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Journal articles on the topic 'Nonlinear anisotropic medium'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

SILI, ALI. "HOMOGENIZATION OF A NONLINEAR MONOTONE PROBLEM IN AN ANISOTROPIC MEDIUM." Mathematical Models and Methods in Applied Sciences 14, no. 03 (2004): 329–53. http://dx.doi.org/10.1142/s0218202504003258.

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This paper deals with an analysis of a nonlinear monotone conduction problem posed on a medium which we assume to be anisotropic and periodically reinforced by thin fibers also assumed to be anisotropic. We consider the case where the conductivity in the fibers are more important than in the material which surrounds it so that the operator we have to consider loses his uniform ellipticity with respect to the size ε of the period; we then investigate the effect of the anisotropy in the homogenization process.

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2

Dadashyan L.H., Trofimov R.R., Konobeeva N.N., and Belonenko M.B. "Extremely short pulses in an anisotropic optical medium containing carbon nanotubes with metal conduction." Optics and Spectroscopy 130, no. 12 (2022): 1587. http://dx.doi.org/10.21883/eos.2022.12.55246.49-22.

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In this work, we study the interaction of extremely short pulses with a nonlinear anisotropic optical medium with carbon nanotubes (armchair and zigzag type) with metallic conductivity. The dependence of the pulse shape, width, and intensity on the nanotube chirality indices is analyzed. The most appropriate type of carbon nanotubes is substantiated for providing localized propagation of an electromagnetic field in a medium with anisotropic properties. Keywords: optical anisotropy, extremely short pulse, carbon nanotubes, metallic conduc.

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3

Bekrenev, Ruslan K., Geser A. Dugarov, and Tatyana V. Nefedkina. "TESTING OF AN OPTIMIZATION ALGORITHM FOR AVAZ INVERSION ON SYNTHETIC DATASET." Interexpo GEO-Siberia 2, no. 1 (2021): 354–61. http://dx.doi.org/10.33764/2618-981x-2021-2-1-354-361.

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In the paper, we study an optimization algorithm for a nonlinear AVAZ inversion of PP reflections from an anisotropic media. The algorithm is based on the exact formulas for PP wave reflection coefficient for an anisotropic HTI medium and could be applied in the case of strong-contrast boundary and various anisotropy degree. Algorithm testing on synthetic dataset for radial survey system shows that estimation of anisotropy parameters γ , δ and HTI medium symmetry axis is robust in the case of signal to noise ratio ≥ 5. For estimation of parameter ε far offset data is needed.

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4

Nefedkina, T. V., P. A. Lykhin, and G. A. Dugarov. "DETERMINATION OF AZIMUTHAL ANISOTROPIC MEDIA ELASTIC PARAMETERS FROM MULTIWAVE AVOA DATA BY NONLINEAR OPTIMIZATION METHOD." Russian Journal of geophysical technologies, no. 2 (January 29, 2019): 14–26. http://dx.doi.org/10.18303/2619-1563-2018-2-2.

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In this paper, we investigate optimization algorithm of joint nonlinear AVOA inversion of PP+PS reflections in anisotropic media. Algorithm is based on the exact solution for PP and PS waves reflection coefficients in anisotropic HTI medium. The PP and PS wave’s reflections from the top of the anisotropic layer are examined. We use synthetic seismograms generated by ray method for the algorithm testing. We show that joint compressional and converted wave’s inversion allows increasing the robustness of the method and the accuracy of medium-parameter estimates. Coefficients of anisotropy are det

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5

Sarkar, Debashish, Andrey Bakulin, and Robert L. Kranz. "Anisotropic inversion of seismic data for stressed media: Theory and a physical modeling study on Berea Sandstone." GEOPHYSICS 68, no. 2 (2003): 690–704. http://dx.doi.org/10.1190/1.1567240.

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Nonhydrostatic stress, an often‐ignored source of seismic anisotropy, is universally present in the subsurface and may be as common as intrinsic or fracture‐induced anisotropy. Nonhydrostatic stress, applied to an initially transversely isotropic solid with vertical symmetry axis (VTI), results in an effective medium having almost orthorhombic symmetry (provided that one of the principal stresses is aligned with the symmetry axis). The symmetry planes observed in this orthorhombic medium are aligned with the orientations of the principal stresses, and anisotropic parameters (ε(1,2), δ(1,2,3),

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6

Berthier, Serge. "Anisotropic effective medium theories." Journal de Physique I 4, no. 2 (1994): 303–18. http://dx.doi.org/10.1051/jp1:1994139.

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7

Wang, Duanliang, Tingbin Li, Shenglai Wang, et al. "Study on nonlinear refractive properties of KDP and DKDP crystals." RSC Advances 6, no. 18 (2016): 14490–95. http://dx.doi.org/10.1039/c5ra24761f.

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The nonlinear refractive index n<sub>2</sub> is an important parameter for the nonlinear optical properties of a medium. Especially for the anisotropic media, the nonlinear refractive index is closely related with the direction.

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8

HONG, QINGQUAN. "POWER-FLOW DENSITY OF ELECTRIC QUADRUPOLE RADIATION IN MAGNETIC ANISOTROPIC MEDIUM." International Journal of Modern Physics B 22, no. 03 (2008): 239–45. http://dx.doi.org/10.1142/s0217979208038569.

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The radium in anisotropic medium is investigated. A general formula is worked out for showing power-flow of electric quadrupole radiation with tensor form in anisotropic magnetic medium. After substituting the radiation field of electric quadrupole into this general formula, an expression of average power-flow density electric quadrupole radium in anisotropic magnetic medium is then obtained at anisotropic rectangular coordinate system through dyadic calculation. After coordinate transformation, an expression of average power-flow density of electric quadrupole radium in anisotropic magnetic m

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9

Dugarov, G. A., T. V. Nefedkina, I. Yu Bogatyrev, N. A. Goreiavchev, G. M. Mitrofanov, and T. V. Olneva. "Application of AVAZ inversion algorithm based on exact formulas to a wide-azimuth seismic survey data." PROneft’. Proffessional’no o nefti 6, no. 2 (2021): 12–19. http://dx.doi.org/10.51890/2587-7399-2021-6-2-12-19.

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Results of applying of nonlinear AVAZ inversion optimization algorithm to data from 3D wide-azimuth seismic survey in the Republic of Serbia are presented. The algorithm is based on exact reflection coefficients formulas for PP reflection from anisotropic medium. We compare it with a conventional algorithm based on Ruger linear approximation of P-wave reflection from a boundary between isotropic and anisotropic (HTI) media. Maps of fracture orientation and anisotropy degree are more detailed in the case of using AVAZ inversion based on exact formulas. The results are in general accordance with

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10

Дадашян, Л. Х., Р. Р. Трофимов, Н. Н. Конобеева та М. Б. Белоненко. "Предельно короткие импульсы в оптически анизотропной среде, содержащей углеродные нанотрубки с металлической проводимостью". Оптика и спектроскопия 130, № 12 (2022): 1861. http://dx.doi.org/10.21883/os.2022.12.54092.49-22.

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In this work, we study the interaction of extremely short pulses with a nonlinear anisotropic optical medium with carbon nanotubes (armchair and zigzag type) with metallic conductivity. The dependence of the pulse shape, width, and intensity on the nanotube chirality indices is analyzed. The most appropriate type of carbon nanotubes is substantiated for providing localized propagation of an electromagnetic field in a medium with anisotropic properties.

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11

Veerakumar, V., and M. Daniel. "Propagation of an electromagnetic soliton in a ferromagnetic medium." ANZIAM Journal 44, no. 1 (2002): 103–10. http://dx.doi.org/10.1017/s1446181100007951.

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AbstractWe study the propagation of electromagnetic waves (EMWs) in both isotropic and anisotropic ferromagnetic material media. As the EMW propagates through linear charge-free isotropic and anisotropic ferromagnetic media, it is found that the magnetic field and the magnetic induction components of the EMW and the magnetization excitations of the medium are in the form of solitons. However, the electromagnetic soliton gets damped and decelerates in the case of a charged medium. In the case of a charge-free nonlinear ferromagnetic medium we obtain results similar to those for the linear case.

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12

Prioul, Romain, Andrey Bakulin, and Victor Bakulin. "Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: Theory and laboratory verification." GEOPHYSICS 69, no. 2 (2004): 415–25. http://dx.doi.org/10.1190/1.1707061.

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We develop a rock physics model based on nonlinear elasticity that describes the dependence of the effective stiffness tensor as a function of a 3D stress field in intrinsically anisotropic formations. This model predicts the seismic velocity of both P‐ and S‐waves in any direction for an arbitrary 3D stress state. Therefore, the model overcomes the limitations of existing empirical velocity‐stress models that link P‐wave velocity in isotropic rocks to uniaxial or hydrostatic stress. To validate this model, we analyze ultrasonic velocity measurements on stressed anisotropic samples of shale an

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13

Parnell, William J. "Nonlinear pre-stress for cloaking from antiplane elastic waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2138 (2011): 563–80. http://dx.doi.org/10.1098/rspa.2011.0477.

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A theory is presented showing that cloaking of objects from antiplane elastic waves can be achieved by employing nonlinear elastic pre-stress in a neo-Hookean elastomeric material. This approach would appear to eliminate the requirement of metamaterials with inhomogeneous anisotropic shear moduli and density. Waves in the pre-stressed medium are bent around the cloaked (cavity) region by inducing inhomogeneous stress fields via pre-stress. The equation governing antiplane waves in the pre-stressed medium is equivalent to the antiplane equation in an unstressed medium with inhomogeneous and ani

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14

SAFONOV, VLADIMIR L. "CONDUCTION ELECTRON IN THE ANISOTROPIC MEDIUM." International Journal of Modern Physics B 07, no. 22 (1993): 3899–905. http://dx.doi.org/10.1142/s0217979293003528.

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A new model for describing free electrons and holes in crystals in the long-wavelength approximation is proposed. The crystalline anisotropy in the framework of this model is introduced by means of corresponding space-time geometry. The generalized Dirac’s equation is constructed and non-relativistic Hamiltonian containing energy terms of the order of c–2 is calculated. It is shown that the spin magnetic components depend on corresponding effective cyclotron masses. Applicability of the results of the proposed model to different experiments is discussed. For the one-dimensional case, a hypothe

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15

Straughan, B. "Anisotropic bidispersive convection." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2227 (2019): 20190206. http://dx.doi.org/10.1098/rspa.2019.0206.

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This paper investigates thermal convection in an anisotropic bidisperse porous medium. A bidisperse porous medium is one which possesses the usual pores, but in addition, there are cracks or fissures in the solid skeleton and these give rise to a second porosity known as micro porosity. The novelty of this paper is that the macro permeability and the micro permeability are each diagonal tensors but the three components in the vertical and in the horizontal directions may be distinct in both the macro and micro phases. Thus, there are six independent permeability coefficients. A linear instabil

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16

Zhou, Bing, Stewart Greenhalgh, and Alan Green. "Nonlinear traveltime inversion scheme for crosshole seismic tomography in tilted transversely isotropic media." GEOPHYSICS 73, no. 4 (2008): D17—D33. http://dx.doi.org/10.1190/1.2910827.

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Crosshole seismic tomography often is applied to image the velocity structure of an interwell medium. If the rocks are anisotropic, the tomographic technique must be adapted to the complex situation; otherwise, it leads to a false interpretation. We propose a nonlinear kinematic inversion method for crosshole seismic tomography in composite transversely isotropic media with known dipping symmetry axes. This method is based on a new version of the first-order traveltime perturbation equation. It directly uses the derivative of the phase velocity rather than the eigenvectors of the body-wave mod

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17

Wang, Dan, Gui-Geng Liu, Jia-Qi Lü, et al. "Femtosecond polarization-structured optical field meets an anisotropic nonlinear medium." Optics Express 26, no. 21 (2018): 27726. http://dx.doi.org/10.1364/oe.26.027726.

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18

Bartsch, Thomas, and Jarosław Mederski. "Nonlinear time-harmonic Maxwell equations in an anisotropic bounded medium." Journal of Functional Analysis 272, no. 10 (2017): 4304–33. http://dx.doi.org/10.1016/j.jfa.2017.02.019.

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19

Borodich, F. M. "Hertz contact problems for an anisotropic physically nonlinear elastic medium." Strength of Materials 21, no. 12 (1989): 1668–76. http://dx.doi.org/10.1007/bf01533408.

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20

Chen, T. C., S. J. Hwang, and C. Q. Chen. "Nonlinear Time-Dependent Thermoelastic Response in a Multilayered Anisotropic Medium." Journal of Applied Mechanics 69, no. 4 (2002): 556–63. http://dx.doi.org/10.1115/1.1458555.

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A time-dependent nonlinear thermoelastic problem of a multilayered anisotropic medium with a certain specific form of temperature-dependent material properties in generalized plane deformation is analyzed by flexibility/stiffness matrix technique in the article. The closed-form general solutions of temperature, displacements, and stresses can then be obtained in the Fourier and the Laplace transform domains by using the technique of Kirchhoff transformation. The effects of temperature-dependent material properties on the distributions of temperature and thermal stresses are also calculated and

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21

Konobeeva N.N., Belibikhin S.V., and Belonenko M.B. "Extremely short pulses in anisotropic optical media with carbon nanotubes taking into account multiphoton absorption." Optics and Spectroscopy 130, no. 6 (2022): 777. http://dx.doi.org/10.21883/eos.2022.06.54716.3043-21.

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In this paper, we study the influence of multiphoton absorption on the propagation of electromagnetic waves in a nonlinear optical anisotropic medium with carbon nanotubes. The effective equation for the vector potential of the electromagnetic field of the pulse is obtained, taking into account the second component of the polarization of the field, as well as two- and three-photon absorption processes. The dependence of the components of the pulse field on the parameters of the problem is revealed. Keywords: optical anisotropy, extremely short pulse, multiphoton absorption.

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22

Lomazov, Alexander V., Vadim A. Lomazov, Olga S. Akupiyan, Vladislav L. Anichin, and Elena V. Nesterova. "Mathematical modeling of diagnostics of thermoelastic layered medium." E3S Web of Conferences 525 (2024): 02005. http://dx.doi.org/10.1051/e3sconf/202452502005.

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The article discusses the problems of non-destructive testing of multilayer composite materials. Technological influences during manufacturing and the influence of external factors during the operation of composite structures can lead to the occurrence of material defects, which manifests itself as heterogeneity and anisotropy of individual layers and, as such, affects thermomechanical processes in multilayer composites. In the work as a model of non-destructive testing, the mathematical problem of determining the thermomechanical characteristics of weakly inhomogeneous and weakly anisotropic

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23

Karmakar, Timir, Meraj Alam, and G. P. Raja Sekhar. "Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel." Communications on Pure & Applied Analysis 21, no. 3 (2022): 845. http://dx.doi.org/10.3934/cpaa.2022001.

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<p style='text-indent:20px;'>We present asymptotic analysis of Couette flow through a channel packed with porous medium. We assume that the porous medium is anisotropic and the permeability varies along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We developed existence and uniqueness results corresponding to the anisotropic Brinkman-Forchheimer extended Darcy's equation in case of fully developed flow using the Browder-Minty theorem. Complemented with the existence and uniqueness analysis, we present an asymptotic solution by taking D

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24

Getman, Veronika A., and Tatiana F. Dolgikh. "Cauchy Problem for Describing the Behavior of a Plane Electromagnetic Wave in an Anisotropic Medium." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 1 (March 31, 2025): 28–39. https://doi.org/10.18522/1026-2237-2025-1-28-39.

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The Cauchy problem is solved by the hodograph method based on the conservation law in the case of a plane electromagnetic wave propagating in an anisotropic medium. To describe the behavior of the wave, Maxwell’s equations for an anisotropic medium in the absence of currents and free charges are used, which in the case of a plane wave leads to a system of two spatially one-dimensional homogeneous quasi-linear partial differential equations of the first order. The anisotropy of the medium is taken into account by nonlinear constitutive relations for electric and magnetic induction, depending, r

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25

S., T. Tolmachev, and V. Il'chenko A. "THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION." Electrical engineering & electromechanics, no. 2 (April 16, 2020): 40–45. https://doi.org/10.20998/2074-272X.2020.2.06.

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<em>The construction of the correct vector material equations for nonlinear anisotropic soft magnetic materials remains one of the main reserves for increasing the accuracy of mathematical models in solving magnetostatic problems in the field formulation. The aim of the work is to establish asymptotic expressions for the reciprocity principle, which is a fundamental property of reversible magnetization processes of nonlinear anisotropic media, and to use the obtained results to optimize the computational process when constructing the vector magnetization characteristic and differential permeab

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26

Liu, Zhengnan, Rui Zhang, Tian Lan, Yu Zhou, and Chao Huang. "Laboratory Test and Constitutive Model for Quantifying the Anisotropic Swelling Behavior of Expansive Soils." Applied Sciences 14, no. 6 (2024): 2255. http://dx.doi.org/10.3390/app14062255.

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Expansive soils exhibit directionally dependent swelling that traditional isotropic models fail to capture. This study investigates the anisotropic swelling characteristics of expansive soil with a medium swelling potential through the use of modified oedometric testing. Vertical swelling strains can reach up to 1.71 times that of the horizontal movements, confirming intrinsic anisotropy. A nonlinear elastic constitutive model incorporates vertical and horizontal elastic moduli with respect to matric suction to characterize anisotropy. Three elastic parameters were determined through the exper

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27

Zolotovskiĭ, I. O., and D. I. Sementsov. "Nonlinear dynamics of a pulse in an anisotropic medium with birefringence." Optics and Spectroscopy 94, no. 1 (2003): 45–49. http://dx.doi.org/10.1134/1.1540199.

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28

Kolokolov, I. V., and K. S. Turitsyn. "Effective equation of nonlinear pulse evolution in a randomly anisotropic medium." Journal of Experimental and Theoretical Physics 98, no. 2 (2004): 348–51. http://dx.doi.org/10.1134/1.1675903.

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29

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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30

Dugarov, Geser, and Tatyana Nefedkina. "OPTIMIZATION ALGORITHM ACCURACY AND STABILITY STUDY OF AVOA INVERSION OF PP+PS REFLECTIONS IN AZIMUTHALLY ANISOTROPIC MEDIA." Interexpo GEO-Siberia 2, no. 3 (2019): 122–30. http://dx.doi.org/10.33764/2618-981x-2019-2-3-122-130.

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The article investigates the accuracy and stability of the optimization algorithm for joint nonlinear AVOA inversion of PP+PS reflections in an anisotropic HTI medium. Algorithm was tested using synthetic seismograms. The analysis of objective functions is performed in order to study the sensitivity of the method to the determination of different parameters of the anisotropic model. Using two types of waves significantly increases the noise robustness of the method and the accuracy of all parameters estimation.

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31

Eftaxiopoulos, Dimitrios A., and Colin Atkinson. "A nonlinear, anisotropic and axisymmetric model for balloon angioplasty." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2056 (2005): 1097–128. http://dx.doi.org/10.1098/rspa.2004.1419.

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A nonlinear elastic, anisotropic and axisymmetric balloon angioplasty model, consisting of the balloon, the atherosclerotic plaque and the artery wall, has been developed and analysed in this paper. The deformation of the angioplasty compound, i.e. the balloon, the plaque and the artery, for slowly increasing dilation pressure within the balloon, is investigated. The plaque has been considered as a circular cylindrical tube extending all around the artery circumference. Normal radial stress and radial displacement boundary conditions have been imposed along the balloon–plaque and the plaque–ar

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32

Dreger, M. A., and J. K. Mclver. "Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion." Journal of the Optical Society of America B 7, no. 5 (1990): 776. http://dx.doi.org/10.1364/josab.7.000776.

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33

Rossikhin, Yuriy A., and Marina V. Shitikova. "Application of Weakly Anisotropic Models of a Continuous Medium for Solving the Problems of Wave Dynamics." Applied Mechanics Reviews 53, no. 3 (2000): 37–86. http://dx.doi.org/10.1115/1.3097339.

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A review of papers dealing with the investigation of wave phenomena occurring in weakly anisotropic elastic media is available in the present article. Several weakly anisotropic models of a continuous medium are presented and discussed which can be used to advantage both for solving the problems of wave dynamics and for carrying out comparison analysis of experimental data on measurements of elastic moduli of slightly anisotropic material by quasilongitudinal and quasitransverse waves with the results of the theoretical investigations. Based on these models, the behavior of harmonic and nonsta

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34

Harfash, Akil J., and Ahmed K. Alshara. "A Direct Comparison between the Negative and Positive Effects of Throughflow on the Thermal Convection in an Anisotropy and Symmetry Porous Medium." Zeitschrift für Naturforschung A 70, no. 5 (2015): 383–94. http://dx.doi.org/10.1515/zna-2015-0049.

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AbstractThe linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium are tested. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account. Then, the accuracy of the linear instability thresholds are tested using a three dimensional simulation. It is shown that the strong stabilising effect of gravity field. Moreover, the results support the assertion that the linear theory, in general, is accurate in predicting the onset of convect

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35

Alshuhail, Abdulrahman A., and Dirk J. Verschuur. "Robust estimation of vertical symmetry axis models via joint migration inversion: Including multiples in anisotropic parameter estimation." GEOPHYSICS 84, no. 1 (2019): C57—C74. http://dx.doi.org/10.1190/geo2017-0856.1.

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Because the earth is predominately anisotropic, the anisotropy of the medium needs to be included in seismic imaging to avoid mispositioning of reflectors and unfocused images. Deriving accurate anisotropic velocities from the seismic reflection measurements is a highly nonlinear and ambiguous process. To mitigate the nonlinearity and trade-offs between parameters, we have included anisotropy in the so-called joint migration inversion (JMI) method, in which we limit ourselves to the case of transverse isotropy with a vertical symmetry axis. The JMI method is based on strictly separating the sc

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36

Zinelabiddine, Mezache, and Benabdelaziz Fatiha. "Effect of the Nonlinear Parameters on the Propagation in Bi-isotropic Media." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 6 (2017): 541–47. http://dx.doi.org/10.1515/ijnsns-2017-0055.

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AbstractThis paper is an attempt to compare the nonlinear chiroptical and non-reciprocity effects of bi-isotropic media. The nonlinearity used is of a Kerr type. Following the approach of Mezache–Benabdelaziz, recently new nonlinear effects are characterized in a bi-anisotropic medium, which is due to the magnetization vector under the influence of a strong electric field. We then use these results to present the solution of nonlinear Schrödinger equation in the general case of bi-isotropic (chiral and non-reciprocal). Numerical simulations were carried out, in order to confirm the effect of t

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37

Zareei, Ahmad, and Mohammad-Reza Alam. "Cloaking in shallow-water waves via nonlinear medium transformation." Journal of Fluid Mechanics 778 (July 30, 2015): 273–87. http://dx.doi.org/10.1017/jfm.2015.350.

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A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell’s equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single

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38

Alekseev, Gennady V., Aleksey Lobanov, and Gleb Grenkin. "Numerical Study of Inverse Problems of Nonscattering Anisotropic Shell Theory." Applied Mechanics and Materials 249-250 (December 2012): 557–62. http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.557.

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The inverse problems are formulated for generalized Helmholtz equation describing propagation of acoustics waves in inhomogeneous anisotropic medium. These problems are connected with constructing nonscattering shells filled with anisotropic fluid. For solving the inverse problems we apply the nonlinear optimization techniques. Based on this approach we formulate the general control problem for the Helmholtz equation under consideration. The control problem consists of minimization of a suitable cost functional depending on the state (acoustic pressure) and unknown functions (controls). The op

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Ahles, Marcus, Kristian Motzek, Andreas Stepken, Friedemann Kaiser, Carsten Weilnau, and Cornelia Denz. "Stabilization and breakup of coupled dipole-mode beams in an anisotropic nonlinear medium." Journal of the Optical Society of America B 19, no. 3 (2002): 557. http://dx.doi.org/10.1364/josab.19.000557.

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40

SHEN, JIAN QI. "ISOTROPIC NEGATIVELY-REFRACTING ATOMIC-VAPOR MEDIUM." Modern Physics Letters B 21, no. 12 (2007): 717–28. http://dx.doi.org/10.1142/s0217984907012979.

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A new scenario to realize negative refraction with a photonic-resonant vapor material that can exhibit both electric and magnetic responses via multilevel quantum coherence is suggested. Compared with the previous method of artificial composite metamaterial, where the mechanism was considered by means of classical electromagnetic theory and the materials produced have anisotropic millimetre-scale composite structures, the present scheme suggested within the framework of quantum optics can be used to design and fabricate isotropic negatively-refracting materials with atomic-scale microscopic st

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41

Huang, Xingguo, and Stewart Greenhalgh. "Linearized formulations and approximate solutions for the complex eikonal equation in orthorhombic media and applications of complex seismic traveltime." GEOPHYSICS 83, no. 3 (2018): C115—C136. http://dx.doi.org/10.1190/geo2017-0620.1.

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We have developed linearized complex eikonal equations for orthorhombic media and the analytic solution for homogeneous acoustic media. The linearized formulations are developed from the highly nonlinear complex eikonal equation using a perturbation analysis. The analytic solution is obtained by expanding the complex traveltime in a Taylor series and constructing its coefficients. A critical factor for deriving this analytic expression is to apply the complex point-source method to the analytic expression for the background anisotropic medium. The analytic expressions show that the complex tra

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Aslanyan, L. S., and H. H. Hovakimyan. "Spatial resonance in an anisotropic medium with modulated gyrotropy." Journal of the Optical Society of America B 37, no. 3 (2020): 847. http://dx.doi.org/10.1364/josab.378809.

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Dewangan, Pawan, and Ilya Tsvankin. "Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part I — Horizontal TTI layer." GEOPHYSICS 71, no. 4 (2006): D107—D121. http://dx.doi.org/10.1190/1.2210970.

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One of the distinctive features of mode-converted waves is their asymmetric moveout (i.e., the PS-wave traveltime in general is different if the source and receiver are interchanged) caused by lateral heterogeneity or elastic anisotropy. If the medium is anisotropic, the PS-wave moveout asymmetry contains valuable information for parameter estimation that cannot be obtained from pure reflection modes. Here, we generalize the so-called [Formula: see text] method, which is designed to replace reflected PS modes in velocity analysis with pure (unconverted) SS-waves, by supplementing the output SS

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Felício Fuck, Rodrigo, Andrey Bakulin, and Ilya Tsvankin. "Theory of traveltime shifts around compacting reservoirs: 3D solutions for heterogeneous anisotropic media." GEOPHYSICS 74, no. 1 (2009): D25—D36. http://dx.doi.org/10.1190/1.3033215.

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Time-lapse traveltime shifts of reflection events recorded above hydrocarbon reservoirs can be used to monitor production-related compaction and pore-pressure changes. Existing methodology, however, is limited to zero-offset rays and cannot be applied to traveltime shifts measured on prestack seismic data. We give an analytic 3D description of stress-related traveltime shifts for rays propagating along arbitrary trajectories in heterogeneous anisotropic media. The nonlinear theory of elasticity helps to express the velocity changes in and around the reservoir through the excess stresses associ

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Shi, Wenjuan, Hongjun Liu, and Zhaolu Wang. "Gain-Assisted Giant Third-Order Nonlinearity of Epsilon-Near-Zero Multilayered Metamaterials." Nanomaterials 12, no. 19 (2022): 3499. http://dx.doi.org/10.3390/nano12193499.

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We investigate the third-order nonlinear optical properties of epsilon-near-zero (ENZ) Au/dye-doped fused silica multilayered metamaterials in the visible spectral range for TM incident by using nonlocal effective medium theory at different incidence angles. The nonlocal response affects the permittivity of anisotropic metamaterials when the thickness of the layer cannot be much smaller than the incident wavelength. By doping pump dye gain material within the dielectric layer to compensate for the metal loss, the imaginary part of the effective permittivity is reduced to 10−4, and the optical

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Hummel, Nicolas, and Serge A. Shapiro. "Nonlinear diffusion-based interpretation of induced microseismicity: A Barnett Shale hydraulic fracturing case study." GEOPHYSICS 78, no. 5 (2013): B211—B226. http://dx.doi.org/10.1190/geo2012-0242.1.

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For the successful development and operation of hydrocarbon or geothermal reservoirs, knowledge of the hydraulic transport is of crucial importance. Because fundamental physical processes of borehole fluid injections are still insufficiently understood, gathering information about transport properties of rocks under field conditions is quite difficult. However, a substantial contribution in determining the permeability evolution can be obtained by understanding the distribution of induced seismicity in space and time. We have analyzed spatio-temporal characteristics of seismicity recorded duri

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Neves, Fernando A., and Maarten V. de Hoop. "Some remarks on nonlinear amplitude versus scattering angle‐azimuth inversion in anisotropic media." GEOPHYSICS 65, no. 1 (2000): 158–66. http://dx.doi.org/10.1190/1.1444706.

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A feasibility study for inverting reflection coefficients for a single‐interface model consisting of a shale overlying a fractured sand is presented. To characterize the medium contact from amplitude versus scattering angles (AVA) behavior associated with the reflection from a particular interface, in view of the anisotropy, wide‐angle scattering data are required. However, wide‐angle scattering turns the inverse problem into an essentially nonlinear one. The inverse problem is hence analyzed with a global optimization procedure—a genetic algorithm with constraints. The key to making a genetic

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Chamoun, Georges. "An Efficient Numerical Study for Anisotropic Nonlinear Models of Competitive Swimming Species." WSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE 22 (October 21, 2024): 37–45. https://doi.org/10.37394/23208.2025.22.4.

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Traditional mathematical modeling and computational efforts have primarily focused on isotropic and linear diffusion or convection of living organisms, assuming uniform motion in all directions. However, these traditional models fail to capture the complexities of the real world where competitive interactions among species in nature often involve spatially heterogeneous and anisotropic diffusive behaviors. Another challenging aspect of such modeling involves scenarios in uid dynamics, where species' movements are in uenced by the ow of the medium. Besides the well-posedness of the mathematical

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Felício Fuck, Rodrigo, and Ilya Tsvankin. "Analysis of the symmetry of a stressed medium using nonlinear elasticity." GEOPHYSICS 74, no. 5 (2009): WB79—WB87. http://dx.doi.org/10.1190/1.3157251.

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Velocity variations caused by subsurface stress changes play an important role in monitoring compacting reservoirs and in several other applications of seismic methods. A general way to describe stress- or strain-induced velocity fields is by employing the theory of nonlinear elasticity, which operates with third-order elastic (TOE) tensors. These sixth-rank strain-sensitivity tensors, however, are difficult to manipulate because of the large number of terms involved in the algebraic operations. Thus, even evaluation of the anisotropic symmetry of a medium under stress/strain proves to be a ch

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Belhadj, M., J. ‐F Gerbeau, and B. Perthame. "A multiscale colloid transport model with anisotropic degenerate diffusion." Asymptotic Analysis 34, no. 1 (2003): 41–54. https://doi.org/10.3233/asy-2003-549.

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We consider a weakly coupled semilinear parabolic‐hyperbolic system with a degenerate and anisotropic diffusion. It arises to model the evolution of a chemical or biological tracer in a porous medium. We study the well‐posedness of the system using a L1 theory. Then, we establish the relaxation limit as the reaction constant becomes large. We prove that the system converges to a nonlinear parabolic‐hyperbolic equation that generalizes the Stefan problem. Two specificities of this paper are (i) to deal with ill‐prepared initial data and (ii) with unique entropy solutions based on a precise entr

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