NOUMIR, Youness, LAFITTE, Olivier · OpenGrey (Institut de l'Information Scientifique et Technique) · 2011
L objectif de cette thèse est la simulation en régime haute fréquence des phénomènes aéroacoustiques en présence d un écoulement réaliste pour une meilleure compréhension des e ets de ce dernier sur la propagation des ondes acoustiques a n de pouvoir réduire les nuisances sonores dans les transports aériens. L inconnue du problème est une perturbation d un écoulement donné, dit moyen ou stationnaire, ce qui conduit naturellement à considérer des équations linéarisées. Contrairement au cas classique de l acoustique sans écoulement, le problème obtenu est vectoriel, car la présence de l écoulement stationnaire couple l acoustique et l hydrodynamique. Dans cette thèse, nous proposons l étude théorique et numérique de l approximation haute fréquence du système d Euler linéarisé, en s a ranchissant de l hypothèse d un écoulement potentiel et en utilisant une nouvelle approche, quali ée d eulérienne, basée sur des schémas numériques de type di érences nies pour la résolution de l équation eikonale sur la phase, ainsi que l équation de transport sur l amplitude. Nous traitons aussi les caustiques de type pli pour un système hyperbolique par des opérateurs intégraux de Fourier et par la représentation d Airy.
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E. Saar · Proceedings of the Academy of Sciences of the Estonian SSR Physics Mathematics · 1971
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Suzanne T. McDaniel · The Journal of the Acoustical Society of America · 1986
Diffractive corrections to the physical optics solution for the scattering of high-frequency sound by a random rough pressure release surface are derived. The correction terms are obtained by applying the composite-roughness theory to an expansion of the scattering integral. Results are presented for a three-dimensional rough surface and are compared with those obtained using a conventional composite-roughness approach.
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Per A. Mykland, Lan Zhang · Scandinavian Journal of Statistics · 2011
Abstract High frequency data have become an important feature of many areas of research. They permit the creation of estimators in highly non‐parametric classes of continuous‐time models. In the context of continuous semi‐martingale models, we here provide a locally parametric ‘double Gaussian’ approximation, to facilitate the analysis of estimators. As in Mykland and Zhang ( Econometrica , 77, 2009, p. 1403), the error in the approximation can be offset with a postasymptotic likelihood correction. The current approximation is valid in large neighbourhoods, permitting a sharp analysis of estimators that use local behaviour over asymptotically increasing numbers of observations.
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J. W. Freeland, R. G. Kouyoumjian, Pathak,Prabhakar H. · Defense Technical Information Center (DTIC) · 1970
The currents on a perfectly conducting strip illuminated by a plane wave are considered. A high frequency, approximate solution is obtained by using the exact half plane currents and employing symmetry conditions, edge conditions, continuity conditions, and the high frequency behavior of the current. The approximate currents are found to agree well with the rigorously calculated currents if the strips are sufficiently wide. The far-zone scattering patterns calculated from the approximate currents are compared with rigorously calculated patterns and patterns calculated from the geometrical theory of diffraction (GTD). The approximate current patterns and the GTD patterns can be used to construct a pattern which is accurate at all aspects. The effect on the pattern of certain types of errors in the current is discussed. It is seen that a small, almost periodic error in the current may result in a large error in the pattern at certain aspects. (Author)
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D. De, Ettore Napoli, A.G.M. Strollo · 2002 IEEE International Solid-State Circuits Conference. Digest of Technical Papers (Cat. No.02CH37315) · 2003
Two 80 MHz 0.35 /spl mu/m 3.3V CMOS ROM-less DDFS using polynomial approximation are compared with Cordic-based circuits. A 60 dBc SFDR DDFS uses 2nd-order polynomials and 0.18 mm/sup 2/, with 15 mW dissipation. An 80 dBc SFDR DDFS uses 3rd-order polynomials and 0.44 mm/sup 2/, with 35 mW dissipation.
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Julian Baumstark, Tobias Jahnke · SIAM Journal on Mathematical Analysis · 2023
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter , and typical solutions oscillate with frequency proportional to in time and space. Moreover, solutions have to be computed on time intervals with length of in order to study nonlinear and diffractive effects. As a consequence, direct numerical simulations are extremely costly or even impossible. We propose an analytical approximation and prove that it approximates the exact solution up to an error of over times of . This is a significant improvement over the classical nonlinear Schrödinger approximation, which only yields an accuracy of .
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Shushu Zhang, Vivak Patel · arXiv (Cornell University) · 2020
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but their frequency results in a plethora of computational problems in data assimilation tasks. The high-frequency of these observations has been traditionally dealt with by using data modification strategies such as accumulation, averaging, and sampling. However, these data modification strategies will reduce the quality of the estimates, which may be untenable for many systems. Therefore, to ensure high-quality estimates, we adapt stochastic approximation methods to address the unique challenges of high-frequency observations in data assimilation. As a result, we are able to produce estimates that leverage all of the observations in a manner that avoids the aforementioned computational problems and preserves the statistical accuracy of the estimates.
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Andrew S. Wixom, J. Gregory McDaniel · The Journal of the Acoustical Society of America · 2015
This paper presents high order modal methods that increase the accuracy of the standard modal truncation scheme with an emphasis on frequency-domain accuracy. The existing Mode Acceleration and Modal Truncation Augmentation methods are compared alongside a new interpretation utilizing the interpolating polynomial. This technique is motivated by taking limits of the modal sum, introducing a residual that appears as a Laurent polynomial. The results presented focus on the case when the frequency range of interest is in the middle of the system’s spectrum of eigenvalues, meaning that at least some of the system’s natural frequencies lie below the lower bound of the frequency range. This case allows for a possible error in the Modal Truncation Augmentation method that is demonstrated here. Also, convergence properties of the methods are discussed and demonstrated.
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Javier Gutiérrez-Meana, José Ã. MartÃnez-Lorenzo, Fernando Las-Heras · Contact-less Assessment of In-vivo Body Signals Using Microwave Doppler Radar (InTech) · 2011
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Javier GutieÌrrez-Meana, JoseÌ AÌ. MartiÌnez-Lorenzo, Fernando Las-Heras · Contact-less Assessment of In-vivo Body Signals Using Microwave Doppler Radar (InTech) · 2011
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Zhikang Ma, Haigang Zhang · Journal of Physics Conference Series · 2025
Abstract Ray theory is widely used in deep-sea sound propagation problems due to its clear physical meaning and concise expressions. The classical high-frequency approximation assumption ( f >10 c / H , where f is the sound frequency, c is the sound speed, and H is the water depth) is often used to determine whether the ray theory is applicable. However, although this classic criterion is simple, it may not be precise enough when dealing with very low frequency ( f <100 Hz) sound propagation problems. To overcome this problem, the curve-fitting goodness index is introduced to compare the differences between normal mode theory and ray theory in calculating distance, time delay, and group velocity. Then, an evaluation criterion was proposed. This criterion is more accurate than the classical one in judging the strong and weak frequency dependence of the sound field and is suitable for any environment. It can be approximated as a high-frequency limit for ray theory.
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Hajer Bahouri, Patrick Gérard · American Journal of Mathematics · 1999
This work is devoted to the description of bounded energy sequences of solutions to the equation (1) □ u + | u | 4 = 0 in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], up to remainder terms small in energy norm and in every Strichartz norm. The proof relies on scattering theory for (1) and on a structure theorem for bounded energy sequences of solutions to the linear wave equation. In particular, we infer the existence of an a priori estimate of Strichartz norms of solutions to (1) in terms of their energy.
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Mahamane Kader, Michel Lenczner, Ž. Mrčarica · Smart Materials and Structures · 2003
This paper focuses on the design of distributed control related to distributed mechanical systems. The sensors and actuators are assumed to be numerous and periodically distributed. The problem addressed in this paper is: 'Can we find a way to approximate an optimal control law with a distributed electronic circuit for vibration reduction?'. Solutions to this problem are proposed in the framework of vibration control using piezoelectric actuators and sensors.
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Ma, Andrew, Engin, Arif Ege · arXiv (Cornell University) · 2022
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for high-energy physics, and approximation of elementary mathematical functions. The unknown denominator polynomial of the model results in a non-linear problem, which can be replaced with successive solutions of linearized problems following the Sanathanan-Koerner (SK) iteration. An orthogonal basis can be obtained based on Arnoldi resulting in a stabilized SK iteration. We present an extension of the stabilized SK, called Orthogonal Rational Approximation (ORA), which ensures real polynomial coefficients and stable poles for realizability of electrical networks. We also introduce an efficient implementation of ORA for multi-port networks based on a block QR decomposition.
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N. Peake, E. J. Kerschen · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1995
Abstract The scattering of harmonic gusts by a two-dimensional, infinite cascade of flat plates is a model problem which is relevant to the prediction of noise generation by rotating turbomachinery. The problem can be solved analytically using the Wiener‒Hopf technique, and the key step involves the exact factorization of a certain generic kernel function, K, using infinite products. An approximate factorization, based on the realistic asymptotic limit of large reduced frequency, has been derived by Peake, and this approach has the advantages of both providing more physical insight and being significantly easier to compute than the exact factors. An important limitation of Peake’s approximation, however, is that it be comes invalid when any of the acoustic modes in the system are close to cut-off, and in this paper we therefore present new asymptotic factors which overcome this non-uniformity. The accuracy of this new approximation, across a whole range of operating parameters, is demonstrated by comparison with the exact results, with typical errors of the order of only 3% even for very modest values of the reduced frequency.
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Julian Baumstark, Tobias Jahnke, Christian Lubich · arXiv (Cornell University) · 2022
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in solutions that are polarized in the sense that up to a small error, the oscillations in the solution depend on only one of the frequencies that satisfy the dispersion relation with a given wave vector appearing in the initial wave packet. The construction and analysis of such polarized solutions is done using modulated Fourier expansions. This approach includes higher harmonics and yields approximations to polarized solutions that are of arbitrary order in the small parameter, going well beyond the known first-order approximation via a nonlinear Schrödinger equation. The given construction of polarized solutions is explicit, uses in addition a linear Schrödinger equation for each further order of approximation, and is accessible to direct numerical approximation.
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PEAKE, N, KERSCHEN, EJ, , · Cambridge University Engineering Department Publications Database · 1995
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I. Ya. Erukhimovich, Yu. A. Kriksin, Yaroslav V. Kudryavtsev · Polymer Science Series A · 2022
The problem of self-assembly in a block copolymer melt placed in a high-frequency AC field is addressed. It is assumed that the melt is a dielectric medium that transforms into a new ordered state under exposure to the external field. The mean-field approach is used as a theoretical description method. It is shown that in the zero approximation the impact of the AC electric field on the melt is equivalent to the impact of the DC electric field with the squared strength equal to the constant component of the AC electric field strength squared. In addition, in the first approximation relative to the electric field oscillation period melt elements perform small oscillations about a new position of equilibrium with the double electric field frequency.
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P. F. Daley, F. Hron · Bulletin of the Seismological Society of America · 1983
abstract When an explosive point source is buried less than one wavelength from the free surface in a perfectly elastic, homogeneous, isotropic half-space, a very strong non-geometric arrival, tentatively denoted as S* by Hron and Mikhailenko (1981), exists in the reflected shear wave field. It has all basic characteristics of an ordinary shear body wave (linear polarization, transverse particle motion, and shear wave velocity) and, as such, it can be also reflected or transmitted upon incidence at an interface according to the rules governing ordinary body waves. Because of its very strong amplitude which at most epicentral distances exceeds even the amplitude of a direct P wave, the S* arrival is undoubtedly responsible for a large part of the shear wave energy content seen in the seismic records in oil exploration, which deals almost exclusively with shallow explosive sources. In our paper, we develop a high-frequency approximation to the S* arrival applying a saddle-point method to the integral representing a shear wave reflected from the free surface due to the incidence of a spherical longitudinal wave radiated by the shallow point source. Numerical results presented in the paper show that our high-frequency approximation preserves all basic features of the S* arrival, thereby making it suitable for easy incorporation into any synthetic seismogram computation based on the ray approach.
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