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Journal articles on the topic 'Propagation equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

AVITAL, ELDAD J., RICARDO E. MUSAFIR, and THEODOSIOS KORAKIANITIS. "NONLINEAR PROPAGATION OF SOUND EMITTED BY HIGH SPEED WAVE PACKETS." Journal of Computational Acoustics 21, no. 02 (2013): 1250027. http://dx.doi.org/10.1142/s0218396x12500270.

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Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervel

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Musielak, Z. E. "A New Fundamental Asymmetric Wave Equation and Its Application to Acoustic Wave Propagation." Advances in Mathematical Physics 2023 (April 12, 2023): 1–11. http://dx.doi.org/10.1155/2023/5736419.

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The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagating waves as it accounts for the Doppler effect, forward and backward waves, and makes the wave speed to be the same in all inertial frames. To demonstrate these properties, the equation is applied to acoustic wave propagation in an isothermal atmosphere, and to determine Lamb’s cutoff frequency.

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van Gestel, Robert A. M., Martijn J. H. Anthonissen, Jan H. M. ten Thije Boonkkamp, and Wilbert L. IJzerman. "An energy conservative hp-scheme for light propagation using Liouville’s equation for geometrical optics." EPJ Web of Conferences 238 (2020): 02005. http://dx.doi.org/10.1051/epjconf/202023802005.

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In this contribution an alternative method to standard forward ray-tracing is briefly outlined. The method is based on a phase-space description of light propagating through an optical system. The propagation of light rays are governed by Hamilton’s equations. Conservation of energy and étendue for a beam of light, allow us to derive a Liouville’s equation for the energy propagation through an optical system. Liouville’s equation is solved numerically using an hp-adaptive scheme, which for a smooth refractive index field is energy conservative. A proper treatment of optical interfaces ensures

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4

Bschorr, Oskar, and Hans-Joachim Raida. "One-Way Wave Equation Derived from Impedance Theorem." Acoustics 2, no. 1 (2020): 164–71. http://dx.doi.org/10.3390/acoustics2010012.

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The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathema

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Meher, Mehrollah, and Davood Rostamy. "Hybrid of differential quadrature and sub-gradients methods for solving the system of Eikonal equations." Nonlinear Engineering 10, no. 1 (2021): 436–49. http://dx.doi.org/10.1515/nleng-2021-0035.

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Abstract Many important natural phenomena of wave propagations are modeled by Eikonal equations and a variety of new methods are needed to solve them. The differential quadrature method (DQM) is an effective numerical method for solving the system of differential equations that can achieve accurate numerical results using fewer grid points and therefore requires relatively little computational effort. In this paper, we focus on the implementation of the non-smooth Eikonal optimization by using a hybrid of polynomial differential quadrature (PDQ) or Fourier differential quadrature (FDQ) method

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Alrefai, Waleed Ahmed Mahmoud. "SCHRÖDINGER EQUATION FOR PROPAGATION IN PHOTONIC CRYSTAL FIBERS." EUREKA: Physics and Engineering 1 (January 29, 2016): 13–20. http://dx.doi.org/10.21303/2461-4262.2016.00021.

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The propagation of light in a guided medium is generally described by the Maxwell’s equations. For long lengths of fiber, the Nonlinear Schrödinger (NLS) wave equation is typically derived under a few approximations on the waveguide properties of the guiding medium. In theoretical physics, the nonlinear Schrödinger equation is a nonlinear variation of the Schrödinger equation. The propagation of the wave is a fundamental phenomenon occurring in several physical systems. It is a classical field equation whose principal applications are to the propagation of light in nonlinear planar waveguides

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CAMPOS, L. M. B. C., and P. M. V. M. MENDES. "On the effects of viscosity and anisotropic resistivity on the damping of Alfvén waves." Journal of Plasma Physics 63, no. 3 (2000): 221–38. http://dx.doi.org/10.1017/s0022377899008259.

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The equations of magnetohydrodynamics (MHD) are written for non-uniform viscosity and resistivity – the latter in the cases of Ohmic and anisotropic resistivity. In the case of Ohmic (anisotropic) diffusivity, there is (are) one (two) transverse components of the velocity and magnetic field perturbation(s), leading to a second-order (fourth-order) dissipative Alfvén- wave equation. In the more general case of dissipative Alfvén waves with isotropic viscosity and anisotropic resistivity, the fourth-order wave equation may be replaced by two decoupled second-order equations for right- and left-p

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8

Smyth, N. F. "Propagation of flame fronts." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, no. 4 (1990): 385–96. http://dx.doi.org/10.1017/s0334270000006743.

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AbstractThe propagation of a flame front in a combusting gas is considered in the limit in which the width of the reaction-zone is small compared with some overall flow dimension. In this approximation, the front propagates along its normals at a speed dependent on the local curvature of the front and is governed by a nonlinear equivalent of the geometric optics equations. Some exact solutions of this equation are found and a numerical scheme is developed to solve the equation for more complicated geometries.

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9

Moya-Cessa, H. M., I. Ramos-Prieto, F. Soto-Eguibar, U. Ruíz, and D. Sánchez-de-la-Llave. "Paraxial wave propagation: Operator techniques." Journal of Physics: Conference Series 2986, no. 1 (2025): 012014. https://doi.org/10.1088/1742-6596/2986/1/012014.

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Abstract The similarity between the Schrödinger equation and the paraxial wave equation permits numerous analogies linking these fields, which is pivotal in advancing both quantum mechanics and wave optics. In this study, we demonstrate the application of operator techniques to an electromagnetic field characterized by the function f(x + ay), leveraging the structural analogies between these equations. Specifically, we employ initial conditions defined by Airy and Bessel functions to illustrate the practical implementation of these techniques.

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10

Chen, Yongze, and Philip L. F. Liu. "The unified Kadomtsev–Petviashvili equation for interfacial waves." Journal of Fluid Mechanics 288 (April 10, 1995): 383–408. http://dx.doi.org/10.1017/s0022112095001182.

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In this paper, the propagation of interfacial waves in a two-layered fluid system is investigated. The interfacial waves are weakly nonlinear and dispersive and propagate in a slowly rotating channel with varying topography and sidewalls, and a weak steady background current field. An evolution equation for the interfacial displacement is derived for waves propagating predominantly in the longitudinal direction of the channel. This new evolution equation is called the unified Kadomtsev–Petviashvili (uKP) equation because most of the KP-type equations existing in the literature for both surface

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11

Smirnov, Aleksandr O., and Eugeni A. Frolov. "On the Propagation Model of Two-Component Nonlinear Optical Waves." Axioms 12, no. 10 (2023): 983. http://dx.doi.org/10.3390/axioms12100983.

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Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. In this paper, we propose a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. To construct the hierarchical equations, we use the monodromy matrix method, as first proposed by B.A. Dubrovin. The method we use consists of solving the following sequence of problems. First, using the Lax operator, we find th

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Kostarev, Danila, Dmitri Klimushkin, and Pavel Mager. "Integral Equations for Problems on Wave Propagation in Near-Earth Plasma." Symmetry 13, no. 8 (2021): 1395. http://dx.doi.org/10.3390/sym13081395.

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We consider the solutions of two integrodifferential equations in this work. These equations describe the ultra-low frequency waves in the dipol-like model of the magnetosphere in the gyrokinetic framework. The first one is reduced to the homogeneous, second kind Fredholm equation. This equation describes the structure of the parallel component of the magnetic field of drift-compression waves along the Earth’s magnetic field. The second equation is reduced to the inhomogeneous, second kind Fredholm equation. This equation describes the field-aligned structure of the parallel electric field pot

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Kudryashov, Nikolay A., and Sofia F. Lavrova. "Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation." Mathematics 12, no. 11 (2024): 1632. http://dx.doi.org/10.3390/math12111632.

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The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium.

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14

Kranysˇ, M. "Causal Theories of Evolution and Wave Propagation in Mathematical Physics." Applied Mechanics Reviews 42, no. 11 (1989): 305–22. http://dx.doi.org/10.1115/1.3152415.

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There are still many phenomena, especially in continuum physics, that are described by means of parabolic partial differential equations whose solution are not compatible with the causality principle. Compatibility with this principle is required also by the theory of relativity. A general form of hyperbolic operators for the most frequently occurring linear governing equations in mathematical physics is written down. It is then easy to convert any given parabolic equation to the hyperbolic form without necessarily entering into the cause of the inadequacy of the governing equation. The method

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15

Chanyal, B. C. "A relativistic quantum theory of dyons wave propagation." Canadian Journal of Physics 95, no. 12 (2017): 1200–1207. http://dx.doi.org/10.1139/cjp-2017-0080.

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Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the el

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Shah, S. A. "Study Of Three Dimensional Propagation Of Waves In Hollow Poroelastic Circular Cylinders." International Journal of Applied Mechanics and Engineering 20, no. 3 (2015): 565–87. http://dx.doi.org/10.1515/ijame-2015-0037.

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Abstract Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic circular cylinder of infinite extent are investigated. General frequency equations for propagation of waves are obtained each for a pervious and an impervious surface. Degenerate cases of the general frequency equations of pervious and impervious surfaces, when the longitudinal wavenumber k and angular wavenumber n are zero, are considered. When k=0, the plane-strain vibrations and longitudinal shear vibrations are uncoupled and when k≠0 these are coupled. It is seen

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17

Basmaci, Ayse. "The Behavior of Electromagnetic Wave Propagation in Photonic Crystals with or without a Defect." Applied Computational Electromagnetics Society 36, no. 6 (2021): 632–41. http://dx.doi.org/10.47037/2020.aces.j.360603.

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In this study, the electromagnetic wave propagation behavior of two-dimensional photonic crystal plates with a defect is investigated. For this purpose, the partial differential equation for the electromagnetic wave propagation in various photonic crystal plates containing a defect or not is obtained by using Maxwell’s equations. The defect is also defined in the electromagnetic wave propagation equation appropriately. In order to solve the electromagnetic wave propagation equation, the finite differences method is used. The material property parameters of the photonic crystal plates are deter

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18

GLENDINNING, PAUL, and MICHAEL PROCTOR. "TRAVELLING WAVES WITH SPATIALLY RESONANT FORCING: BIFURCATIONS OF A MODIFIED LANDAU EQUATION." International Journal of Bifurcation and Chaos 03, no. 06 (1993): 1447–55. http://dx.doi.org/10.1142/s0218127493001148.

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Normal form equations are derived representing the effects of spatially resonant forcing on a bifurcation to travelling waves in a nonreflexionally invariant system. The equations also describe the effects of forcing on the van der Pol–Duffing equation. It is found that the forcing prevents the propagation of the wave if it is sufficiently strong: the transition to a nonuniformly propagating solution can occur either via an oscillatory bifurcation or due to a saddle node bifurcation on a closed invariant curve.

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19

Hemmati, Mostafa. "Electron shock waves moving into an ionized medium." Laser and Particle Beams 13, no. 3 (1995): 377–82. http://dx.doi.org/10.1017/s0263034600009502.

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The propagation of electron driven shock waves has been investigated by employing a one-dimensional, three-component fluid model. In the fluid model, the basic set of equations consists of equations of conservation of mass, momentum, and energy, plus Poisson's equation. The wave is assumed to be a shock front followed by a dynamical transition region. Following Fowler's (1976) categorization of breakdown waves, the waves propagating into a preionized medium will be referred to as Class II Waves. To describe the breakdown waves, Shelton and Fowler (1968) used the terms proforce and antiforce wa

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20

GRAY, L. J., D. O. POTYONDY, E. D. LUTZ, P. A. WAWRZYNEK, L. F. MARTHA, and A. R. INGRAFFEA. "CRACK PROPAGATION MODELING." Mathematical Models and Methods in Applied Sciences 04, no. 02 (1994): 179–202. http://dx.doi.org/10.1142/s021820259400011x.

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In this paper, we review recent advances in mathematical and computer science techniques for modeling crack propagation in solids. The fracture mechanics aspect of this problem is attacked by boundary integral equation methods, in particular the use of hypersingular integral equations for analyzing crack geometries. Key issues in the development of a software system capable of efficient crack propagation studies are also discussed. As an illustration of these techniques, calculations analyzing crack growth in a fuel door hinge on the Space Shuttle are presented.

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21

Engquist, Björn, and Olof Runborg. "Computational high frequency wave propagation." Acta Numerica 12 (May 2003): 181–266. http://dx.doi.org/10.1017/s0962492902000119.

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Numerical simulation of high frequency acoustic, elastic or electro-magnetic wave propagation is important in many applications. Recently the traditional techniques of ray tracing based on geometrical optics have been augmented by numerical procedures based on partial differential equations. Direct simulations of solutions to the eikonal equation have been used in seismology, and lately approximations of the Liouville or Vlasov equation formulations of geometrical optics have generated impressive results. There are basically two techniques that follow from this latter approach: one is wave fro

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22

Zuo, Da-Wei, and Xiao-Shuo Xiang. "Soliton interaction in the Bose–Einstein condensate." Modern Physics Letters B 34, no. 32 (2020): 2050362. http://dx.doi.org/10.1142/s0217984920503625.

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Wave function of the Bose–Einstein condensate satisfies the nonlinear evolution equation set, which is composed of the driven-dissipative Gross–Pitaevskii equations and rate equation (GPR). In this paper, a three coupled GPR equation is studied. By virtue of the bilinear method, multi-soliton solutions of this GPR equation are attained. Propagation and interaction of the solitons are discussed: propagation direction of the solitons are determined by the wave number; repellent and attractive two solitons are obtained by virtue of adjustment the wave numbers; interaction of the two solitons boun

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23

RICO, L. M., and M. KIRCHBACH. "CAUSAL PROPAGATION OF SPIN-CASCADES." Modern Physics Letters A 21, no. 39 (2006): 2961–69. http://dx.doi.org/10.1142/s0217732306020779.

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We gauge the direct product of the Proca with the Dirac equation that describes the coupling to the electromagnetic field of the spin-cascade (1/2, 3/2) residing in the four-vector spinor ψμ and analyze propagation of its wave fronts in terms of the Courant–Hilbert criteria. We show that the differential equation under consideration is unconditionally hyperbolic and the propagation of its wave fronts unconditionally causal. In this way we prove that the irreducible spin-cascade embedded within ψμ is free from the Velo–Zwanziger problem that plagues the Rarita–Schwinger description of spin-3/2.

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24

Gribble, J. J., and J. M. Arnold. "Beam-propagation method ray equation." Optics Letters 13, no. 8 (1988): 611. http://dx.doi.org/10.1364/ol.13.000611.

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DEBSARMA, SUMA, K. P. DAS, and JAMES T. KIRBY. "Fully nonlinear higher-order model equations for long internal waves in a two-fluid system." Journal of Fluid Mechanics 654 (May 11, 2010): 281–303. http://dx.doi.org/10.1017/s0022112010000601.

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Fully nonlinear model equations, including dispersive effects at one-order higher approximation than in the model of Choi & Camassa (J. Fluid Mech., vol. 396, 1999, pp. 1–36), are derived for long internal waves propagating in two spatial horizontal dimensions in a two-fluid system, where the lower layer is of infinite depth. The model equations consist of two coupled equations for the displacement of the interface and the horizontal velocity of the upper layer at an arbitrary elevation, and they are correct to O(μ2) terms, where μ is the ratio of thickness of the upper-layer fluid to a ty

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TÜLÜCE DEMİRAY, Şeyma, Uğur BAYRAKCI, and Vehpi YILDIRIM. "Application of the GKM of to some nonlinear partial equations." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 1 (2023): 274–84. http://dx.doi.org/10.31801/cfsuasmas.1313970.

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In this manuscript, the strain wave equation, which plays an important role in describing different types of wave propagation in microstructured solids and the (2+1) dimensional Bogoyavlensky Konopelchenko equation, is defined in fluid mechanics as the interaction of a Riemann wave propagating along the $y$-axis and a long wave propagating along the $x$-axis, were studied. The generalized Kudryashov method (GKM), which is one of the solution methods of partial differential equations, was applied to these equations for the first time. Thus, a series of solutions of these equations were obtained

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27

Chukkol, Y. B., I. Bello, and M. Abdullahi. "Non-linear wave propagation in a weakly compressible Kelvin-Voigt liquid containing bubbly clusters." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 33, no. 1 (2023): 171–94. http://dx.doi.org/10.35634/vm230112.

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The effect of bubble-bubble interaction on wave propagation in homogeneous weakly compressible viscoelastic bubbly flow is investigated using the reductive perturbation method. The bubble dynamics equation is derived using the kinetic energy conservation approach. The bubble dynamics and mixture equations are coupled with the equation of state for gas to investigate the shock wave propagation phenomenon in the mixture. A two-dimensional Korteweg-de VriesBurger (KdVB) equation in terms of a pressure profile is derived. It is found that the bubble-bubble interaction has no effect when using the

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Stovas, Alexey, Yuriy Roganov, and Vyacheslav Roganov. "Pure mode P- and S-wave phase velocity equations in elastic orthorhombic media." GEOPHYSICS 86, no. 5 (2021): C143—C156. http://dx.doi.org/10.1190/geo2021-0067.1.

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In an elastic model with orthorhombic (ORT) symmetry, there are nine independent stiffness coefficients that control the propagation of all intrinsically coupled wave modes. For practical applications in P-wave modeling and inversion, it is important to derive the approximate solutions that support propagation of P-waves only and depend on fewer independent parameters. Due to the increasing interest in S-wave propagation in anisotropic media, we also derive an approximate equation that supports propagation of S-waves only. However, the reduction in the number of independent parameters for the

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Alkhalifah, Tariq. "An acoustic wave equation for anisotropic media." GEOPHYSICS 65, no. 4 (2000): 1239–50. http://dx.doi.org/10.1190/1.1444815.

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A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave

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CHEN, CHIFANG, YING-TSONG LIN, and DING LEE. "A THREE-DIMENSIONAL AZIMUTHAL WIDE-ANGLE MODEL FOR THE PARABOLIC WAVE EQUATION." Journal of Computational Acoustics 07, no. 04 (1999): 269–86. http://dx.doi.org/10.1142/s0218396x99000187.

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In predicting wave propagations in either direction, the size of the angle of propagation plays an important role; thus, the concept of wide-angle is introduced. Most existing acoustic propagation prediction models do have the capability of treating the wide-angle but the treatment, in practice, is vertical. This is desirable for solving two-dimensional (range and depth) problems. In extending the two-dimensional treatment to 3 dimensions, even though the wide-angle capability is maintained in most 3D models, it is still vertical. Owing to the need of a wide-angle capability in the azimuth dir

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Wang, Rujia, Shiping Wu, and Wei Chen. "Unified wave equation and numerical simulation of mechanical wave propagation in alloy solidification." SIMULATION 95, no. 1 (2018): 3–10. http://dx.doi.org/10.1177/0037549718774842.

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A unified wave equation of mechanical wave propagation during solidification of an alloy was established and the numerical solution of the wave equation was obtained. A three-element model (KSLS) used to describe the stress–strain constitutive relation of the alloy in the mushy zone was established by the analysis of rheological characteristics of molten melt during solidification. Based on the KSLS model, we could describe the constitutive relation of the liquid alloy, a Maxwell medium, and of the solidified alloy, an elastic medium, by the various Lame coefficients. The wave propagation duri

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Destrade, Michel, Alain Goriely, and Giuseppe Saccomandi. "Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2131 (2010): 1823–34. http://dx.doi.org/10.1098/rspa.2010.0508.

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We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy–Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materia

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Srinivasan, Bhuvana, Ammar Hakim, and Uri Shumlak. "Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena." Communications in Computational Physics 10, no. 1 (2011): 183–215. http://dx.doi.org/10.4208/cicp.230909.020910a.

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AbstractThe finite volume wave propagation method and the finite element Runge-Kutta discontinuous Galerkin (RKDG) method are studied for applications to balance laws describing plasma fluids. The plasma fluid equations explored are dispersive and not dissipative. The physical dispersion introduced through the source terms leads to the wide variety of plasma waves. The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications. The linearized Euler equations with dispersive source terms are used as a model equation system to compare the

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Sinkala, Winter, and Tembinkosi F. Nkalashe. "Studying a Tumor Growth Partial Differential Equation via the Black–Scholes Equation." Computation 8, no. 2 (2020): 57. http://dx.doi.org/10.3390/computation8020057.

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Two equations are considered in this paper—the Black–Scholes equation and an equation that models the spatial dynamics of a brain tumor under some treatment regime. We shall call the latter equation the tumor equation. The Black–Scholes and tumor equations are partial differential equations that arise in very different contexts. The tumor equation is used to model propagation of brain tumor, while the Black–Scholes equation arises in financial mathematics as a model for the fair price of a European option and other related derivatives. We use Lie symmetry analysis to establish a mapping betwee

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Ihara, C., and T. Misawa. "Stochastic Models Related to Fatigue Damage of Materials." Journal of Energy Resources Technology 113, no. 4 (1991): 215–21. http://dx.doi.org/10.1115/1.2905903.

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The stochastic models for the fatigue damage phenomena are proposed. They describe the uncertainty caused by inhomogeneity of materials for fatigue crack propagation of metals and fatigue damage of carbon fiber composite (CFRP). The models are given by the stochastic differential equations derived from the randomized Paris-Erdogan’s fatigue crack propagation law and Kachonov’s equation of fatigue damage. The sample paths and life distribution of fatigue crack propagation in metals or of damage accumulation in CFRP are obtained by using the solution of the stochastic differential equation and t

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Amiranashvili, Sh, and A. Demircan. "Ultrashort Optical Pulse Propagation in terms of Analytic Signal." Advances in Optical Technologies 2011 (November 1, 2011): 1–8. http://dx.doi.org/10.1155/2011/989515.

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We demonstrate that ultrashort optical pulses propagating in a nonlinear dispersive medium are naturally described through incorporation of analytic signal for the electric field. To this end a second-order nonlinear wave equation is first simplified using a unidirectional approximation. Then the analytic signal is introduced, and all nonresonant nonlinear terms are eliminated. The derived propagation equation accounts for arbitrary dispersion, resonant four-wave mixing processes, weak absorption, and arbitrary pulse duration. The model applies to the complex electric field and is independent

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Lee, Sen Yung, and Huei Yaw Ke. "Flexural Wave Propagation in an Elastic Beam With Periodic Structure." Journal of Applied Mechanics 59, no. 2S (1992): S189—S196. http://dx.doi.org/10.1115/1.2899487.

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The theory of flexural waves in an elastic beam with periodic structure is developed in terms of Floquet waves. Special relationships have been determined among the fundamental solutions of the governing equation. Two lemmas about the properties of the fundamental solutions are proved. With the help of these relations and lemmas, the analysis and classification of the dynamic nature of the problem is greatly simplified. We show that the flexural wave propagation in a periodic beam can be interpreted as the superposition of two pairs of waves propagating in opposite directions, of which one pai

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Zhang, X., X. X. Chen, and C. L. Morfey. "Acoustic Radiation from a Semi-Infinite Duct With a Subsonic Jet." International Journal of Aeroacoustics 4, no. 1-2 (2005): 169–84. http://dx.doi.org/10.1260/1475472053730075.

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The radiation of high-order spinning modes from a semi-infinite exhaust duct is studied numerically. The issues involved have applications to noise radiation from the exhaust duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near field, and the acoustic analogy for far field radiation. A 2.5D formulation of a linearised Euler equation model is employed to accommodate a single spinning mode propagating over an axisymmetric mean flow field. In the solution process, acoustic waves are admitted into the propag

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Liu, Quansheng, and Liguo Chen. "Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas." Complexity 2020 (April 22, 2020): 1–16. http://dx.doi.org/10.1155/2020/9075823.

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In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF

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KIM, JEONG-HOON. "REFRACTION AND DIFFUSION OF ACOUSTIC WAVES IN A RANDOM FLUID MEDIUM." Journal of Computational Acoustics 10, no. 02 (2002): 265–74. http://dx.doi.org/10.1142/s0218396x02001632.

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Based upon the asymptotic and stochastic formulation of the acoustic wave equations, this article considers a stochastic wave propagation problem in a random multilayer which is totally refracting. Both the WKB analysis and the diffusion limit theory of stochastic differential equations are used to analyze the interplay of refraction (macrostructure) and diffusion (microstructure) of the propagating waves. The probabilistic distribution of solutions to the resultant Kolmogorov–Fokker–Planck equation is given as a computable form from the pseudodifferential operator theory and Wiener's path int

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RENTERIA, LUCIANO ALONSO, and JUAN M. PEREZ ORIA. "A MODIFIED FINITE DIFFERENCES METHOD FOR ANALYSIS OF ULTRASONIC PROPAGATION IN NONHOMOGENEOUS MEDIA." Journal of Computational Acoustics 18, no. 01 (2010): 31–45. http://dx.doi.org/10.1142/s0218396x10004048.

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The propagation of ultrasonic waves is generally studied in homogeneous media, although in certain industrial applications the conditions of propagation differ from the ideal conditions and the predicted results are not valid. This work is focused on the resolution of the Helmholtz equation for the study of the ultrasonic propagation in nonhomogeneous media. In this way, the solution of the Helmholtz equation has been obtained by means of Finite Differences, using a nonconventional scheme that substantially improves the results obtained with other techniques such as standard Finite Differences

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Smit, P. B., and T. T. Janssen. "The Evolution of Nonlinear Wave Statistics through a Variable Medium." Journal of Physical Oceanography 46, no. 2 (2016): 621–34. http://dx.doi.org/10.1175/jpo-d-15-0146.1.

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AbstractIn coastal areas and on beaches, nonlinear effects in ocean waves are dominated by so-called triad interactions. These effects can result in large energy transfers across the wave spectrum and result in non-Gaussian wave statistics, which is important for coastal wave propagation and wave-induced transport processes. To model these effects in a stochastic wave model based on the radiative transfer equation (RTE) requires a transport equation for three-wave correlators (the bispectrum) that is compatible with quasi-homogeneous theory. Based on methods developed in optics and quantum mec

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McEvily, A. J. "A Method for the Analysis of the Growth of Short Fatigue Cracks." Materials Science Forum 482 (April 2005): 3–10. http://dx.doi.org/10.4028/www.scientific.net/msf.482.3.

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The behavior of short fatigue cracks is a matter of importance not only because much of the fatigue lifetime is spent in propagating these cracks, but also because the boundary between propagation and non-propagation separates the safe from the potentially unsafe fatigue regimes. The method of analysis is based upon the following equation:

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LAU, STEPHEN R. "DIFFERENTIAL FORMS AND WAVE EQUATIONS FOR GENERAL RELATIVITY." International Journal of Modern Physics D 07, no. 06 (1998): 857–85. http://dx.doi.org/10.1142/s0218271898000577.

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In recent papers, Choquet–Bruhat and York and Abrahams, Anderson, Choquet–Bruhat, and York (we refer to both works jointly as AACY) have cast the 3 + 1 evolution equations of general relativity in gauge-covariant and causal "first-order symmetric hyperbolic form," thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equ

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Assanto, Gaetano, Panayotis Panayotaros, and Noel F. Smyth. "Mechanical analogies for nonlinear light beams in nonlocal nematic liquid crystals." Journal of Nonlinear Optical Physics & Materials 27, no. 04 (2018): 1850046. http://dx.doi.org/10.1142/s0218863518500467.

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The equations governing nonlinear light beam propagation in nematic liquid crystals form a [Formula: see text]-dimensional system consisting of a nonlinear Schrödinger-type equation for the electric field of the wavepacket and an elliptic equation for the reorientational response of the medium. The latter is “nonlocal” in the sense that it is much wider than the size of the beam. Due to these nonlocal, nonlinear features, there are no known general solutions of the nematic equations; hence, approximate methods have been found convenient to analyze nonlinear beam propagation in such media, part

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Colas, Jules, Ariane Emmanuelli, Didier Dragna, Philippe Blanc-Benon, Benjamin Cotté, and Richard J. A. M. Stevens. "Wind turbine sound propagation: Comparison of a linearized Euler equations model with parabolic equation methods." Journal of the Acoustical Society of America 154, no. 3 (2023): 1413–26. http://dx.doi.org/10.1121/10.0020834.

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Noise generated by wind turbines is significantly impacted by its propagation in the atmosphere. Hence, for annoyance issues, an accurate prediction of sound propagation is critical to determine noise levels around wind turbines. This study presents a method to predict wind turbine sound propagation based on linearized Euler equations. We compare this approach to the parabolic equation method, which is widely used since it captures the influence of atmospheric refraction, ground reflection, and sound scattering at a low computational cost. Using the linearized Euler equations is more computati

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Galenko, P. K., and A. Salhoumi. "The hodograph equation for slow and fast anisotropic interface propagation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2205 (2021): 20200324. http://dx.doi.org/10.1098/rsta.2020.0324.

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Using the model of fast phase transitions and previously reported equation of the Gibbs–Thomson-type, we develop an equation for the anisotropic interface motion of the Herring–Gibbs–Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship ‘velocity—Gibbs free energy’, Klein–Gordon and Born–Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained

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Kumar, Rajneesh, and Vandana Gupta. "Effect of phase-lags on Rayleigh wave propagation in thermoelastic medium with mass diffusion." Multidiscipline Modeling in Materials and Structures 11, no. 4 (2015): 474–93. http://dx.doi.org/10.1108/mmms-12-2014-0066.

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Purpose – The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion. Design/methodology/approach – The field equations for the linear theory of homogeneous isotropic thermoelastic diffusion medium are taken into consideration by using dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be comple

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HRUšKA, Viktor, Aneta FURMANOVá, and Michal BEDNAříK. "Potential of data-driven discovery of nonlinear wave equations." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 8 (2024): 3079–83. http://dx.doi.org/10.3397/in_2024_3271.

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Data-driven partial differential equation discovery techniques have been growing in importance in recent years. This paper discusses its possible applications in the field of finite-amplitude sound propagation and the related phenomena (such as generation of higher harmonics and shock formation). Two cases are investigated, namely the propagation of pressure pulses as travelling waves and the interference of pressure pulses, the former leading to the Westervelt equation and the latter to the Kuznetsov equation. It is shown how representative wave equations can be extracted from data obtained b

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SINGH, S. V., and N. N. RAO. "Adiabatic dust-acoustic waves with dust-charge fluctuations." Journal of Plasma Physics 60, no. 3 (1998): 541–50. http://dx.doi.org/10.1017/s0022377898006916.

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We study the effect of charge fluctuations on the propagation of adiabatic linear and nonlinear dust-acoustic waves by considering the electrons and ions to be in Boltzmann equilibria, and the dust grains to satisfy the fluid equations with full adiabatic equation of state. Linear dust-acoustic waves are damped owing to the dust-charge fluctuations, and the damping rate decreases with increasing adiabatic dust pressure. Nonlinear dust-acoustic waves are governed by the set of coupled Boussinesq-like and dust-charge perturbation equations. It is shown that for unidirectional propagation, the Bo

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