. The formulation is based on a velocity representation defined by a series of local vertical modes containing the propagating and evanescent modes, able to accurately treat the continuity condition and the bottom boundary condition on sloping parts of the seabed. Using the above representation in Euler equations, a coupled system of differential equations on the horizontal plane is derived, with respect to the unknown horizontal velocity modal amplitudes. In the case of small-amplitude waves, a linearized version of the above coupled-mode system is obtained, and the dispersion characteristics are studied for various interesting cases of wave–seabed–current interaction. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system is reduced to a one-equation, non-linear model, generalizing Boussinesq models. The analytical structure of the present coupled-mode system facilitates extensions to treat non-linear effects and further applications concerning wave scattering by inhomogeneous currents in coastal regions with general 3D bottom topography.
5
Wongthongsiri, Supawat, and Sohichi Hirose. "Scattering Analysis and Detection of Layered Plate Debonding Using Guided SH Waves with Boundary Element Method." Shock and Vibration 2022 (July 16, 2022): 1–10. http://dx.doi.org/10.1155/2022/8799555.
Анотація:
This paper investigates the scattering behavior of guided shear horizontal (SH) waves in a two-dimensional, isotropic, and linear elastic layered plate with partially debonded interface by analyzing the reflection and transmission coefficients of scattered waves. The partial wave technique is established to form the displacement and stress of guided wave functions, and the boundary element method (BEM) is utilized to handle the numerical calculation with elastodynamic fundamental solutions in the frequency domain. After applying proper boundary conditions including continuity condition on the interface with traction-free debonding, the scattering coefficients can be obtained in terms of boundary element solutions. Two different materials (steel and aluminum) with various debonding lengths and locations in a 1 mm double-layered plate are considered. With several modes of the incident wave over a frequency range up to 4.5 MHz, the variations of scattering coefficients and scattering phenomena are numerically investigated as several parameters such as mode of the incident wave, materials, locations, and length of debonding are changed. The numerical results also suggest the potential of the suitable wave mode for the debonding detection, which can be useful for non-destructive inspection.
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Baltenkov, Arkadiy S., and Igor Woiciechowski. "Interference Phenomenon in Electron-Molecule Collisions." Atoms 10, no. 4 (October 1, 2022): 105. http://dx.doi.org/10.3390/atoms10040105.
Анотація:
This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions Zλ(r) other than spherical harmonics Ylm(r). General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions Zλ(r) and determine the scattering phases ηλ(k) for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.
7
Li, Hong Liang. "Far Field Solution of Circular Inclusion and Linear Crack by SH-Wave." Key Engineering Materials 462-463 (January 2011): 455–60. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.455.
Анотація:
Circular inclusion exists widely in natural media, engineering materials and structures, and defects are usually found around the inclusion. When a composite material with circular inclusion and cracks is impacted by the dynamic load, on the one hand, the scattering field produced by the circular inclusion and cracks determines the dynamic stress concentration factor around the circular inclusion, and therefore determines whether the material is damaged or not; on the other hand, the scattering field also presents many characteristic parameters of the inclusion and cracks such as defect composition, location and shape, so the research on the scattering far-field is important to the geological prospects, seismological investigation, non-destruction evaluation and the other fields. In the ocean acoustics, the scattering far-field of the acoustic wave is also used in the under-water survey, object distinguishing and so on. In theory, the scattering solution of elastic waves is one of the basic topics of reverse problems on elastic wave. On the basis of literature, few paper concentrates on the scattering far-field solution of SH-wave by a circular inclusion and a linear crack around the inclusion. In the paper a new model and a new method are presented in order to investigate deeply on this kind problem. The paper uses the Green’s function to study the scattering far-field of an elastic wave by a circular inclusion and a linear crack. The Green’s function should be a fundamental solution of displacement field for an elastic space possessing a circular inclusion while bearing out-of-plane harmonic line source force at any point. In terms of the solution of SH-wave’s scattering by an elastic space with a circular inclusion, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the linear crack is in existent actually; Then, the expressions of the displacement and stresses are given when the circular inclusion and linear crack exist at the same time. When the special Green’s function has been constructed and close field solution has been illustrated, the far field of scattered wave is studied. The displacement mode of scattered wave at far field and scattering cross-section are given. At last, an example is given and its numerical results are discussed.
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Meylan, M. H., and L. G. Bennetts. "Three-dimensional time-domain scattering of waves in the marginal ice zone." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2129 (August 20, 2018): 20170334. http://dx.doi.org/10.1098/rsta.2017.0334.
Анотація:
Three-dimensional scattering of ocean surface waves in the marginal ice zone (MIZ) is determined in the time domain. The solution is found using spectral analysis of the linear operator for the Boltzmann equation. The method to calculate the scattering kernel that arises in the Boltzmann model from the single-floe solution is also presented along with new identities for the far-field scattering, which can be used to validate the single-floe solution. The spectrum of the operator is computed, and it is shown to have a universal structure under a special non-dimensionalization. This universal structure implies that under a scaling wave scattering in the MIZ has similar properties for a large range of ice types and wave periods. A scattering theory solution using fast Fourier transforms is given to find the solution for directional incident wave packets. A numerical solution method is also given using the split-step method and this is used to validate the spectral solution. Numerical calculations of the evolution of a typical wave field are presented. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.
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Grimshaw, R., L. A. Ostrovsky, A. S. Topolnikov, and K. R. Khusnutdinova. "Influence of Internal Wave on the Sound Propagation in the Subsurface Bubble Layer." Proceedings of the Mavlyutov Institute of Mechanics 8, no. 1 (2011): 54–64. http://dx.doi.org/10.21662/uim2011.1.005.
Анотація:
In the paper the influence of non-linear internal wave on the propagation of acoustic signal in the subsurface ocean layer containing gas bubbles is considered. During interaction with surface waves the internal wave causes its collapse and influences the structure of bubble layer. Inhomogeneous structure of the layer promotes the local speed of sound and intensity of scattering near the ocean surface to modulate by internal wave with slight shift in phase in the direction of its propagation, which agree with recent experimental observations made on the shelf of Japan Sea.
10
ATASSI, O. V., and J. J. GILSON. "Acoustic mode scattering from a heat source." Journal of Fluid Mechanics 651 (April 30, 2010): 1–26. http://dx.doi.org/10.1017/s0022112010000261.
Анотація:
The scattering of an incident acoustic wave by a non-uniform mean flow resulting from a heat source is investigated. The heat source produces gradients in the mean flow and the speed of sound that scatter the incident duct acoustic mode into vortical, entropic, and higher-order acoustic modes. Linear solutions utilizing the compact source limit and nonlinear solutions to the Euler equations are computed to understand how variations in the amplitude and axial extent of the heat source as well as the incident acoustic wave propagation angle and amplitude modify the scattered solution. For plane wave excitation, significant entropy waves are produced as the net heat addition increases at the expense of the transmitted acoustic energy. When the net heat addition is held constant, increasing the axial extent of the heat source results in a reduction of the entropy waves produced downstream and a corresponding increase in the downstream scattered acoustic energy. For circumferential acoustic mode excitations the incident acoustic wave angle, characterized by the cutoff ratio, significantly modifies the scattered acoustic energy. As the propagating mode cutoff ratio approaches unity, a rise in the scattered vortical disturbance and a decrease in the entropic disturbance amplitude is observed. As the cutoff ratio increases, the scattered solution approaches the plane wave results. Moreover, incident acoustic waves with different frequencies and circumferential mode orders but similar cutoff ratios yield similar scattered wave coefficients. Finally, for large amplitude incident acoustic waves the scattered solution is modified by nonlinear effects. The pressure field exhibits nonlinear steepening of the wavefront and the nonlinear interactions produce higher harmonic frequency content which distorts the sinusoidal variation of the outgoing scattered acoustic waves.
Дисертації з теми "Non-Linear wave scattering":
1
Lehner, Thierry. "Interaction quadratique onde-onde en plasma : battement d'ondes, couplage onde-fluctuations." Paris 6, 1987. http://www.theses.fr/1987PA066482.
Анотація:
Lorsque les deux ondes se couplent en basse frequence, on obtient un effet de pression de radiation ou lieu de force ponderomotrice. Ces notions sont etudiees dans un plasma magnetise ou non, ainsi que le cas ou la force ponderomotrice depend lentement du temps. On envisage deux applications : on etudie, a l'aide d'un double blanc microonde la generation d'une resonance par battement d'ondes, avec une detection sensible au transfert d'action. On considere la possibilite de diagnostic du plasma magnetise par optique non lineaire. L'analyse de la polarisation d'une onde diffusee par des fluctuations electromagnetiques est enfin traitee
2
Lafontaine, David. "Effets dispersifs et asymptotique en temps long d'équations d'ondes dans des domaines extérieurs." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4067/document.
Анотація:
L'objet de cette thèse est l'étude des équations de Schrödinger et des ondes, à la fois linéaires et non linéaires, dans des domaines extérieurs. Nous nous intéressons en particulier aux inégalités dites de Strichartz, qui sont une famille d'estimations dispersives mesurant la décroissance du flot linéaire, particulièrement utiles à l'étude des problèmes non linéaires correspondants. Dans des géométries dites non-captantes, c'est à dire où tous les rayons de l'optique géométrique partent à l'infini, de nombreux résultats montrent que de telles estimations sont aussi bonnes que dans l'espace libre. D'autre part, la présence d'une trajectoire captive induit nécessairement une perte au niveau d'une autre famille d'estimations à priori, les estimations d'effet régularisant et de décroissance locale de l'énergie, respectivement pour Schrödinger et pour les ondes. En contraste de quoi, nous montrons des estimations de Strichartz sans perte dans une géométrie captante instable : l'extérieur de plusieurs obstacles strictement convexes vérifiant la condition d'Ikawa. La seconde partie de cette thèse est dédiée à l'étude du comportement en temps long des équations non-linéaires sous-jacentes. Lorsque le domaine dans lequel elles vivent n'induit pas trop de concentration de l'énergie, on s'attend à ce qu'elles diffusent, c'est à dire se comportent de manière linéaire asymptotiquement en temps. Nous montrons un tel résultat pour les ondes non linéaires critiques à l'extérieur d'une classe d'obstacles généralisant la notion d'étoilé. A l'extérieur de deux obstacles strictement convexes, nous obtenons un résultat de rigidité concernant les solutions à flot compact, premier pas vers un résultat général. Enfin, nous nous intéressons à l'équation de Schrödinger non linéaire, dans l'espace libre, mais avec un potentiel. Nous montrons que les solutions diffusent si l'on prend un potentiel répulsif, ainsi qu'une somme de deux potentiels répulsifs ayant des surfaces de niveau convexes, ce qui fournit un exemple de diffusion dans une géométrie captante analogue à l'extérieur de deux convexes strictsWe are concerned with Schrödinger and wave equations, both linear and non linear, in exterior domains. In particular, we are interested in the so-called Strichartz estimates, which are a family of dispersive estimates measuring decay for the linear flow. They turn out to be particularly useful in order to study the corresponding non linear equations. In non-captive geometries, where all the rays of geometrical optics go to infinity, many results show that Strichartz estimates hold with no loss with respect to the flat case. Moreover, the local smoothing estimates for the Schrödinger equation, respectively the local energy decay for the wave equation, which are another family of dispersive estimates, are known to fail in any captive geometry. In contrast, we show Strichartz estimates without loss in an unstable captive geometry: the exterior of many strictly convex obstacles verifying Ikawa's condition. The second part of this thesis is dedicated to the study of the long time asymptotics of the corresponding non linear equations. We expect that they behave linearly in large times, or scatter, when the domain they live in does not induce too much concentration effect. We show such a result for the non linear critical wave equation in the exterior of a class of obstacles generalizing star-shaped bodies. In the exterior of two strictly convex obstacles, we obtain a rigidity result concerning compact flow solutions, which is a first step toward a general result. Finally, we consider the non linear Schrödinger equation in the free space but with a potential. We prove that solutions scatter for a repulsive potential, and for a sum of two repulsive potentials with strictly convex level surfaces. This provides a scattering result in a framework similar to the exterior of two strictly convex obstacles
3
Tretinnikov, Pavel. "New developments on the interpretative model of ITER diagnostics using microwaves." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0027.
Анотація:
La turbulence dans le plasma de fusion thermonucléaire peut entraîner une augmentation du coefficient de transport de l’énergie et des particules détériorant ainsi le confinement du plasma. C’est pourquoi les mesures de la turbulence du plasma sont importantes pour la description des processus de transport du plasma. Le diagnostic plasma micro-ondes est un type efficace de diagnostic plasma actif pour caractériser la turbulence. Leurs principes reposent sur la collecte d’informations intégrées dans le volume de plasma sondé, et contenu dans les ondes réfléchies ou diffusées atteignant le détecteur. Pour extraire les propriétés de turbulence, des modèles interprétatifs sont nécessaires. La réflectométrie de corrélation radiale (RCR) et la réflectométrie Doppler sont des techniques largement utilisées qui fournissent des informations sur les caractéristiques de la turbulence du plasma. La diffusion Thomson collective (CTS) est un diagnostic micro-ondes intéressant qui peut donner des informations sur des paramètres plasma tels que la température des ions en vrac, la composition des ions en vrac, la distribution de vitesse des particules rapides (particules alpha ou ions d’un faisceau chauffant). La connaissance de la distribution de la vitesse des particules alpha est particulièrement recherchée et importante pour évaluer les performances d’ITER où l’amplification énergétique de la puissance de chauffage du plasma Q devrait atteindre la valeur d’environ 10. L’analyse des données réelles des diagnostics micro-ondes, ou les interprétations d’une mesure signal suppose un faisceau de sondage gaussien lisse. Il a été démontré que les faisceaux de micro-ondes peuvent être considérablement déformés en raison de la turbulence du plasma de bord. Ceci peut conduire à des interprétations trompeuses du signal de diagnostic, basées sur les micro-ondes. En conséquence les modèles interprétatifs des diagnostics doivent être analysés en tenant compte de la distorsion du faisceau de sondage. L’amélioration des modèles interprétatifs de diagnostic hyperfréquence est l’objet principal des études présentées dans cette thèseThe turbulence in thermonuclear fusion plasma can lead to increase of the plasma transport coefficient that enhances the particles and energy losses therefore deteriorates the plasma confinement. That is why measurements of the plasma turbulence is important for description of the plasma transport processes. Microwave plasma diagnostics is an efficient kind of the active plasma diagnostics to characterize the turbulence. Their principles are based on the collection of information integrated over the probed plasma volume, and printed on the reflected or scattered waves reaching the detector, for which interpretative models are required to extract the turbulence properties. The radial correlation reflectometry (RCR) and the Doppler reflectometry are widely used technics that provide information on plasma turbulence characteristics. The Collective Thomson Scattering (CTS) is a valuable microwave diagnostic that can give the information about such plasma parameters as the bulk ion temperature, bulk ion composition, the fast particles (alpha particles or ions of a heating beam) velocity distribution. The knowledge of the alpha particle velocity distribution is especially interesting and important to evaluate the ITER performance where the energy amplification of plasma heating power Q is expected to achieve the value about 10. The actual data analysis of the microwave diagnostics, or interpretations of a measured signal is fulfilled assuming a smooth Gaussian probing beam. It was demonstrated that the microwave beams can be significantly distorted due to the edge plasma turbulence, that may lead to misleading interpretations of the diagnostic signal, based on the microwaves, so the diagnostics interpretative models should be analyzed taken into account to the probing beam distortion. The improvement of the microwave diagnostics interpretative models is the main object of the study presented in this thesis.The aim of this PhD work is to include these missing effects in an interpretative model for CTS using X-mode probing beam
4
Pham, Truong Xuan. "Peeling et scattering conforme dans les espaces-temps de la relativité générale." Thesis, Brest, 2017. http://www.theses.fr/2017BRES0034/document.
Анотація:
Nous étudions l’analyse asymptotique en relativité générale sous deux aspects: le peeling et le scattering (diffusion) conforme. Le peeling est construit pour les champs scalaires linéaire et non-linéaires et pour les champs de Dirac en espace-temps de Kerr (qui est non-stationnaire et à symétrie simplement axiale), généralisant les travaux de L. Mason et J-P. Nicolas (2009, 2012). La méthode des champs de vecteurs (estimations d’énergie géométriques) et la technique de compactification conforme sont développées. Elles nous permettent de formuler les définitions du peeling à tous ordres et d’obtenir les données initiales optimales qui assurent ces comportements. Une théorie de la diffusion conforme pour les équations de champs sans masse de spîn n/2 dans l’espace-temps de Minkowski est construite.En effectuant les compactifications conformes (complète et partielle), l’espace-temps est complété en ajoutant une frontière constituée de deux hypersurfaces isotropes représentant respectivement les points limites passés et futurs des géodésiques de type lumière. Le comportement asymptotique des champs s’obtient en résolvant le problème de Cauchy pour l’équation rééchelonnée et en considérant les traces des solutions sur ces bords. L’inversibilité des opérateurs de trace, qui associent le comportement asymptotique passé ou futur aux données initiales, s’obtient en résolvant le problème de Goursat sur le bord conforme. L’opérateur de diffusion conforme est alors obtenu par composition de l’opérateur de trace futur avec l’inverse de l’opérateur de trace passéThis work explores two aspects of asymptotic analysis in general relativity: peeling and conformal scattering.On the one hand, the peeling is constructed for linear and nonlinear scalar fields as well as Dirac fields on Kerr spacetime, which is non-stationary and merely axially symmetric. This generalizes the work of L. Mason and J-P. Nicolas (2009, 2012). The vector field method (geometric energy estimates) and the conformal technique are developed. They allow us to formulate the definition of the peeling at all orders and to obtain the optimal space of initial data which guarantees these behaviours. On the other hand, a conformal scattering theory for the spin-n/2 zero rest-mass equations on Minkowski spacetime is constructed. Using the conformal compactifications (full and partial), the spacetime is completed with two null hypersurfaces representing respectively the past and future end points of null geodesics. The asymptotic behaviour of fields is then obtained by solving the Cauchy problem for the rescaled equation and considering the traces of the solutions on these hypersurfaces. The invertibility of the trace operators, that to the initial data associate the future or past asymptotic behaviours, is obtained by solving the Goursat problem on the conformal boundary. The conformal scattering operator is then obtained by composing the future trace operator with the inverse of the past trace operator
5
Watson, Francis Maurice. "Better imaging for landmine detection : an exploration of 3D full-wave inversion for ground-penetrating radar." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/better-imaging-for-landmine-detection-an-exploration-of-3d-fullwave-inversion-for-groundpenetrating-radar(720bab5f-03a7-4531-9a56-7121609b3ef0).html.
Анотація:
Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the large-scale, non-linear and ill-posed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from small-scale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finite-element boundary-integral solver utilising first order curl-conforming N\'d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface. We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to pre-condition the GPR FWI problem.
6
Tomasini, Franco. "Contribution a l'etude des non-linearites optiques de chlorure de cuivre." Université Louis Pasteur (Strasbourg) (1971-2008), 1986. http://www.theses.fr/1986STR13111.
Анотація:
Nous etudions la reponse optique non-lineaire d'un cristal de chlorure de cuivre en interaction avec un faisceau laser intense et de grande finesse spectrale. Un calcul non perturbatif utilisant le formalisme de la matrice densite permet d'obtenir la fonction dielectrique du cristal, represente par un modele a trois ou quatre niveaux (niveau fondamental, excitonique, biexcitonique) dans ces conditions. Les renormalisations des courbes de dispersion, du coefficient d'absorption et de reflexion normale sont calculees. L'utilisation de lasers a colorants a incidence rasante pompes par un laser a excimere permet l'etude experimentale de ces renormalisations par diffusion hyper-raman, melange de quatre ondes et reflexion normale.
7
Ferrier, Jean-Louis. "Contribution à l'étude de la conjugaison de phase, en régime d'excitation picoseconde, dans les milieux liquides et cristallins : faisabilité, caractérisation et applications." Angers, 1986. http://www.theses.fr/1986ANGE0003.
Анотація:
Par l'utilisation de lasers de puissance de type picoseconde (longueur d'onde 532 nm, durée 25ps) dans des milieux liquides et cristallins, nous avons apporté notre contribution a : - l'aspect faisabilité de la conjugaison de phase en picoseconde, -l'évaluation du comportement transitoire ou pas des phénomènes, - des applications particulières a ce domaine. Nous avons caractérisé et étudie par voie expérimentale et théorique différents paramètres entrant en jeu dans les deux types d'expériences susceptibles de produire la conjugaison de phase- mélange quatre ondes et rétrodiffusions stimulées- en vue d'applications de type temporel ou imagerie, dans les liquides (principalement sulfure de carbone et benzène). Le comportement en excitation picoseconde des matériaux photoréfractifs (oxyde de bismuth silicium et niobate de lithium) a été étudié par des expériences de mélange quatre ondes et mélange deux ondes. Il ressort des principaux résultats -expérimentaux et théoriques- que certains sont propre au régime d'excitation picoseconde alors que d'autres sont d'ordre général et indépendants du régime temporel d'excitation.
8
PORTELLA, MARCIA TEREZA. "Spectroscopie coherente et etude d'un espace poreux par melange a quatre ondes." Paris 6, 1987. http://www.theses.fr/1987PA066586.
Анотація:
Nous avons construit des lasers qui ont servi a des experiences de melange a quatres ondes (reseau transitoire). Nous avons d'abord etudie la reponse non lineaire du troisieme ordre lorsque le milieu presente un continuum large d'etats (colorants). Le signal obtenu sur le cresyl-violet en film mince de colle cellulosique a ete analyse. La technique du reseau transitoire a ete ensuite utilisee pour caracteriser la dynamique de molecules dans un milieu poreux (vycor) et etudier la geometrie des connexions entre pores. Nous avons etudie la rotation de l'azobenzene en solution soit libre soit contenue a l'interieur de l'espace poreux. Ces experiences peuvent etre realisees sur des echelles allant de la femtoseconde a la seconde, permettant ainsi l'etude tant du temps de coherence que des proprietes de diffusion des materiaux
9
Diallo, Souleymane. "Utilisation des non-linéarités Kerr et Brillouin dans les résonateurs à mode de galerie cristallins pour la synthèse de micro-ondes." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2028/document.
Анотація:
Les résonateurs à modes de galerie sont des cavités diélectriques qui supportent des modes à très haut facteur de qualité et à faible volume qui demeurent confinés à l'interface air-diélectrique pour des durées pouvant atteindre voire dépasser la microseconde. L'intérêt de ce fort confinement des modes pour de longues durées est l'accentuation de l'interaction lumière-matière. Par conséquent, de nombreuses interactions non-linéaires telles que l'effet Kerr ou encore l'effet Brillouin à des puissances seuil inversement proportionnelles au carré voire au cube du facteur de qualité du résonateur ont lieu en son sein. Ces propriétés donnent accès à de nombreuses applications dans des domaines divers et variés tels que la spectroscopie, les télécommunications ou encore les micro-ondes. Les travaux de cette thèse ont pour but d'exploiter les non-linéarités Kerr et Brillouin dans les résonateurs à mode galerie à la longueur d'onde de 1550 nm afin de générer des micro-ondes ultra-stables à des fréquences comprises entre 5 et 30 GHz. Le premier chapitre introduit la théorie, la fabrication, le couplage et la caractérisation de résonateurs à des modes de galerie. Le second chapitre concerne la génération de micro-ondes. Nous y présentons nos résultats expérimentaux, la modélisation numérique de peignes de Kerr, ainsi que l'analyse d'instabilités oscillatoires d'origine thermique observées lors de nos travaux expérimentaux, puis nous concluons. Le dernier chapitre traite de l'interaction photons-phonons via le processus de diffusion Brillouin stimulée dans ces mêmes expérimentaux ainsi que le modèle temporel que nous avons développé pour suivre la dynamique de l'onde transmise et de celle rétrodiffusée. Le dernier chapitre conclue nos travaux. Les travaux présentés dans ce manuscrit ont été financé par l'European Research Council dans le cadre du projet NextPhaseWhispering galery mode resonators are dielectric cavities that support modes with ultra-high quality factor and small volume that remain confined in their inner periphery for time duratioons that can be as long as few microseconds. The strong confinement of these modes for such long durations strongly enhances nonlinear effect suchs as Kerr effect or Brillouin effect. These resonators can therefore be used for several applications such as spectroscopy, telecommunications or microwave generation. The objective of this thesis is to use Kerr and Brillouin nonlinearities in these resonators at the laser wavelength of 1550 nm, in order to generate high spectral purity microwave signals with frequencies rangong fros 5 to 30 GHz. The first chapter oh the thesis intriduces the theory, fabrication, coupling and characterisation of whispering gallery mode resonators. The second chapter is about the generation of Kerr optical frequency combs in these resonators and their application to the generation of microwave signals. We present our experimental resuktsdn the numerical modelling of Kerr combs, the analysis of oscillatory instabilities (due to thermal effect) observed during our experiments, and conclue. The third chapter concerns photon-phonon interactions via stimulated Brillouin scattering in these resonators and their application to the generation of microwave signals. We present our experimental results and the temporal model that we developed to track the dynamics of the forward and backscattered fields. The last chapter conclude the thesis. The research presented in this thesis has benne funded by the European Research Council through the project Nextphase
Книги з теми "Non-Linear wave scattering":
1
Reed, Michael. Abstract Non Linear Wave Equations. Springer London, Limited, 2006.
2
Asano, N., and Y. Kato. Algebraic and Spectral Methods for Non-Linear Wave Equations (Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 49). Longman Sc & Tech, 1991.
3
Furst, Eric M., and Todd M. Squires. Microrheology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199655205.001.0001.
Анотація:
We present a comprehensive overview of microrheology, emphasizing the underlying theory, practical aspects of its implementation, and current applications to rheological studies in academic and industrial laboratories. Key methods and techniques are examined, including important considerations to be made with respect to the materials most amenable to microrheological characterization and pitfalls to avoid in measurements and analysis. The fundamental principles of all microrheology experiments are presented, including the nature of colloidal probes and their movement in fluids, soft solids, and viscoelastic materials. Microrheology is divided into two general areas, depending on whether the probe is driven into motion by thermal forces (passive), or by an external force (active). We present the theory and practice of passive microrheology, including an in-depth examination of the Generalized Stokes-Einstein Relation (GSER). We carefully treat the assumptions that must be made for these techniques to work, and what happens when the underlying assumptions are violated. Experimental methods covered in detail include particle tracking microrheology, tracer particle microrheology using dynamic light scattering and diffusing wave spectroscopy, and laser tracking microrheology. Second, we discuss the theory and practice of active microrheology, focusing specifically on the potential and limitations of extending microrheology to measurements of non-linear rheological properties, like yielding and shear-thinning. Practical aspects of magnetic and optical tweezer measurements are preseted. Finally, we highlight important applications of microrheology, including measurements of gelation, degradation, high-throughput rheology, protein solution viscosities, and polymer dynamics.
Частини книг з теми "Non-Linear wave scattering":
1
Wiskin, J., D. T. Borup, S. A. Johnson, M. Berggren, T. Abbott, and R. Hanover. "Full-Wave, Non-Linear, Inverse Scattering." In Acoustical Imaging, 183–93. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/1-4020-5721-0_20.
2
Tsytovich, Vadim N. "Stimulated Scattering of Waves by Particles." In Lectures on Non-linear Plasma Kinetics, 137–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-78902-1_6.
3
Vu, Pham Loi. "Inverse Scattering for Integration of The Continual System of Non-Linear Interaction Waves." In Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations, 167–234. 2nd ed. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003370543-5.
4
Logvin, Aleksander I., and Anatolij I. Kozlov. "Formulation of Scattering Matrix for Electromagnetic Waves under Non-Linear Transformation: Non-Linear Oxidized Metal Junction Higher Harmonics Reradiation Effects." In Direct and Inverse Methods in Radar Polarimetry, 1057–64. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-010-9243-2_46.
5
Akhmanov, S. A., and S. YU Nikitin. "Theoretical non-linear optics." In Physical Optics, 461–82. Oxford University PressOxford, 1997. http://dx.doi.org/10.1093/oso/9780198517955.003.0023.
Анотація:
Abstract Optical second-harmonic generation. Stimulated Raman scattering. Self-focusing of light. The theory of non-linear optical effects is based on Maxwell’s equations and the material equations. From Maxwell’s equations one can obtain the wave equation (see Chapter 22).
6
Roy, Arabinda, and Rasajit Kumar Bera. "Two-Dimensional Low Frequency Scattering of Acoustic Wave by a Rough Surface." In Linear and Non-Linear Deformations of Elastic Solids, 256–60. CRC Press, 2019. http://dx.doi.org/10.1201/9780429319426-14.
7
He, Sailing, Staffan Strom, and Vaughan H. Weston. "Time Domain Wave-Splitting Green’S Function Approaches." In Time Domain Wave-Splittings and Inverse Problems, 38–43. Oxford University PressOxford, 1998. http://dx.doi.org/10.1093/oso/9780198565499.003.0002.
Анотація:
Abstract The scattering kernels introduced in Chapter 1 and determined by means of the imbedding approach provide a framework for solving direct and inverse scattering problems, but the full wave propagation problem, i.e., including the determination of the field inside the scattering region, is not solved by the scattering kernels. However, during recent years the time domain wave-splitting approach has been extended to include the determination of the fields inside the inhomogeneous region. This extension, called the Green’s functions approach, is one of the main themes of the presentation in the rest of this book. The term Green’s functions refers to the regular parts of the split components of the fundamental solution. These regular parts are determined by the initial and boundary values of the propagation problem under consideration. Furthermore, the boundary values of the Green’s functions are related to the physical scattering kernels studied in Chapter 1, and thus a close connection with the imbedding approach is established. The system of equations for the Green’s functions is linear (and thus is one order faster to solve numerically than the non-linear imbedding equation for the reflection kernel), and is suitable for parallel processing. Thus it provides an approach to both direct and inverse scattering problems, which has some advantages as compared to the imbedding approach. In particular, in the three-dimensional case the Green’s function approach allows a simpler handling of the singularities (see Chapter 7).
8
Zakharov, V. E., and S. V. Manakov. "Asymptotic behavior of non-linear wave systems integrated by the inverse scattering method." In 30 Years of the Landau Institute — Selected Papers, 358–64. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814317344_0047.
9
Dunajski, Maciej. "Soliton equations and the inverse scattering transform." In Solitons, Instantons, and Twistors, 20–42. Oxford University PressOxford, 2009. http://dx.doi.org/10.1093/oso/9780198570622.003.0002.
Анотація:
Abstract A universally accepted definition of integrability does not exist for partial differential equations (PDEs). The phase space is infinite dimensional but having ‘infinitely many’ first integrals may not be enough – we could have missed every second one. One instead focuses on properties of solutions and solution-generation techniques. We shall study solitons – solitary non-linear waves which preserve their shape (and other characteristics) in the evolution. These soliton solutions will be constructed by means of an inverse problem: recovering a potential from the scattering data.
10
Haddar, H., and P. Joly. "Stability of Thin Layer Approximation of Electromagnetic Waves Scattering by Linear and Non Linear Coatings." In Nonlinear Partial Differential Equations and their Applications - Collège de France Seminar Volume XIV, 415–56. Elsevier, 2002. http://dx.doi.org/10.1016/s0168-2024(02)80020-0.
Тези доповідей конференцій з теми "Non-Linear wave scattering":
1
Zang, J., R. Gibson, P. H. Taylor, R. Eatock Taylor, and C. Swan. "Non-Linear Wave Diffraction Around a Moored Ship." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51589.
Анотація:
The objective of this research, part of the FP5 REBASDO Programme, is to examine the effects of directional wave spreading on the nonlinear hydrodynamic loads and the wave run-up around the bow of a floating vessel (FPSO) in random seas. In this work, the non-linear wave scattering problem is solved by employing a quadratic boundary element method. An existing scheme (DIFFRACT developed in Oxford) has been extended to deal with uni-directional and directional bi-chromatic input wave systems, calculating second-order wave diffraction under regular waves and focused wave groups. The second order wave interaction with a floating vessel in a unidirectional focused wave group is presented in this paper. Comparison of numerical results and the experimental measurements conducted at Imperial College shows excellent agreement. The second-order free surface components at the bow of the ship are very significant, and cannot be neglected if one requires accurate prediction of the wave-structure interaction; otherwise a major underestimation of the wave impact on the structure could occur.
2
Kim, J. W., R. C. Ertekin, and K. J. Bai. "Linear and Non-Linear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29747.
Анотація:
Recently, two wave models based on the stream-function theory have been derived from Hamilton’s principle for gravity waves. One is the Irrotational Green-Naghdi (IGN) equation and the other is the Complementary Mild-Slope Equation (CMSE). The IGN equation has been derived to describe refraction and diffraction of nonlinear gravity waves in the time domain and in water of finite but arbitrary bathymetry. The CMSE has been derived to consider the same problem in the (linear) frequency domain. In this paper, we first describe the discuss the two models from the viewpoint of Hamilton’s principle. Then the two models are applied to a resonant scattering of Stokes waves over periodic undulations, or the Bragg scattering problem. The numerical results are compared with existing numerical predictions and experimental data. It is found here that Level 3 IGN equation can describe Bragg scattering well for arbitrary bathymetry.
3
Niklès, Marc, Luc Thévenaz, and Philippe Robert. "Brillouin Gain Spectrum Measurements using a Single Laser Source." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.md.5.
Анотація:
Stimulated Brillouin scattering (SBS) is a non-linear process that occurs in optical fibres at much lower pump power than most other non-linear effects. The pump wave is scattered into a backward-propagating Stokes wave that experiences a frequency shift lying in the 12-13 GHz range at 1300 nm. This shift is proportional to the acoustic velocity within the fibre, making SBS an efficient tool for sensing applications, e.g. for monitoring strains in installed fibres [1].
4
New, M. J., P. Ewart, A. Dreizler, and T. Dreier. "Multiplex polarization spectroscopy of OH for flame thermometry." In Laser Applications to Chemical and Environmental Analysis. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/lacea.1996.lthc.9.
Анотація:
Laser-based techniques for combustion diagnostics are becoming increasingly important as they allow remote and non-intrusive measurements of flame parameters with high spatial and temporal resolution. Linear light scattering methods such as Laser Induced Fluorescence, Rayleigh and Raman scattering have been successfully applied [1]. In some situations non-linear processes such as coherent anti-Raman scattering (CARS) offer certain advantages over linear techniques. CARS is a four-wave mixing process and generates a signal in the form of a coherent beam of radiation but is suitable only for the detection of majority species [1]. Degenerate four-wave mixing (DFWM) is an important resonant technique which has been used to detect [2] and image [3] minority species in flames and also has the advantages inherent to a coherent process.
5
Hsu, Tai-Wen, Shan-Hwei Ou, Chin-Yen Tsai, and Jian-Feng Lin. "Kinetic, Dynamic and Energy Characteristics of Vortex Evolution on Bragg Scattering of Water Waves." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-21092.
Анотація:
The vortex generation and dissipation under Bragg scattering of water wave propagation over a series of submerged rectangular breakwaters are investigated both numerically and experimentally. A Reynolds Averaged Navier-Stokes (RANS) model combined with a k–ε turbulence closure is applied to simulate the entire vortex evolution process as water waves pass over a series of artificial rectangular bars. The Particle Image Velocimetry (PIV) is also used to measure the velocity field in the vicinity of the obstacles. The numerical model is validated through the comparisons of water surface elevations and velocity field with the measurements. The mechanism of vortex evolution and its influence on the interaction of water waves with submerged structures for both cases of resonance and non-resonance were studied. Wave reflection coefficients for both resonant and non-resonant cases were calculated and compared with experiments and solutions based on the linear wave theory. It is also found that the calculated vortex intensity at the last bar is only one third of that at the leading bar for the near-resonant case. The local kinetic energy is also found to attain its minimum value at a place where potential energy became larger in Bragg scattering of water waves.
6
Arzoumanian, Sevag, and Nigel Peake. "Fluid Structure Interaction With Mean Flow: Over-Scattering and Unstable Resonance Growth." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31170.
Анотація:
It is known theoretically [1–3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the ‘long time’ limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinuities. Moreover, linear instability waves can only grow over a limited number of cycles before non-linear effects become dominant. We have undertaken an analytical and computational study to investigate the response of finite, discontinuous plates to ascertain if these unusual effects might be realized in practice. Analytically, we take a “wave scattering” [2,4] — as opposed to a “modal superposition” [5] — view of the fluttering plate problem. First, we solve for the scattering coefficients of localized plate discontinuities and identify a range of parameter space, well outside the convective instability regime, where over-scattering or amplified reflection/transmission occurs. These are scattering processes that draw energy from the mean flow into the plate. Next, we use the Wiener-Hopf technique to solve for the scattering coefficients from the leading and trailing edges of a baffled plate. Finally, we construct the response of a finite, baffled plate by a superposition of infinite plate propagating waves continuously scattering off the plate ends and solve for the unstable resonance frequencies and temporal growth rates for long plates. We present a comparison between our computational results and the infinite plate theory. In particular, the resonance response of a moderately sized plate is shown to be in excellent agreement with our long plate analytical predictions.
7
Wait, P. C., T. P. Newson, C. N. Pannell, and P. St J. Russell. "Experimental Measurement of Multiple Brillouin Stokes Orders in a Fibre Amplifier Under Pulsed Excitation." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.mb.3.
Анотація:
In long passive optical fibres excited by narrow linewidth sources, stimulated Brillouin scattering (SBS) is the first non-linear effect to reach threshold [1]. In optically amplifying fibre, the SBS characteristics are drastically modified, and the threshold power can reach μW levels [2]. This is particularly important in long lengths of fibre lightly doped with Erbium to provide distributed gain, as has been proposed for practical amplifier systems [3]. Above a certain threshold power, the electrostrictive phonon gain provided by interference of the forward pump and backward Stokes waves coherently amplifies the phonon population at the resonant frequency, resulting in a sudden stimulated surge in Stokes power. At sufficiently high pump powers, this process can continue, producing a cascade of successive Stokes orders. In passive fibre, the threshold power at which SBS becomes significant is governed by the temperature, the modal area and the pump laser linewidth [2]. In this paper, SBS in a 60 m long Erbium-doped fibre amplifier (EDFA) is explored for excitation by 80 nsec pulses at various different levels of EDFA gain. A cascade of first, second, third and fourth Stokes orders is observed; previous work reported only two Stokes orders under similar conditions [4].
8
Belibassakis, K. A., and G. A. Athanassoulis. "A Fast Convergent Modal-Expansion of the Wave Potential With Application to the Hydrodynamic and Hydroelastic Analysis of Floating Bodies in General Bathymetry." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79681.
Анотація:
A non-linear coupled-mode system of horizontal equations has been derived with the aid of Luke’s (1967) variational principle, modelling the evolution of nonlinear water waves in intermediate depth and over a general bathymetry Athanassoulis & Belibassakis (2002, 2008). Following previous work by the authors in the case of linearised water waves (Athanassoulis & Belibassakis 1999), the vertical structure of the wave field is exactly represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional modes, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The coupled-mode system fully accounts for the effects of non-linearity and dispersion. The main feature of this approach that a small number of modes (of the order of 5–6) are enough for the precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included in the local-mode series. The consistent coupled-mode system has been applied to numerical investigation of families of steady nonlinear travelling wave solutions in constant depth (Athanassoulis & Belibassakis 2007) showing good agreement with known solutions both in the Stokes and the cnoidal wave regimes. In the present work we focus on the hydroelastic analysis of floating bodies lying over variable bathymetry regions, with application to the non-linear scattering of water waves by large floating structures (of VLFS type or ice sheets) characterised by variable thickness (draft), flexural rigidity and mass distributions, modelled as thin plates of variable thickness, extending previous approaches (see, e.g., Porter & Porter 2004, Belibassakis & Athanassoulis 2005, 2006, Bennets et al 2007). Numerical examples are presented, showing that useful results can be obtained for the analysis of large floating elastic bodies or structures very efficiently by keeping only a few terms in the expansion. Ideas for extending our approach to 3D are also discussed.
9
Gommerstadt, B. Y. "The J and M Integrals for a Cylindrical Cavity in a Time-Harmonic Wave Field." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65353.
Анотація:
The invariant integrals are being widely used in the study of defects and fracture mechanics, mostly in elastostatics. However, the properties and the interpretation of these integrals in elastodynamics, especially in the case of time-harmonic excitation, have remained unexplored. Their study has a variety of engineering and geophysical implications, in particular, for the further development of non-destructive evaluation techniques. This contribution is focused on the derivation of the time average J integral for a cylindrical inhomogeneity and M integral for a cylindrical cavity placed in a monochromatic plane elastic wave of arbitrary wavelength. It is shown in the context of antiplane linear elasticity, that the J integral or the material force acting on the inhomogeneity resembles the radiation pressure force exerted on a dielectric cylinder by the normally incident electromagnetic wave. Based on the existing solution of this electrodynamic problem and the corresponding acoustic problem, the J integral is expressed as a function of the nondimensional wave number in the form of the partial wave expansion of the scattering theory. Employing the same classical method as for the J integral, the closed-form solution for the time average M integral for a traction-free cavity is also obtained as a function of the nondimensional wave number. The M integral, i.e., the expansion moment per unit length on an infinitely long circular cavity, is represented in terms of the scattering phase shifts as in the case of the J integral. Rather different expressions for the cavity are also derived for both integrals, which can be used more conveniently for numerical calculations, and these calculations are carried out for J and M integrals in a wide spectrum of frequencies. Asymptotic approximations of both integrals for low and high frequencies are presented. The long wavelength approximation, including the monopole and dipole contributions, has been provided for the J integral in the form of simple analytical expression. The value of M integral in the vanishing frequency limit is also presented. In the opposite short wavelength limit, the corresponding asymptotic values are derived for both integrals. These solutions which are valid for the empty cavity are extended to the case of inviscid fluid-filled cavity. The obtained results can be used in the area of non-destructive evaluation for the flaw characterization by ultrasonic scattering methods. The derived frequency dependence of the J and M integral can be related to the measurable far-field scattering amplitudes. This relationship is relevant to the inverse-scattering approach, which can be applied to the characterization of materials in an attempt to infer geometrical characteristics of flow structures.
10
Belibassakis, K. A., Th P. Gerostathis, and G. A. Athanassoulis. "A Weakly Nonlinear Coupled-Mode Model for Wave-Current-Seabed Interaction Over General Bottom Topography." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57636.
Анотація:
A weakly nonlinear, coupled-mode model is developed for the wave-current-seabed interaction problem, with application to wave scattering by steady currents over general bottom topography. Based on previous work by the authors (Athanassoulis & Belibassakis [1], Belibassakis et al [2]), the vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus an additional term accounting for the bottom boundary condition when the bottom slope is not negligible. Using the above representation, in conjunction with Luke’s [3] variational principle, the wave-current-seabed interaction problem is reduced to a coupled system of differential equations on the horizontal plane. If only the propagating mode is retained in the vertical expansion of the wave potential, and after simplifications, the present system is reduced to an one-equation model compatible with Kirby’s [4] mild-slope model with application to the problem of wave-current interaction over slowly varying topography. The present coupled-mode system is discretized on the horizontal plane by using a second-order finite difference scheme and numerically solved by iterations. Numerical results are presented for two representative test cases, demonstrating the importance of the first evanescent modes and the sloping-bottom mode. The analytical structure of the present model facilitates its extension to treat fully non-linear waves, and it can be further elaborated to study wave propagation over random bottom topography and general currents.
Звіти організацій з теми "Non-Linear wave scattering":
1
Lavery, Andone C. Analysis of High-Frequency Broadband Acoustic Scattering from Non-Linear Internal Waves During SW06. Fort Belvoir, VA: Defense Technical Information Center, September 2009. http://dx.doi.org/10.21236/ada531378.
2
Lavery, Andone C. Continued Analysis of High-Frequency Broadband Acoustic Scattering from Non-Linear Internal Waves during SW06. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada542102.
3
Lavery, Andone C. High-Frequency Broadband Acoustic Scattering from Temperature and Salinity Microstructure: From Non-Linear Internal Waves to Estuarine Plumes. Fort Belvoir, VA: Defense Technical Information Center, September 2007. http://dx.doi.org/10.21236/ada541144.
4
Lavery, Andone C. Laboratory Measurements of Multi-Frequency and Broadband Acoustic Scattering from Turbulent and Double-Diffusive Microstructure. High-Frequency Broadband Acoustic Scattering from Non-Linear Internal Waves during SW06. Fort Belvoir, VA: Defense Technical Information Center, May 2010. http://dx.doi.org/10.21236/ada521009.