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Journal articles on the topic 'Wiener-Hopf technique'

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Published: 18 May 2024

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1

Tiryakioglu, Burhan. "Analysis of Sound Waves with Semi Perforated Pipe." Academic Perspective Procedia 2, no. 3 (November 22, 2019): 704–10. http://dx.doi.org/10.33793/acperpro.02.03.77.

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The paper presents analytical results of radiation phenomena at the far field and solution of the wave equation with adequate boundary condition imposed by the pipe wall. An infinite pipe with perforated part is considered. The solution is obtained by using the Fourier transform technique in conjunction with the Wiener-Hopf Method. Applying the Fourier transform technique, the boundary value problem is described by Wiener Hopf equation and then solved analytically.

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2

Noor, M. A., and E. A. Al-Said. "Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities." Journal of Optimization Theory and Applications 103, no. 3 (December 1999): 705–14. http://dx.doi.org/10.1023/a:1021796326831.

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3

Nonlaopon, Kamsing, Awais Gul Khan, Muhammad Aslam Noor, and Muhammad Uzair Awan. "A study of Wiener-Hopf dynamical systems for variational inequalities in the setting of fractional calculus." AIMS Mathematics 8, no. 2 (2022): 2659–72. http://dx.doi.org/10.3934/math.2023139.

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<abstract><p>In this paper, we consider a new fractional dynamical system for variational inequalities using the Wiener Hopf equations technique. We show that the fractional Wiener-Hopf dynamical system is exponentially stable and converges to its unique equilibrium point under some suitable conditions. We also discuss some special cases, which can be obtained from our main results.</p></abstract>

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4

Lawrie, Jane B., and I. David Abrahams. "A brief historical perspective of the Wiener–Hopf technique." Journal of Engineering Mathematics 59, no. 4 (October 17, 2007): 351–58. http://dx.doi.org/10.1007/s10665-007-9195-x.

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5

Noor, Muhammad Aslam. "On certain classes of variational inequalities and related iterative algorithms." Journal of Applied Mathematics and Stochastic Analysis 9, no. 1 (January 1, 1996): 43–56. http://dx.doi.org/10.1155/s1048953396000056.

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In this paper, we introduce and study some new classes of variational inequalities and Wiener-Hopf equations. Essentially using the projection technique, we establish the equivalence between the multivalued general quasi-variational inequalities and the multivalued implicit Wiener-Hopf equations. This equivalence enables us to suggest and analyze a number of iterative algorithms for solving multivalued general quasi-variational inequalities. We also consider the auxiliary principle technique to prove the existence of a unique solution of the variational-like inequalities. This technique is used to suggest a general and unified iterative algorithm for computing the approximate solution. Several special cases which can be obtained from our main results are also discussed. The results proved in this paper represent a significant refinement and improvement of the previously known results.

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6

BOYARCHENKO, SVETLANA, and SERGEI LEVENDORSKIĬ. "EFFICIENT LAPLACE INVERSION, WIENER-HOPF FACTORIZATION AND PRICING LOOKBACKS." International Journal of Theoretical and Applied Finance 16, no. 03 (May 2013): 1350011. http://dx.doi.org/10.1142/s0219024913500118.

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We construct fast and accurate methods for (a) approximate Laplace inversion, (b) approximate calculation of the Wiener-Hopf factors for wide classes of Lévy processes with exponentially decaying Lévy densities, and (c) approximate pricing of lookback options. In all cases, we use appropriate conformal change-of-variable techniques, which allow us to apply the simplified trapezoid rule with a small number of terms (the changes of variables in the outer and inner integrals and in the formulas for the Wiener-Hopf factors must be compatible in a certain sense). The efficiency of the method stems from the properties of functions analytic in a strip (these properties were explicitly used in finance by Feng and Linetsky 2008). The same technique is applicable to the calculation of the pdfs of supremum and infimum processes, and to the calculation of the prices and sensitivities of options with lookback and barrier features.

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7

Kobayashi, Kazuya. "Diffraction of a plane electromagnetic wave by a parallel plate grating with dielectric loading: the case of transverse magnetic incidence." Canadian Journal of Physics 63, no. 4 (April 1, 1985): 453–65. http://dx.doi.org/10.1139/p85-071.

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Wave scattering and diffraction problems concerning objects with complex cross sections have been widely investigated so far with the advance of electronic computers. In this paper, a periodically placed parallel plate grating with dielectric loading is considered, and the problem of diffraction of a TM polarized plane wave is analyzed with the aid of the Wiener–Hopf technique. Introducing the Fourier transform pair for the unknown scattered field and applying boundary conditions in the transform domain, one can formulate this problem as the single Wiener–Hopf equation. This functional equation is then solved by a decomposition procedure and a rigorous solution is obtained. Furthermore, approximate solutions are derived by applying the modified residue calculus technique. Based on the above analysis, several numerical examples are given and the characteristics of this grating are discussed.

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8

Ferreiro-Castilla, Albert, and Kees van Schaik. "Applying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes to Path Functionals." Journal of Applied Probability 52, no. 1 (March 2015): 129–48. http://dx.doi.org/10.1239/jap/1429282611.

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In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential time can be sampled from. This includes classic examples such as stable processes, subclasses of spectrally one-sided Lévy processes, and large new families such as meromorphic Lévy processes. Finally, we present some examples. A particular aspect that is illustrated is that the Wiener-Hopf Monte Carlo simulation technique (provided that it applies) performs much better at approximating first passage times than a ‘plain’ Monte Carlo simulation technique based on sampling increments of the Lévy process.

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9

Ferreiro-Castilla, Albert, and Kees van Schaik. "Applying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes to Path Functionals." Journal of Applied Probability 52, no. 01 (March 2015): 129–48. http://dx.doi.org/10.1017/s0021900200012249.

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In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential time can be sampled from. This includes classic examples such as stable processes, subclasses of spectrally one-sided Lévy processes, and large new families such as meromorphic Lévy processes. Finally, we present some examples. A particular aspect that is illustrated is that the Wiener-Hopf Monte Carlo simulation technique (provided that it applies) performs much better at approximating first passage times than a ‘plain’ Monte Carlo simulation technique based on sampling increments of the Lévy process.

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10

Aslam Noor, Muhammad, and Zhenyu Huang. "Wiener–Hopf equation technique for variational inequalities and nonexpansive mappings." Applied Mathematics and Computation 191, no. 2 (August 2007): 504–10. http://dx.doi.org/10.1016/j.amc.2007.02.117.

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11

Kuznetsov, A., A. E. Kyprianou, J. C. Pardo, and K. van Schaik. "A Wiener–Hopf Monte Carlo simulation technique for Lévy processes." Annals of Applied Probability 21, no. 6 (December 2011): 2171–90. http://dx.doi.org/10.1214/10-aap746.

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12

Kisil, Anastasia V. "A constructive method for an approximate solution to scalar Wiener–Hopf equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2154 (June 8, 2013): 20120721. http://dx.doi.org/10.1098/rspa.2012.0721.

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This paper presents a novel method of approximating the scalar Wiener–Hopf equation, and therefore constructing an approximate solution. The advantages of this method over the existing methods are reliability and explicit error bounds. Additionally, the degrees of the polynomials in the rational approximation are considerably smaller than in other approaches. The need for a numerical solution is motivated by difficulties in computation of the exact solution. The approximation developed in this paper is with a view of generalization to matrix Wiener–Hopf problems for which the exact solution, in general, is not known. The first part of the paper develops error bounds in L p for . These indicate how accurately the solution is approximated in terms of how accurately the equation is approximated. The second part of the paper describes the approach of approximately solving the Wiener–Hopf equation that employs the rational Carathéodory–Fejér approximation. The method is adapted by constructing a mapping of the real line to the unit interval. Numerical examples to demonstrate the use of the proposed technique are included (performed on C hebfun ), yielding errors as small as 10 −12 on the whole real line.

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13

Thompson, Ian, and I. David Abrahams. "Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I Formal solution." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2063 (September 5, 2005): 3413–36. http://dx.doi.org/10.1098/rspa.2004.1418.

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The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotropy. For incident plane waves, an exact analytical expression for the scattered field is derived by means of the Wiener–Hopf technique. In this model problem, the Wiener–Hopf kernel is scalar and its factorization is expressed in terms of simple, definite, non-singular contour integrals. A detailed numerical evaluation of the solution will be provided in the second part of this work.

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14

Suhel, Farhat, S. K. Srivastava, and Suhel Ahmad Khan. "A Wiener-Hopf Dynamical System for Mixed Equilibrium Problems." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/102578.

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We suggest and analyze dynamical systems associated with mixed equilibrium problems by using the resolvent operator technique. We show that these systems have globally asymptotic property. The concepts and results presented in this paper extend and unify a number of previously known corresponding concepts and results in the literature.

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15

Albertson, Fredrik. "The Wiener–Hopf technique and scattering of acoustic waves in ducts." Journal of the Acoustical Society of America 103, no. 5 (May 1998): 2968. http://dx.doi.org/10.1121/1.422378.

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16

Green, Ross, Gianluca Fusai, and I. David Abrahams. "THE WIENER-HOPF TECHNIQUE AND DISCRETELY MONITORED PATH-DEPENDENT OPTION PRICING." Mathematical Finance 20, no. 2 (April 2010): 259–88. http://dx.doi.org/10.1111/j.1467-9965.2010.00397.x.

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17

Olek, Shmuel. "Wiener-Hopf Technique Solution to a Rewetting Model with Precursory Cooling." Nuclear Science and Engineering 105, no. 3 (July 1990): 271–77. http://dx.doi.org/10.13182/nse90-a19191.

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18

Daniele, V. G. "The Wiener--Hopf Technique for Impenetrable Wedges Having Arbitrary Aperture Angle." SIAM Journal on Applied Mathematics 63, no. 4 (January 2003): 1442–60. http://dx.doi.org/10.1137/s0036139901400239.

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19

Uchida, Kazunori, Takeaki Noda, and Toshiaki Matsunaga. "Application and study of the wiener-hopf technique from filtering viewpoint." Electronics and Communications in Japan (Part II: Electronics) 76, no. 12 (1993): 1–10. http://dx.doi.org/10.1002/ecjb.4420761201.

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20

Brannan, James R., Vincent J. Ervin, Jinqiao Duan, and Leonid Razoumov. "A Wiener–Hopf approximation technique for a multiple plate diffraction problem." Mathematical Methods in the Applied Sciences 27, no. 1 (December 18, 2003): 19–34. http://dx.doi.org/10.1002/mma.432.

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21

Peake, N. "The interaction between a high-frequency gust and a blade row." Journal of Fluid Mechanics 241 (August 1992): 261–89. http://dx.doi.org/10.1017/s0022112092002039.

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The ingestion of convected vorticity by a high-solidity rotating blade row is a potent noise source in modern aeroengines, due largely to the high level of mutual aerodynamic interactions between adjacent blades. In order to model this process we solve the problem of determining the unsteady lift on an infinite cascade of finite-chord flat plates due to an incident vorticity wave. The method of solution is the Wiener–Hopf technique, and we consider the case of the reduced frequency, Ω, being large, allowing application of asymptotic analysis in the formal limit Ω → ∞. This approach yields considerable simplification, both in allowing the truncation of an infinite reflection series to just two terms, and in allowing algebraic expressions for the Wiener–Hopf split functions to be found. The unsteady lift distribution is derived in closed form, and the accuracy of the asymptotic Wiener–Hopf factorization demonstrated for even modest values of Ω by comparison with exact (but less tractable) methods. Our formulae can easily be incorporated into existing noise prediction codes: the advantage of our scheme is that it handles a regime in which conventional numerical approaches become unwieldy, as well as providing significant physical insight into the underlying mechanisms.

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22

Veitch, Benjamin H., and I. David Abrahams. "On the commutative factorization of n × n matrix Wiener–Hopf kernels with distinct eigenvalues." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2078 (November 3, 2006): 613–39. http://dx.doi.org/10.1098/rspa.2006.1780.

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In this article, we present a method for factorizing n × n matrix Wiener–Hopf kernels where n >2 and the factors commute. We are motivated by a method posed by Jones (Jones 1984 a Proc. R. Soc. A 393 , 185–192) to tackle a narrower class of matrix kernels; however, no matrix of Jones' form has yet been found to arise in physical Wiener–Hopf models. In contrast, the technique proposed herein should find broad application. To illustrate the approach, we consider a 3×3 matrix kernel arising in a problem from elastostatics. While this kernel is not of Jones' form, we shall show how it can be factorized commutatively. We discuss the essential difference between our method and that of Jones and explain why our method is a generalization. The majority of Wiener–Hopf kernels that occur in canonical diffraction problems are, however, strictly non-commutative. For 2×2 matrices, Abrahams has shown that one can overcome this difficulty using Padé approximants to rearrange a non-commutative kernel into a partial-commutative form; an approximate factorization can then be derived. By considering the dynamic analogue of Antipov's model, we show for the first time that Abrahams' Padé approximant method can also be employed within a 3×3 commutative matrix form.

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23

Ayton, Lorna J. "Acoustic scattering by a finite rigid plate with a poroelastic extension." Journal of Fluid Mechanics 791 (February 24, 2016): 414–38. http://dx.doi.org/10.1017/jfm.2016.59.

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The scattering of sound by a finite rigid plate with a finite poroelastic extension interacting with an unsteady acoustic source is investigated to determine the effects of porosity, elasticity and the length of the extension when compared to a purely rigid plate. The problem is solved using the Wiener–Hopf technique, and an approximate Wiener–Hopf factorisation process is implemented to yield reliable far-field results quickly. Importantly, finite chord-length effects are taken into account, principally the interaction of a rigid leading-edge acoustic field with a poroelastic trailing-edge acoustic field. The model presented discusses how the poroelastic trailing-edge property of owls’ wings could inspire quieter aeroacoustic designs in bladed systems such as wind turbines, and provides a framework for analysing the potential noise reduction of these designs.

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24

Brock, L. M. "Analytic results for roots of two irrational functions in elastic wave propagation." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 1 (July 1998): 72–79. http://dx.doi.org/10.1017/s0334270000012376.

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AbstractThe velocities of Rayleigh surface waves and, when they exist, Stoneley interface waves can be obtained as the roots of two irrational functions. Here previous results are extended by using standard operations related to the Wiener-Hopf technique to provide expressions in quadrature for these roots.

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25

Bera, R. K., and A. Chakrabarti. "The sputtering temperature of a cooling cylindrical rod without and with an insulated core in a two-fluid medium." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 1 (July 1996): 87–100. http://dx.doi.org/10.1017/s0334270000000485.

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AbstractUtilising Jones' method associated with the Wiener-Hopf technique, explicit solutions are obtained for the temperature distributions on the surface of a cylindrical rod without an insulated core as well as that inside a cylindrical rod with an insulated inner core when the rod, in either of the two cases, is allowed to enter, with a uniform speed, into two different layers of fluid with different cooling abilities. Simple expressions are derived for the values of the sputtering temperatures of the rod at the points of entry into the respective layers, assuming the upper layer of the fluid to be of finite depth and the lower of infinite extent. Both the problems are solved through a three-part Wiener-Hopf problem of special type and the numerical results under certain special circumstances are obtained and presented in tabular forms.

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26

Mitsioulis, George. "Renormalization of the energies stored around a Wiener–Hopf structure: I." Canadian Journal of Physics 69, no. 7 (July 1, 1991): 875–90. http://dx.doi.org/10.1139/p91-142.

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A programme of renormalization of the electromagnetic energy stored around a structure admitting a solution through the Wiener–Hopf technique is proposed. The infinites of the stored magnetic energy also appear in the stored electric energy and they are suppressed freely. There are divergencies due to spatial integrations that prove to be completely renormalizable. Moreover the Wiener–Hopf procedure for the solution of the radiation from the semi-infinite parallel-plate duct gives rise to two other kinds of divergencies. First, the form of the spectrum eigenfunction causes a contribution to the stored energies from the wave-number visible region where the eigenfunction is "peaked" at certain points. Second, the squared spectrum eigenfunctions have a nonsummable singularity at the lower boundary of the visible region. The renormalizability of the formulae of the energies in both of these cases is proved.

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27

Islam, Z., A. Mukherjee, and S. Karanjai. "Exact and unique solution of a transport equation in a semi-infinite medium by Laplace transform and Wiener-Hopf technique." Tamkang Journal of Mathematics 35, no. 4 (December 31, 2004): 347–50. http://dx.doi.org/10.5556/j.tkjm.35.2004.192.

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The equation of radiative transfer in non-conservative case for diffuse reflection in a plane-parallel semi-infinite atmosphere with axial symmetry has been solved by Laplace transform and Wiener-Hopf technique. We have determined the emergent intensity in terms of Chandrasekhar's H-function and the intensity at any optical depth by inversion.

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28

Smith, M. J. A., M. A. Peter, I. D. Abrahams, and M. H. Meylan. "On the Wiener–Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (October 2020): 20200360. http://dx.doi.org/10.1098/rspa.2020.0360.

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A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener–Hopf technique. The derivation of the Wiener–Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.

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29

Bera, R. K., and A. Chakrabarti. "Cooling of an infinite slab in a two-fluid medium." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 33, no. 4 (April 1992): 474–85. http://dx.doi.org/10.1017/s0334270000007177.

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AbstractA mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.

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30

Asghar, S., and F. D. Zaman. "Diffraction of Love waves by a finite rigid barrier." Bulletin of the Seismological Society of America 76, no. 1 (February 1, 1986): 241–57. http://dx.doi.org/10.1785/bssa0760010241.

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Abstract The diffraction of Love waves, traveling in a layer overlying a half-space, normally incident upon a finite rigid barrier is considered using the Wiener-Hopf technique. The transmitted waves are calculated analytically, and it has been observed that the case of the infinite rigid barrier can be obtained as a special case of this problem.

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31

Chen, X. N., and K. Kirchgässner. "Asymptotic approximation of the Wiener-Hopf technique as applied to jet atomisation." Physica D: Nonlinear Phenomena 97, no. 1-3 (October 1996): 45–64. http://dx.doi.org/10.1016/0167-2789(96)00148-0.

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32

Colbrook, Matthew J., Lorna J. Ayton, and Athanassios S. Fokas. "The unified transform for mixed boundary condition problems in unbounded domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2222 (February 2019): 20180605. http://dx.doi.org/10.1098/rspa.2018.0605.

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This paper implements the unified transform to problems in unbounded domains with solutions having corner singularities. Consequently, a wide variety of mixed boundary condition problems can be solved without the need for the Wiener–Hopf technique. Such problems arise frequently in acoustic scattering or in the calculation of electric fields in geometries involving finite and/or multiple plates. The new approach constructs a global relation that relates known boundary data, such as the scattered normal velocity on a rigid plate, to unknown boundary values, such as the jump in pressure upstream of the plate. By approximating the known data and the unknown boundary values by suitable functions and evaluating the global relation at collocation points, one can accurately obtain the expansion coefficients of the unknown boundary values. The method is illustrated for the modified Helmholtz and Helmholtz equations. In each case, comparisons between the traditional Wiener–Hopf approach, other spectral or boundary methods and the unified transform approach are discussed.

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He, Kewen, and Kazuya Kobayashi. "Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: The Case of H-Polarization." Applied Sciences 13, no. 6 (March 14, 2023): 3715. http://dx.doi.org/10.3390/app13063715.

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In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail.

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COQUERET, GUILLAUME. "LOOKBACK OPTION PRICES UNDER A SPECTRALLY NEGATIVE TEMPERED-STABLE MODEL." International Journal of Theoretical and Applied Finance 16, no. 03 (May 2013): 1350012. http://dx.doi.org/10.1142/s021902491350012x.

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We perform a Laplace transform inversion in the time parameter on the two Wiener-Hopf factors for a spectrally negative tempered stable Lévy process. This yields the issuing price of continuously monitored lookback options. We also propose a simulation technique for the purpose of Monte-Carlo valuation and discuss the convergence rate to continuous prices when the number of discretization steps (i.e. monitoring dates) goes to infinity.

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35

Balooee, Javad, Yeol Cho, and Mee Kang. "The Wiener-Hopf Equation Technique for Solving General Nonlinear Regularized Nonconvex Variational Inequalities." Fixed Point Theory and Applications 2011, no. 1 (2011): 86. http://dx.doi.org/10.1186/1687-1812-2011-86.

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36

Abrahams, I. David. "On the application of the Wiener–Hopf technique to problems in dynamic elasticity." Wave Motion 36, no. 4 (October 2002): 311–33. http://dx.doi.org/10.1016/s0165-2125(02)00027-6.

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37

Kuo, M. K., and T. Y. Chen. "The Wiener-Hopf technique in elastodynamic crack problems with characteristic lengths in loading." Engineering Fracture Mechanics 42, no. 5 (July 1992): 805–13. http://dx.doi.org/10.1016/0013-7944(92)90061-i.

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38

Alkinidri, Mohammed, Sajjad Hussain, and Rab Nawaz. "Analysis of noise attenuation through soft vibrating barriers: an analytical investigation." AIMS Mathematics 8, no. 8 (2023): 18066–87. http://dx.doi.org/10.3934/math.2023918.

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<abstract><p>In this article, the impact of fluid flow and vibration on the acoustics of a subsonic flow is examined. Specifically, it focuses on the noise generated by a convective gust in uniform flow that is scattered by a vibrating plate of limited size. The study analyzes the interaction between acoustics and structures by considering the scattering of sound waves by a soft finite barrier. To achieve this, the Wiener-Hopf technique is utilized for the analytical treatment of the acoustic model. The approach involves performing temporal and spatial Fourier transforms on the governing convective boundary value problem, then formulating the resulting Wiener-Hopf equations. The product decomposition theorem, an extended version of Liouville's theorem, and analytic continuation are employed to solve these equations. Finally, the scattered potential integral equations are computed asymptotically. This study can be significant for understanding the acoustic properties of structures and how they interact with fluid flow in subsonic environments, which could have applications in fields such as aerospace engineering, noise reduction, and structural acoustics.</p></abstract>

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39

Buchwald, V. T., and F. Viera. "Linearised evaporation from a soil of finite depth above a water table." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 4 (April 1998): 557–76. http://dx.doi.org/10.1017/s0334270000007803.

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AbstractThe quasi-linear infiltration problem of flow from a semi-infinite wetted region on a soil of finite depth above a horizontal water table is considered in the presence of linearised evaporative loss away from the region. The resulting equations are solved by the Wiener-Hopf technique in terms of certain infinite products. Expressions for the porosity and stream function are derived, and appropriately plotted throughout the layer.

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Caglar, Bulent, Beytullah Afsin, Erdal Eren, Ahmet Tabak, Cagri Cirak, and Osman Cubuk. "Key words: Sound Diffraction; Lined Duct; Integral Transform; Wiener-Hopf Technique; Expansion Coefficients; Pole Removal Technique." Zeitschrift für Naturforschung A 65, no. 11 (November 1, 2010): 1009–19. http://dx.doi.org/10.1515/zna-2010-1111.

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The intercalation of dimethyl sulphoxide (DMSO), pyridine (Py), ethanolamine (Ea), and Nmethyl formamide (NMF) molecules into the kaolinite interlayers led to an appreciable decrease of 3697 cm−1 of the hydroxyl band. The appearance of the peaks at 3662, 3541, and 3504 cm−1 proved that the DMSO species are intercalated between the kaolinite layers through forming H-bonds with internal-surface hydroxyl groups. The intensities of the 942 and 796 cm-1 bending peaks arising from inner-surface hydroxyls decreased and new vibrational features appeared due to the intercalation of the guest species. The d001 value of pure kaolinite was found at 7.18 A° , and the d001 values were seen at 11.26, 11.62, 10.77, and 10.67 °A for kaolinite-dimethyl sulphoxide (K-DMSO), kaolinite-pyridine (K-Py), kaolinite-ethanolamine (K-EA), and kaolinite-N-methyl formamide (K-NMF) composites, respectively. The endothermic differential thermal analysis (DTA) peaks at a temperature of 108 - 334 ◦C reflected the changes in the physicochemical properties of the intercalated species. The thermal stability increase followed the order of K-Py<K-NMF<K-Ea<K-DMSO. Based on the thermal analysis data, the intercalation ratios of the composites above were determined as 80.0, 40.0, 81.6, and 82.0%, respectively. The specific surface areas are affected by the intercalation geometry of the composites within the gallery spacing. The surface areas of the K-DMSO, K-Py, and K-EA complexes increased whereas the surface area of K-NMF decreased with respect to that of untreated kaolinite.

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Birbir, F., and A. Büyükaksoy. "Plane wave diffraction by two parallel overlapped thick semiinfinite impedance plates." Canadian Journal of Physics 77, no. 11 (February 18, 2000): 873–91. http://dx.doi.org/10.1139/p99-064.

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A new approach consisting of employing the mode matching method inconjunction with the Fourier transform technique is used to analyse thediffraction of time harmonic plane waves by two parallel overlapped thickimpedance half-planes. The problem is formulated as a pair of uncoupledmodified Wiener-Hopf equations and solved approximately. Numerical resultsillustrating the effects of various parameters such as wall thickness, plateto plate separation distance, wall impedance, etc. on the diffractionphenomenon are presented.PACS No.: 41.20jb

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42

Noor, Muhammad Aslam. "On a class of multivalued variational inequalities." Journal of Applied Mathematics and Stochastic Analysis 11, no. 1 (January 1, 1998): 79–93. http://dx.doi.org/10.1155/s1048953398000070.

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In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These variational inequalities include as special cases, the previously known classes of variational inequalities. Using projection techniques, we show that multivalued variational inequalities are equivalent to fixed point problems and Wiener-Hopf equations. These alternate formulations are used to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to study the existence of a solution of multivalued variational inequalities and suggest a novel iterative algorithm. In addition, we have shown that the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.

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Çinar, G., and A. Büyükaksoy. "Diffraction by a set of three parallel impedance half-planes with the one amidst located in the opposite direction." Canadian Journal of Physics 80, no. 8 (August 1, 2002): 893–909. http://dx.doi.org/10.1139/p02-039.

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The problem of diffraction of plane waves by a set of three parallel half-planes with different surface impedances on upper and lower faces where the one in the middle is placed in the opposite direction, is solved by the mode-matching method where available, and by Fourier-transform technique elsewhere. The solution includes two independent WienerHopf equations each involving an infinite number of expansion coefficients that satisfy an infinite system of linear algebraic equations. PACS No.: 41.20J

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Georgiadis, H. G., and G. A. Papadopoulos. "Determination of SIF in a cracked plane orthotropic strip by the Wiener-Hopf technique." International Journal of Fracture 34, no. 1 (May 1987): 57–64. http://dx.doi.org/10.1007/bf00042124.

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Ayub, M., A. Naeem, and R. Nawaz. "Line-source diffraction by a slit in a moving fluid." Canadian Journal of Physics 87, no. 11 (November 2009): 1139–49. http://dx.doi.org/10.1139/p09-104.

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The diffraction of a cylindrical acoustic wave from a slit in a moving fluid using Myers condition (J. Sound Vib. 71, 429 (1980)) is investigated, and an improved form of the analytical solution for the diffracted field is presented. The problem is solved analytically using an integral transform, Wiener–Hopf technique, and the modified method of stationary phase. The mathematical results are well supported by graphical discussion showing how the absorbing parameter and Mach number affect the amplitude of the velocity potential.

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Chakrabarti, A. "On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions." ANZIAM Journal 42, no. 2 (October 2000): 277–86. http://dx.doi.org/10.1017/s1446181100011925.

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AbstractClosed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

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Ayub, M., M. H. Tiwana, A. B. Mann, and H. Zaman. "Acoustic Wave Propagation in a Trifurcated Lined Waveguide." ISRN Applied Mathematics 2011 (June 20, 2011): 1–19. http://dx.doi.org/10.5402/2011/532682.

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The diffraction of sound from a semi-infinite soft duct is investigated. The soft duct is symmetrically located inside an acoustically lined but infinite duct. A closed-form solution is obtained using integral transform and Jones' method based on Wiener-Hopf technique. The graphical results are presented, which show how effectively the unwanted noise can be reduced by proper selection of different parameters. The kernel functions are factorized with different approaches. The results may be used to design acoustic barriers and noise reduction devices.

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Davidson, Rodney F. "Waves below first cutoff in a duct." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 29, no. 4 (April 1988): 448–60. http://dx.doi.org/10.1017/s0334270000005944.

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AbstractThe two-dimensional Helmholtz equation is studied for an infinite region with two semi-infinite plates extending to infinity in opposite directions and a finite duct in the overlapping region. The solution technique leads to coupled Wiener-Hopf equations, and subsequently to an infinite set of simultaneous linear equations. As an example, an asymptotic expansion is calculated and graphed for the case when the duct length divided by duct width is large enough to ensure damping of all but the zero mode wave in the duct.

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Manosueb, Anchalee, Jeerasuda Koseeyaporn, and Paramote Wardkein. "PLI Cancellation in ECG Signal Based on Adaptive Filter by Using Wiener-Hopf Equation for Providing Initial Condition." Computational and Mathematical Methods in Medicine 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/471409.

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This paper presents a technique for finding the optimal initial weight for adaptive filter by using difference equation. The obtained analytical response of the system identifies the appropriate weights for the system and shows that the MSE depends on the initial weight. The proposed technique is applied to eliminate the known frequency power line interference (PLI) signal in the electrocardiogram (ECG) signal. The PLI signal is considered as a combination of cosine and sine signals. The adaptive filter, therefore, attempts to adjust the amplitude of cosine and sine signals to synthesize a reference signal very similar to the contaminated PLI signal. To compare the potential of the proposed technique to other techniques, the system is simulated by using the Matlab program and the TMS320C6713 digital board. The simulation results demonstrate that the proposed technique enables the system to eliminate the PLI signal with the fastest time and gains the superior results of the recovered ECG signal.

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Nethercote, M. A., A. V. Kisil, and R. C. Assier. "Diffraction of acoustic waves by multiple semi-infinite arrays." Journal of the Acoustical Society of America 154, no. 3 (September 1, 2023): 1493–504. http://dx.doi.org/10.1121/10.0020844.

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Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate. However, there are some strict limitations to its use, usually the boundary conditions need to be imposed on parallel lines (after a suitable mapping). Such mappings exist for wedges with continuous boundaries, but for discrete boundaries, they have not yet been constructed. In our previous article, we have overcome this limitation and studied the diffraction of acoustic waves by a wedge consisting of point scatterers. Here, the problem is generalised to an arbitrary number of periodic semi-infinite arrays with arbitrary orientations. This is done by constructing several coupled systems of equations (one for every semi-infinite array) which are treated independently. The derived systems of equations are solved using the discrete Wiener-Hopf technique and the resulting matrix equation is inverted using elementary matrix arithmetic. Of course, numerically this matrix needs to be truncated, but we are able to do so such that thousands of scatterers on every array are included in the numerical results. Comparisons with other numerical methods are considered, and their strengths/weaknesses are highlighted.

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