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Journal articles on the topic 'Periodic and quasi-Periodic media'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Su, Xifeng, and Rafael de la Llave. "KAM Theory for Quasi-periodic Equilibria in One-Dimensional Quasi-periodic Media." SIAM Journal on Mathematical Analysis 44, no. 6 (2012): 3901–27. http://dx.doi.org/10.1137/12087160x.

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2

Pang, Gen-Di. "Optical properties of quasi-periodic media." Journal of Physics C: Solid State Physics 21, no. 31 (1988): 5455–63. http://dx.doi.org/10.1088/0022-3719/21/31/016.

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3

Sinai, Yakov G. "Anomalous transport in quasi-periodic media." Russian Mathematical Surveys 54, no. 1 (1999): 181–208. http://dx.doi.org/10.1070/rm1999v054n01abeh000120.

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4

Su, Xifeng, and Rafael de la Llave. "KAM theory for quasi-periodic equilibria in 1D quasi-periodic media: II. Long-range interactions." Journal of Physics A: Mathematical and Theoretical 45, no. 45 (2012): 455203. http://dx.doi.org/10.1088/1751-8113/45/45/455203.

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5

Kimura, S., G. Schubert, and J. M. Straus. "Instabilities of Steady, Periodic, and Quasi-Periodic Modes of Convection in Porous Media." Journal of Heat Transfer 109, no. 2 (1987): 350–55. http://dx.doi.org/10.1115/1.3248087.

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Instabilities of steady and time-dependent thermal convection in a fluid-saturated porous medium heated from below have been studied using linear perturbation theory. The stability of steady-state solutions of the governing equations (obtained numerically) has been analyzed by evaluating the eigenvalues of the linearized system of equations describing the temporal behavior of infinitesimal perturbations. Using this procedure, we have found that time-dependent convection in a square cell sets in at Rayleigh number Ra=390. The temporal frequency of the simply periodic (P(1)) convection at Raylei

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6

de la Llave, Rafael, Xifeng Su, and Lei Zhang. "Resonant Equilibrium Configurations in Quasi-Periodic Media: KAM Theory." SIAM Journal on Mathematical Analysis 49, no. 1 (2017): 597–625. http://dx.doi.org/10.1137/15m1048598.

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7

de la Llave, Rafael, Xifeng Su, and Lei Zhang. "Resonant Equilibrium Configurations in Quasi-periodic Media: Perturbative Expansions." Journal of Statistical Physics 162, no. 6 (2016): 1522–38. http://dx.doi.org/10.1007/s10955-016-1464-5.

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8

Gao, Yixian, Weipeng Zhang, and Shuguan Ji. "Quasi-Periodic Solutions of Nonlinear Wave Equation with x-Dependent Coefficients." International Journal of Bifurcation and Chaos 25, no. 03 (2015): 1550043. http://dx.doi.org/10.1142/s0218127415500431.

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This paper is devoted to the study of quasi-periodic solutions of a nonlinear wave equation with x-dependent coefficients. Such a model arises from the forced vibration of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. Based on the partial Birkhoff normal form and an infinite-dimensional KAM theorem, we can obtain the existence of quasi-periodic solutions for this model under the general boundary conditions.

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9

Pang, Gen-Di, and Fu-Cho Pu. "Non-linear optical effects in quasi-periodic multi-layered media." Journal of Physics C: Solid State Physics 21, no. 22 (1988): L853—L856. http://dx.doi.org/10.1088/0022-3719/21/22/014.

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10

Ben-Messaoud, Tahar, Jason Riordon, Alexandre Melanson, P. V. Ashrit, and Alain Haché. "Photoactive periodic media." Applied Physics Letters 94, no. 11 (2009): 111904. http://dx.doi.org/10.1063/1.3095478.

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11

Chulaevsky, Victor. "The KAM approach to the localization in “haarsch” quasi-periodic media." Journal of Mathematical Physics 59, no. 1 (2018): 013509. http://dx.doi.org/10.1063/1.4995024.

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12

Cluni, F., and V. Gusella. "Estimation of residuals for the homogenized solution of quasi-periodic media." Probabilistic Engineering Mechanics 54 (October 2018): 110–17. http://dx.doi.org/10.1016/j.probengmech.2017.09.001.

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13

Werner, P. "Resonances in periodic media." Mathematical Methods in the Applied Sciences 14, no. 4 (1991): 227–63. http://dx.doi.org/10.1002/mma.1670140403.

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14

Ayoul-Guilmard, Quentin, Anthony Nouy, and Christophe Binetruy. "Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (2018): 869–91. http://dx.doi.org/10.1051/m2an/2018022.

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This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic diffusion equation defined on a domain D such that D̅ is the union of cells {D̅i}i∈I and we introduce a two-scale representation by identifying any function v(x) defined on D with a bi-variate function v(i,y), where i ∈ I relates to the index of the cell containing the point x and y ∈ Y relates to a local coordinate in a reference cell Y. We introduce a weak formulation of the problem in a broken Sobolev space V(D) usin

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15

Gorshkov, A. S., and K. I. Volyak. "The Interaction Video Pulses and Quasi-Harmonic Signals in Periodic Nonlinear Media." Japanese Journal of Applied Physics 34, Part 1, No. 9A (1995): 5070–75. http://dx.doi.org/10.1143/jjap.34.5070.

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16

Simbolon, Winda D. E., and Ajat Sudrajat. "Pengaruh Media Pembelajaran Berbasis Problem Based Learning dan Motivasi terhadap Hasil Belajar Siswa pada Materi Sistem Periodik Unsur Sma Kelas X." EduInovasi: Journal of Basic Educational Studies 4, no. 3 (2024): 1356–71. http://dx.doi.org/10.47467/edu.v4i3.3865.

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This research aims to find out whether there are differences in student learning outcomes taught with PBL-based Powtoon and PBL-based Canva, to find out whether there are differences in student learning outcomes with varying learning motivation on the Periodic System of Elements material, and to see whether there is an interaction between media and learning motivation. on student learning outcomes. This research uses a quasi-experimental method with a 2x2 factorial design, the population is all class X students at SMA N 14 Medan. Samples were taken by random cluster sampling in 2 classes with

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17

Krejčí, Pavel. "Periodic solutions to Maxwell equations in nonlinear media." Czechoslovak Mathematical Journal 36, no. 2 (1986): 238–58. http://dx.doi.org/10.21136/cmj.1986.102088.

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18

Kuznetsov, Sergey V. "Fundamental Solutions for Periodic Media." Advances in Mathematical Physics 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/473068.

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Necessity for the periodic fundamental solutions arises when the periodic boundary value problems should be analyzed. The latter are naturally related to problems of finding the homogenized properties of the dispersed composites, porous media, and media with uniformly distributed microcracks or dislocations. Construction of the periodic fundamental solutions is done in terms of the convergent series in harmonic polynomials. An example of the periodic fundamental solution for the anisotropic porous medium is constructed, along with the simplified lower bound estimate.

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19

Mikaeeli, Ameneh, Alireza Keshavarz, Ali Baseri, and Michal Pawlak. "Controlling Thermal Radiation in Photonic Quasicrystals Containing Epsilon-Negative Metamaterials." Applied Sciences 13, no. 23 (2023): 12947. http://dx.doi.org/10.3390/app132312947.

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The transfer matrix approach is used to study the optical characteristics of thermal radiation in a one-dimensional photonic crystal (1DPC) with metamaterial. In this method, every layer within the multilayer structure is associated with its specific transfer matrix. Subsequently, it links the incident beam to the next layer from the previous layer. The proposed structure is composed of three types of materials, namely InSb, ZrO2, and Teflon, and one type of epsilon-negative (ENG) metamaterial and is organized in accordance with the laws of sequencing. The semiconductor InSb has the capability

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20

Alcocer, F. J., V. Kumar, and P. Singh. "Permeability of periodic porous media." Physical Review E 59, no. 1 (1999): 711–14. http://dx.doi.org/10.1103/physreve.59.711.

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21

Griffiths, David J., and Carl A. Steinke. "Waves in locally periodic media." American Journal of Physics 69, no. 2 (2001): 137–54. http://dx.doi.org/10.1119/1.1308266.

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22

Haché, Alain, Mohit Malik, Marcus Diem, Lasha Tkeshelashvili, and Kurt Busch. "Measuring randomness with periodic media." Photonics and Nanostructures - Fundamentals and Applications 5, no. 1 (2007): 29–36. http://dx.doi.org/10.1016/j.photonics.2006.11.001.

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23

Molotkov, L. A., and A. E. Khilo. "Averaging periodic, nonideal elastic media." Journal of Soviet Mathematics 32, no. 2 (1986): 186–92. http://dx.doi.org/10.1007/bf01084156.

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24

Blank, Carsten, Martina Chirilus-Bruckner, Vincent Lescarret, and Guido Schneider. "Breather Solutions in Periodic Media." Communications in Mathematical Physics 302, no. 3 (2011): 815–41. http://dx.doi.org/10.1007/s00220-011-1191-3.

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25

Sab, K., and F. Pradel. "Homogenisation of periodic Cosserat media." International Journal of Computer Applications in Technology 34, no. 1 (2009): 60. http://dx.doi.org/10.1504/ijcat.2009.022703.

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26

Manela, Ofer, Mordechai Segev, and Demetrios N. Christodoulides. "Nondiffracting beams in periodic media." Optics Letters 30, no. 19 (2005): 2611. http://dx.doi.org/10.1364/ol.30.002611.

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27

Caffarelli, Luis A., and Rafael de la Llave. "Planelike minimizers in periodic media." Communications on Pure and Applied Mathematics 54, no. 12 (2001): 1403–41. http://dx.doi.org/10.1002/cpa.10008.

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28

Eberhard, J. P., N. Suciu, and C. Vamoş. "On the self-averaging of dispersion for transport in quasi-periodic random media." Journal of Physics A: Mathematical and Theoretical 40, no. 4 (2007): 597–610. http://dx.doi.org/10.1088/1751-8113/40/4/002.

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29

Danilenko, V. A., and S. I. Skurativskyy. "Invariant chaotic and quasi-periodic solutions of nonlinear nonlocal models of relaxing media." Reports on Mathematical Physics 59, no. 1 (2007): 45–51. http://dx.doi.org/10.1016/s0034-4877(07)80003-6.

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30

Parnell, W. J., and I. D. Abrahams. "Dynamic homogenization in periodic fibre reinforced media. Quasi-static limit for SH waves." Wave Motion 43, no. 6 (2006): 474–98. http://dx.doi.org/10.1016/j.wavemoti.2006.03.003.

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31

Blass, Timothy, and Rafael de la Llave. "The Analyticity Breakdown for Frenkel-Kontorova Models in Quasi-periodic Media: Numerical Explorations." Journal of Statistical Physics 150, no. 6 (2013): 1183–200. http://dx.doi.org/10.1007/s10955-013-0718-8.

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32

Topolnikov, A. S. "Argumentation of Application if Quasi-Stationary Model to Describe the Periodic Regime of Oil Well." Proceedings of the Mavlyutov Institute of Mechanics 12, no. 1 (2017): 15–26. http://dx.doi.org/10.21662/uim2017.1.003.

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In the paper the argumentation of application of quasi-stationary model of gas-liquid flow is presented to describe periodic regime of oil well operating. It is shown that this simplification actually does not affect the solution accuracy, but allows to essentially diminish the calculating time. In view of the considered problem specification the transition from non-stationary model of media to the quasi-stationary model greatly increases the computational speed, which is the necessary condition for execution the optimization calculations.

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33

Roshid, Md Mamunur, Mohammad Safi Ullah, M. M. Rahman, and Harun-Or Roshid. "Chaotic behavior, sensitivity analysis and Jacobian elliptic function solution of M-fractional paraxial wave with Kerr law nonlinearity." PLOS ONE 20, no. 2 (2025): e0314681. https://doi.org/10.1371/journal.pone.0314681.

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This study investigates the paraxial approximation of the M-fractional paraxial wave equation with Kerr law nonlinearity. The paraxial wave equation is most important to describe the propagation of waves under the paraxial approximation. This approximation assumes that the wavefronts are nearly parallel to the axis of propagation, allowing for simplifications that make the equation particularly useful in studying beam-like structures such as laser beams and optical solitons. The paraxial wave equation balances linear dispersion and nonlinear effects, capturing the essential dynamics of wave ev

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34

LEVENSON, J. A., and P. VIDAKOVIC. "QUANTUM NOISE REDUCTION IN TRAVELLING-WAVE QUASI-PHASE-MATCHED SECOND HARMONIC GENERATION." Journal of Nonlinear Optical Physics & Materials 05, no. 04 (1996): 879–98. http://dx.doi.org/10.1142/s0218863596000623.

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The present calculation on squeezing capabilities of quadratic nonlinear media in which the phase matching condition is achieved artificially by a periodic poling of the nonlinear susceptibility shows that interesting performance can be obtained for highly integrable and nonlinear materials, using technologies already developed. The origin of squeezing in quasi-phase matched (QPM) media is the cascading of two second order nonlinearities, which at small second harmonic conversion rates has properties similar to a more familiar, purely third order nonlinear effect—Kerr effect.

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35

Dohnal, Tomáš, Dmitry E. Pelinovsky, and Guido Schneider. "Travelling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media." Nonlinearity 37, no. 5 (2024): 055005. http://dx.doi.org/10.1088/1361-6544/ad3097.

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Abstract Travelling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrödinger equation arising as the envelope equation. We are interested in a rigorous existence proof of such solutions for a nonlinear wave equation with spatially periodic coefficients. Such solutions are quasi-periodic in a reference frame co-moving with the envelope. We use spatial dynamics, invariant manifolds, and near-identity transformations to constr

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36

Ji, Shuguan. "Time-periodic solutions to a nonlinear wave equation with periodic or anti-periodic boundary conditions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2103 (2008): 895–913. http://dx.doi.org/10.1098/rspa.2008.0272.

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This paper is concerned with the existence of time-periodic solutions to the nonlinear wave equation with x -dependent coefficients u ( x ) y tt − ( u ( x ) y x ) x + au ( x ) y +| y | p −2 y = f ( x , t ) on (0, π )× under the periodic or anti-periodic boundary conditions y (0, t )=± y ( π , t ), y x (0, t )=± y x ( π , t ) and the time-periodic conditions y ( x , t + T )= y ( x , t ), y t ( x , t + T )= y t ( x , t ). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. A main concept is the notion ‘weak solut

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37

Lipton, Robert, and Robert Viator Jr. "Creating Band Gaps in Periodic Media." Multiscale Modeling & Simulation 15, no. 4 (2017): 1612–50. http://dx.doi.org/10.1137/16m1083396.

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38

Carlsson, N., A. Mahanti, Zongpeng Li, and D. Eager. "Optimized Periodic Broadcast of Nonlinear Media." IEEE Transactions on Multimedia 10, no. 5 (2008): 871–84. http://dx.doi.org/10.1109/tmm.2008.922847.

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39

Delyon, François, Yves-Emmanuel Lévy, and Bernard Souillard. "Nonperturbative Bistability in Periodic Nonlinear Media." Physical Review Letters 57, no. 16 (1986): 2010–13. http://dx.doi.org/10.1103/physrevlett.57.2010.

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40

Liao, Shih-Gang, and Chin-Chin Wu. "Propagation failure in discrete periodic media." Journal of Difference Equations and Applications 19, no. 8 (2013): 1268–75. http://dx.doi.org/10.1080/10236198.2012.739169.

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41

Conca, Carlos, Rafael Orive, and Muthusamy Vanninathan. "On Burnett coefficients in periodic media." Journal of Mathematical Physics 47, no. 3 (2006): 032902. http://dx.doi.org/10.1063/1.2179048.

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42

Hizi, Uzi, and David J. Bergman. "Molecular diffusion in periodic porous media." Journal of Applied Physics 87, no. 4 (2000): 1704–11. http://dx.doi.org/10.1063/1.372081.

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43

Frankel, Michael, and Victor Roytburd. "Dynamics of SHS in periodic media." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (2005): e1507-e1515. http://dx.doi.org/10.1016/j.na.2005.01.046.

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44

Bankov, S. E. "Electrodynamics of Inhomogeneous 2D Periodic Media." Journal of Communications Technology and Electronics 64, no. 11 (2019): 1159–69. http://dx.doi.org/10.1134/s1064226919110044.

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45

Saeger, R. B., L. E. Scriven, and H. T. Davis. "Transport processes in periodic porous media." Journal of Fluid Mechanics 299 (September 25, 1995): 1–15. http://dx.doi.org/10.1017/s0022112095003399.

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The Stokes equation system and Ohm's law were solved numerically for fluid in periodic bicontinuous porous media of simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) symmetry. The Stokes equation system was also solved for fluid in porous media of SC arrays of disjoint spheres. The equations were solved by Galerkin's method with finite element basis functions and with elliptic grid generation. The Darcy permeability k computed for flow through SC arrays of spheres is in excellent agreement with predictions made by other authors. Prominent recirculation patterns are found

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46

Claes, I., and C. Van den Broeck. "Dispersion of particles in periodic media." Journal of Statistical Physics 70, no. 5-6 (1993): 1215–31. http://dx.doi.org/10.1007/bf01049429.

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47

Molotkov, L. A., and A. E. Khilo. "Effective media for periodic anisotropic systems." Journal of Soviet Mathematics 30, no. 5 (1985): 2445–50. http://dx.doi.org/10.1007/bf02107408.

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48

Drouot, A., C. L. Fefferman, and M. I. Weinstein. "Defect Modes for Dislocated Periodic Media." Communications in Mathematical Physics 377, no. 3 (2020): 1637–80. http://dx.doi.org/10.1007/s00220-020-03787-0.

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49

Blonskyi, I., V. Kadan, Y. Shynkarenko, et al. "Periodic femtosecond filamentation in birefringent media." Applied Physics B 120, no. 4 (2015): 705–10. http://dx.doi.org/10.1007/s00340-015-6186-x.

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50

Kaminer, Ido, Carmel Rotschild, Ofer Manela, and Mordechai Segev. "Periodic solitons in nonlocal nonlinear media." Optics Letters 32, no. 21 (2007): 3209. http://dx.doi.org/10.1364/ol.32.003209.

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