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Journal articles on the topic 'Quasiperiodic systems'

Author: Grafiati

Published: 6 September 2023

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1

Redkar, Sangram. "Lyapunov Stability of Quasiperiodic Systems." Mathematical Problems in Engineering 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/721382.

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We present some observations on the stability and reducibility of quasiperiodic systems. In a quasiperiodic system, the periodicity of parametric excitation is incommensurate with the periodicity of certain terms multiplying the state vector. We present a Lyapunov-type approach and the Lyapunov-Floquet (L-F) transformation to derive the stability conditions. This approach can be utilized to investigate the robustness, stability margin, and design controller for the system.

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2

Yamaguchi, Atsushi, and Toshiyuki Ninomiya. "Artificial systems with quasiperiodic structure." Bulletin of the Japan Institute of Metals 29, no. 10 (1990): 839–44. http://dx.doi.org/10.2320/materia1962.29.839.

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3

Janssen, T. "The symmetry of quasiperiodic systems." Acta Crystallographica Section A Foundations of Crystallography 47, no. 3 (May 1, 1991): 243–55. http://dx.doi.org/10.1107/s0108767390013745.

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4

WALGRAEF, D., G. DEWEL, and P. BORCKMANS. "Quasiperiodic order in dissipative systems." Nature 318, no. 6047 (December 1985): 606. http://dx.doi.org/10.1038/318606a0.

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5

Zhong, J. X., and R. Mosseri. "Quantum dynamics in quasiperiodic systems." Journal of Physics: Condensed Matter 7, no. 44 (October 30, 1995): 8383–404. http://dx.doi.org/10.1088/0953-8984/7/44/008.

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6

Salazar, F. "Phonon localization in quasiperiodic systems." Journal of Non-Crystalline Solids 329, no. 1-3 (November 1, 2003): 167–70. http://dx.doi.org/10.1016/j.jnoncrysol.2003.08.034.

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7

TUTOR, J., and V. R. VELASCO. "SOME PROPERTIES OF THE TRANSVERSE ELASTIC WAVES IN QUASIPERIODIC STRUCTURES." International Journal of Modern Physics B 15, no. 21 (August 20, 2001): 2925–34. http://dx.doi.org/10.1142/s0217979201007129.

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We have studied the integrated density of states and fractal dimension of the transverse elastic waves spectrum in quasiperiodic systems following the Fibonacci, Thue–Morse and Rudin–Shapiro sequences. Due to the finiteness of the quasiperiodic generations, in spite of the high number of materials included, we have studied the possible influence of the boundary conditions, infinite periodic or finite systems, together with that of the different ways to generate the constituent blocks of the quasiperiodic systems, on the transverse elastic waves spectra. No relevant differences have been found for the different boundary conditions, but the different ways of generating the building blocks produce appreciable consequences in the properties of the transverse elastic waves spectra of the quasiperiodic systems studied here.

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8

SANCHEZ, VICENTA, and CHUMIN WANG. "RESONANT AC CONDUCTING SPECTRA IN QUASIPERIODIC SYSTEMS." International Journal of Computational Materials Science and Engineering 01, no. 01 (March 2012): 1250003. http://dx.doi.org/10.1142/s2047684112500030.

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Based on the Kubo-Greenwood formula, a renormalization plus convolution method is developed to investigate the frequency-dependent electrical conductivity of quasiperiodic systems. This method combines the convolution theorem with the real-space renormalization technique which is able to address multidimensional systems with 1024 atoms. In this article, an analytical evaluation of the Kubo-Greenwood formula is presented for the ballistic ac conductivity in periodic chains. For quasiperiodic Fibonacci lattices connected to two semi-infinite periodic leads, the electrical conductivity, is calculated by using the renormalization method and the results show that at several frequencies, their ac conductivities could be larger than the ballistic ones. This fact might be related to the resonant scattering process in quasiperiodic systems. Finally, calculations made in segmented Fibonacci nanowires reveal that this improvement to the ballistic ac conductivity via quasiperiodicity is also present in multidimensional systems.

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9

V.R. Krasheninnikov, O.E. Malenova, O.E. Malenova, and A.Yu. Subbotin. "MODELS OF SYSTEMS OF QUASIPERIODIC PROCESSES BASED ON CYLINDRICAL AND CIRCULAR IMAGES." Izvestiya of Samara Scientific Center of the Russian Academy of Sciences 23, no. 1 (2021): 103–10. http://dx.doi.org/10.37313/1990-5378-2021-23-1-103-110.

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The behavior of objects in many practical situations has a quasiperiodic character - the presence of noticeable periodicity with random variations of quasiperiods. For example, noise and vibration of an aircraft engine, hydroelectric unit, seasonal and daily fluctuations in atmospheric temperature, etc. In this case, the object can have several parameters, therefore the object is described by a system of several time series, that is, several random processes. The emerging monitoring tasks (assessing the state of an object and its forecast) require setting a model of such a system of processes and identifying it for a particular object based on the results of its observations. In this paper, to represent a quasi-periodic process, an autoregressive model is used in the form of sweeps of several cylindrical or circular images along a spiral. Choosing the values of a small number of parameters of this model, one can describe and simulate a wide class of systems of quasiperiodic processes. The problem of identifying a model is considered, that is, determining the values of its parameters at which it, in a certain sense, best corresponds to the actually observed process. This problem is solved using a pseudo-gradient adaptive procedure, the advantage of which is its real-time operation with low computational costs.

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10

Morozov, A. D., and K. E. Morozov. "On Synchronization of Quasiperiodic Oscillations." Nelineinaya Dinamika 14, no. 3 (2018): 367–76. http://dx.doi.org/10.20537/nd180307.

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11

SEIMENIS, J. "RATIONAL QUASIPERIODIC SOLUTIONS FOR DYNAMICAL SYSTEMS." Modern Physics Letters B 04, no. 09 (May 10, 1990): 635–38. http://dx.doi.org/10.1142/s0217984990000787.

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We investigate the possibility to give analytically approximate quasiperiodic solutions of the Hamiltonian equations of motion in simple rational functions. In this paper we give a formula for these solutions which is in very good agreement with the numerical solutions, although it is extremely simple.

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12

Dumont, Randall S., and Paul Brumer. "Nonstatistical unimolecular decay in quasiperiodic systems." Journal of Chemical Physics 90, no. 1 (January 1989): 96–104. http://dx.doi.org/10.1063/1.456474.

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13

Janssen, T. "The symmetry of quasiperiodic systems. Erratum." Acta Crystallographica Section A Foundations of Crystallography 47, no. 5 (September 1, 1991): 605. http://dx.doi.org/10.1107/s0108767391006499.

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14

Kramer, P. "Algebraic structures for 1D quasiperiodic systems." Journal of Physics A: Mathematical and General 26, no. 2 (January 21, 1993): 213–28. http://dx.doi.org/10.1088/0305-4470/26/2/010.

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15

Valls, Claudia. "Quasiperiodic Solutions for Dissipative Boussinesq Systems." Communications in Mathematical Physics 265, no. 2 (April 28, 2006): 305–31. http://dx.doi.org/10.1007/s00220-006-0026-0.

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16

Tkachenko, V. I. "On uniformly stable linear quasiperiodic systems." Ukrainian Mathematical Journal 49, no. 7 (July 1997): 1102–8. http://dx.doi.org/10.1007/bf02528755.

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17

Xue, Nina, and Wencai Zhao. "On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation." Journal of Function Spaces 2020 (May 5, 2020): 1–11. http://dx.doi.org/10.1155/2020/6260253.

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In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Qt. Applications to the Schrödinger equation are also given.

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18

Žnidarič, Marko, and Marko Ljubotina. "Interaction instability of localization in quasiperiodic systems." Proceedings of the National Academy of Sciences 115, no. 18 (April 16, 2018): 4595–600. http://dx.doi.org/10.1073/pnas.1800589115.

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Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

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19

Pnevmatikos, St, O. Yanovitskii, Th Fraggis, and E. N. Economou. "Polaron formation in one-dimensional quasiperiodic systems." Physical Review Letters 68, no. 15 (April 13, 1992): 2370–73. http://dx.doi.org/10.1103/physrevlett.68.2370.

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20

Hu, Bambi, Baowen Li, and Peiqing Tong. "Disturbance spreading in incommensurate and quasiperiodic systems." Physical Review B 61, no. 14 (April 1, 2000): 9414–18. http://dx.doi.org/10.1103/physrevb.61.9414.

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21

Desideri, Jean-Pierre, Louis Macon, and Didier Sornette. "Observation of critical modes in quasiperiodic systems." Physical Review Letters 63, no. 4 (July 24, 1989): 390–93. http://dx.doi.org/10.1103/physrevlett.63.390.

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22

Morozov, A. D., and K. E. Morozov. "Quasiperiodic Perturbations of Two-Dimensional Hamiltonian Systems." Differential Equations 53, no. 12 (December 2017): 1557–66. http://dx.doi.org/10.1134/s0012266117120047.

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23

Vadivasova, T. E., O. V. Sosnovtseva, A. G. Balanov, and V. V. Astakhov. "Desynchronization in coupled systems with quasiperiodic driving." Physical Review E 61, no. 4 (April 1, 2000): 4618–21. http://dx.doi.org/10.1103/physreve.61.4618.

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24

Chow, Shui-Nee, Kening Lu, and Yun Qiu Shen. "Normal form and linearization for quasiperiodic systems." Transactions of the American Mathematical Society 331, no. 1 (January 1, 1992): 361–76. http://dx.doi.org/10.1090/s0002-9947-1992-1076612-1.

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25

Dumont, Randall S., and Paul Brumer. "Relaxation rates in chaotic and quasiperiodic systems." Journal of Chemical Physics 87, no. 11 (December 1987): 6437–48. http://dx.doi.org/10.1063/1.453425.

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26

Abe, Shuji, and Hisashi Hiramoto. "Unusual transport of excitations in quasiperiodic systems." Journal of Luminescence 38, no. 1-6 (December 1987): 3–7. http://dx.doi.org/10.1016/0022-2313(87)90047-0.

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27

Roche, S., and D. Mayou. "Conductivity of Quasiperiodic Systems: A Numerical Study." Physical Review Letters 79, no. 13 (September 29, 1997): 2518–21. http://dx.doi.org/10.1103/physrevlett.79.2518.

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28

Chakravarthy, S. K., and C. V. Nayar. "Quasiperiodic (QP) oscillations in electrical power systems." International Journal of Electrical Power & Energy Systems 18, no. 8 (November 1996): 483–92. http://dx.doi.org/10.1016/0142-0615(96)00008-7.

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29

Chow, S. N., and K. N. Lu. "Invariant Manifolds and Foliations for Quasiperiodic Systems." Journal of Differential Equations 117, no. 1 (March 1995): 1–27. http://dx.doi.org/10.1006/jdeq.1995.1046.

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30

Wang, Xingang, Gang Hu, Kai Hu, and C. H. Lai. "Transition to Measure Synchronization in Coupled Hamiltonian Systems." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 4349–54. http://dx.doi.org/10.1142/s021797920302243x.

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The transition to measure synchronization in two coupled φ4 equations are investigated numerically both for quasiperiodic and chaotic cases. Quantities like the bare energy and phase difference are employed to study the underlying behaviors during this process. For transition between quasiperiodic states, the distribution of phase difference tends to concentrate at large angles before measure synchronization, and is confined to within a certain range after measure synchronization. For transition between quasiperiodicity and chaos, phase locking is not achieved and a random-walk-like behavior of the phase difference is found in the measure synchronized region. The scaling relationship of the phase distribution and the behavior of the bare energy are also discussed.

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31

SHUAI, J. W., and D. M. DURAND. "STRANGE NONCHAOTIC ATTRACTOR IN LOW-FREQUENCY QUASIPERIODICALLY DRIVEN SYSTEMS." International Journal of Bifurcation and Chaos 10, no. 09 (September 2000): 2269–76. http://dx.doi.org/10.1142/s0218127400001444.

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To generate strange nonchaotic attractor in quasiperiodically driven systems, there must be an unstable region in its phase-space. In this paper, a theoretical analysis shows that the quasiperiodic force acts as noise to lead the trajectory running into different expanding orbits when the trajectory repeatedly runs into the unstable region. Thus the resulting attractor is strange. The local-phase Lyapunov exponent is introduced for the study of low-frequency quasiperiodically driven systems. It is shown that the local-phase Lyapunov exponents can be approximated by the exponents of autonomous systems. The statistical properties of SNA system driven by low-frequency quasiperiodic force can then be approached by a set of autonomous systems.

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32

ZOU, Y., M. THIEL, M. C. ROMANO, and J. KURTHS. "ANALYTICAL DESCRIPTION OF RECURRENCE PLOTS OF DYNAMICAL SYSTEMS WITH NONTRIVIAL RECURRENCES." International Journal of Bifurcation and Chaos 17, no. 12 (December 2007): 4273–83. http://dx.doi.org/10.1142/s0218127407019949.

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In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ∊ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ∊ to analyze experimental data by means of RPs.

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33

Rubezic, Vesna, and Ana Jovanovic. "Erbium - doped fiber laser systems: Routes to chaos." Serbian Journal of Electrical Engineering 11, no. 4 (2014): 551–63. http://dx.doi.org/10.2298/sjee1404551r.

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Erbium-doped fiber laser systems exhibit a large variety of complex dynamical behaviors, bifurcations and attractors. In this paper, the chaotic behavior which can be achieved under certain conditions in a laser system with erbium-doped fiber, is discussed. The chaos in this system occurs through several standard scenarios. In this paper, the simulation sequence of quasiperiodic, intermittent and period-doubling scenario transitions to chaos is shown. Quasiperiodic and intermittent transitions to chaos are shown on the example system with a single ring. The electro-optical modulator was applied to the system for modulating the loss in the cavity. We used the sinusoidal and rectangular signals for modulation. Generation of chaos is achieved by changing the parameters of signal for modulation. Period-doubling transition to chaos is illustrated in a system with two rings. Simulation results are shown in the time domain and phase space.

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34

Sevryuk, M. B. "New cases of quasiperiodic motions in reversible systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 3, no. 2 (April 1993): 211–14. http://dx.doi.org/10.1063/1.165993.

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35

Schmithüsen, F., G. Cappello, and J. Chevrier. "Periodic X-ray standing waves in quasiperiodic systems." Ferroelectrics 250, no. 1 (February 2001): 289–92. http://dx.doi.org/10.1080/00150190108225084.

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36

Hiramoto, Hisashi, and Mahito Kohmoto. "Scaling analysis of quasiperiodic systems: Generalized Harper model." Physical Review B 40, no. 12 (October 15, 1989): 8225–34. http://dx.doi.org/10.1103/physrevb.40.8225.

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37

Niu, Qian, and Franco Nori. "Renormalization-Group Study of One-Dimensional Quasiperiodic Systems." Physical Review Letters 57, no. 16 (October 20, 1986): 2057–60. http://dx.doi.org/10.1103/physrevlett.57.2057.

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38

Belogortsev, Andrey B., Dmitry M. Vavriv, and Oleg A. Tretyakov. "Destruction of Quasiperiodic Oscillations in Weakly Nonlinear Systems." Applied Mechanics Reviews 46, no. 7 (July 1, 1993): 372–84. http://dx.doi.org/10.1115/1.3120366.

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We consider the main regularities of the arising of the dynamical chaos in weakly nonlinear oscillatory systems. We show that the chaotic oscillations in such systems can occur due to the destruction of quasiperiodic oscillations. Various analytical approaches are applied to study the properties of the quasiperiodically forced passive and active single-mode oscillators as well as the conditions for the appearance of chaos. The results of numerical and experimental investigations are also discussed.

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39

Zhong, J. X., J. Q. You, J. R. Yan, and X. H. Yan. "Local electronic properties of one-dimensional quasiperiodic systems." Physical Review B 43, no. 16 (June 1, 1991): 13778–81. http://dx.doi.org/10.1103/physrevb.43.13778.

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40

Hsueh, W. J., C. H. Chen, and C. H. Chang. "Bound states in the continuum in quasiperiodic systems." Physics Letters A 374, no. 48 (November 2010): 4804–7. http://dx.doi.org/10.1016/j.physleta.2010.10.008.

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41

Carpena, P. "Anomalous electric field-induced localization in quasiperiodic systems." Physics Letters A 231, no. 5-6 (July 1997): 439–48. http://dx.doi.org/10.1016/s0375-9601(97)00329-0.

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42

Schreiber, Michael, Uwe Grimm, Rudolf A. Römer, and Jian-Xin Zhong. "Application of random matrix theory to quasiperiodic systems." Physica A: Statistical Mechanics and its Applications 266, no. 1-4 (April 1999): 477–80. http://dx.doi.org/10.1016/s0378-4371(98)00634-7.

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43

Demenchuk, A. K. "Weakly irregular quasiperiodic solutions of nonlinear Pfaff systems." Differential Equations 44, no. 2 (February 2008): 186–91. http://dx.doi.org/10.1134/s0012266108020055.

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44

Machida, Kazushige, and Mitsutaka Fujita. "Quantum energy spectra and one-dimensional quasiperiodic systems." Physical Review B 34, no. 10 (November 15, 1986): 7367–70. http://dx.doi.org/10.1103/physrevb.34.7367.

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45

Shung, Kenneth W. K., L. M. Sander, and R. Merlin. "Effective Mass and Impurity States of Quasiperiodic Systems." Physical Review Letters 61, no. 4 (July 25, 1988): 455–58. http://dx.doi.org/10.1103/physrevlett.61.455.

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46

Bibikov, Yu N. "The existence of quasiperiodic motions in quasilinear systems." Journal of Applied Mathematics and Mechanics 59, no. 1 (January 1995): 19–26. http://dx.doi.org/10.1016/0021-8928(95)90007-1.

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47

Baeta Segundo, J. A., Heyder Hey, and Walter F. Wreszinski. "On quantum stability for systems under quasiperiodic perturbations." Journal of Statistical Physics 76, no. 5-6 (September 1994): 1479–93. http://dx.doi.org/10.1007/bf02187072.

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48

Iguchi, Kazumoto. "Quasiperiodic systems without Cantor‐set‐like energy bands." Journal of Mathematical Physics 33, no. 11 (November 1992): 3736–39. http://dx.doi.org/10.1063/1.529870.

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49

Lu, Jian Ping, and Joseph L. Birman. "Acoustic.wave propagation in quasiperiodic, incommensurate, and random systems." Journal of the Acoustical Society of America 87, S1 (May 1990): S113. http://dx.doi.org/10.1121/1.2027847.

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50

Maciá, Enrique, Francisco Domínguez-Adame, and Angel Sánchez. "Energy spectra of quasiperiodic systems via information entropy." Physical Review E 50, no. 2 (August 1, 1994): R679—R682. http://dx.doi.org/10.1103/physreve.50.r679.

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