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

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Published: 8 June 2024

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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 (January 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 (November 10, 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 (February 28, 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 (October 19, 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 (May 1, 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 Rayleigh numbers exceeding this value is given by the imaginary part of the complex eigenvalue. The stability of this (P(1)) state has also been studied; transition to quasi-periodic convection (QP2) occurs at Ra ≈ 510. A reverse transition to a simply periodic state (P(2)) occurs at Ra ≈ 560; a slight jump in the frequency of the P(2) state occurs at Ra between 625 and 640. The jump coincides with a second narrow (in terms of Ra) region of quasi-periodicity.

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 (January 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 (February 8, 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 (March 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.

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 (August 10, 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 (March 16, 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 (January 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 (May 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 (May 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) using a discontinuous Galerkin framework. The problem is then interpreted as a tensor-structured equation by identifying V(D) with a tensor product space ℝI⊗ V(Y) of functions defined over the product set I × Y. Tensor numerical methods are then used in order to exploit approximability properties of quasi-periodic solutions by low-rank tensors.

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 (September 15, 1995): 5070–75. http://dx.doi.org/10.1143/jjap.34.5070.

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16

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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17

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.

18

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

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19

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

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20

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 (February 2007): 29–36. http://dx.doi.org/10.1016/j.photonics.2006.11.001.

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21

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

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22

Blank, Carsten, Martina Chirilus-Bruckner, Vincent Lescarret, and Guido Schneider. "Breather Solutions in Periodic Media." Communications in Mathematical Physics 302, no. 3 (February 1, 2011): 815–41. http://dx.doi.org/10.1007/s00220-011-1191-3.

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23

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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24

Manela, Ofer, Mordechai Segev, and Demetrios N. Christodoulides. "Nondiffracting beams in periodic media." Optics Letters 30, no. 19 (October 1, 2005): 2611. http://dx.doi.org/10.1364/ol.30.002611.

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25

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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26

Mikaeeli, Ameneh, Alireza Keshavarz, Ali Baseri, and Michal Pawlak. "Controlling Thermal Radiation in Photonic Quasicrystals Containing Epsilon-Negative Metamaterials." Applied Sciences 13, no. 23 (December 4, 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 to adjust bandgaps by utilizing its thermally responsive permittivity, allowing for tunability with temperature changes, while the metamaterial modifies the bandgaps according to its negative permittivity. Using quasi-periodic shows that, in contrast to employing absolute periodic arrangements, it produces more diverse results in modifying the structure’s band-gaps. Using a new sequence arrangement mixed-quasi-periodic (MQP) structure, which is a combination of two quasi periodic structures, provides more freedom of action for modifying the properties of the medium than periodic arrangements do. The ability to control thermal radiation is crucial in a range of optical applications since it is frequently unpolarized and incoherent in both space and time. These configurations allow for the suppression and emission of thermal radiation in a certain frequency range due to their fundamental nature as photonic band-gaps (PBGs). So, we are able to control the thermal radiation by changing the structure arrangement. Here, the We use an indirect method based on the second Kirchoff law for thermal radiation to investigate the emittance of black bodies based on a well-known transfer matrix technique. We can measure the transmission and reflection coefficients with associated transmittance and reflectance, T and R, respectively. Here, the effects of several parameters, including the input beam’s angle, polarization, and period on tailoring the thermal radiation spectrum of the proposed structure, are studied. The results show that in some frequency bands, thermal radiation exceeded the black body limit. There were also good results in terms of complete stop bands for both TE and TM polarization at different incident angles and frequencies. This study produces encouraging results for the creation of Terahertz (THz) filters and selective thermal emitters. The tunability of our media is a crucial factor that influences the efficiency and function of our desired photonic outcome. Therefore, exploiting MQP sequences or arrangements is a promising strategy, as it allows us to rearrange our media more flexibly than quasi-periodic sequences and thus achieve our optimal result.

27

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 (January 9, 2007): 597–610. http://dx.doi.org/10.1088/1751-8113/40/4/002.

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28

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 (February 2007): 45–51. http://dx.doi.org/10.1016/s0034-4877(07)80003-6.

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29

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 (June 2006): 474–98. http://dx.doi.org/10.1016/j.wavemoti.2006.03.003.

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30

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 (February 20, 2013): 1183–200. http://dx.doi.org/10.1007/s10955-013-0718-8.

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31

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.

32

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 (October 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.

33

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

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34

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

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35

Delyon, François, Yves-Emmanuel Lévy, and Bernard Souillard. "Nonperturbative Bistability in Periodic Nonlinear Media." Physical Review Letters 57, no. 16 (October 20, 1986): 2010–13. http://dx.doi.org/10.1103/physrevlett.57.2010.

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36

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

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37

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

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38

Hizi, Uzi, and David J. Bergman. "Molecular diffusion in periodic porous media." Journal of Applied Physics 87, no. 4 (February 15, 2000): 1704–11. http://dx.doi.org/10.1063/1.372081.

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39

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

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40

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

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41

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 for Stokes flow in bicontinuous porous media. The results of the analysis of Stokes flow and Ohmic conduction through bicontinuous porous media were used to test the permeability scaling law proposed by Johnson, Koplik & Schwartz (1986), which introduces a length parameter Λ to relate Darcy permeability k and the formation factor F. As reported in our earlier work on the SC bicontinuous porous media, the scaling law holds approximately for the BCC and FCC families except when the porespace becomes nearly spherical pores connected by small orifice-like passages. We also found that, except when the porespace was connected by the small orifice-like passages, the permeability versus porosity curve of the bicontinuous media agrees very well with that of arrays of disjoint and fused spheres of the same crystallographic symmetry.

42

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

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43

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

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44

Drouot, A., C. L. Fefferman, and M. I. Weinstein. "Defect Modes for Dislocated Periodic Media." Communications in Mathematical Physics 377, no. 3 (June 19, 2020): 1637–80. http://dx.doi.org/10.1007/s00220-020-03787-0.

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45

Blonskyi, I., V. Kadan, Y. Shynkarenko, O. Yarusevych, P. Korenyuk, V. Puzikov, and L. Grin’. "Periodic femtosecond filamentation in birefringent media." Applied Physics B 120, no. 4 (August 7, 2015): 705–10. http://dx.doi.org/10.1007/s00340-015-6186-x.

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46

Kaminer, Ido, Carmel Rotschild, Ofer Manela, and Mordechai Segev. "Periodic solitons in nonlocal nonlinear media." Optics Letters 32, no. 21 (October 29, 2007): 3209. http://dx.doi.org/10.1364/ol.32.003209.

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47

Craster, R. V., J. Kaplunov, and A. V. Pichugin. "High-frequency homogenization for periodic media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2120 (March 10, 2010): 2341–62. http://dx.doi.org/10.1098/rspa.2009.0612.

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An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.

48

Bulgakov, A. A., S. A. Bulgakov, and M. Nieto-Vesperinas. "Complex polaritons in periodic layered media." Physical Review B 52, no. 15 (October 15, 1995): 10788–91. http://dx.doi.org/10.1103/physrevb.52.10788.

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49

de Sterke, C. Martijn. "Stability analysis of nonlinear periodic media." Physical Review A 45, no. 11 (June 1, 1992): 8252–58. http://dx.doi.org/10.1103/physreva.45.8252.

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50

Ketcheson, David I., and Randall J. Leveque. "Shock dynamics in layered periodic media." Communications in Mathematical Sciences 10, no. 3 (2012): 859–74. http://dx.doi.org/10.4310/cms.2012.v10.n3.a7.

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