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Academic literature on the topic 'Quasiperiodic systems'

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Published: 6 September 2023

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Journal articles on the topic "Quasiperiodic systems"

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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Dissertations / Theses on the topic "Quasiperiodic systems"

1

Deloudi, Sofia. "Modeling of quasiperiodic systems /." Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=18107.

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2

Zou, Yong. "Exploring recurrences in quasiperiodic systems." Phd thesis, kostenfrei, 2007. http://opus.kobv.de/ubp/volltexte/2008/1649/.

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3

Thiem, Stefanie. "Electronic and Photonic Properties of Metallic-Mean Quasiperiodic Systems." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-83831.

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Understanding the connection of the atomic structure and the physical properties of materials remains one of the elementary questions of condensed-matter physics. One research line in this quest started with the discovery of quasicrystals by Shechtman et al. in 1982. It soon became clear that these materials with their 5-, 8-, 10- or 12-fold rotational symmetries, which are forbidden according to classical crystallography, can be described in terms of mathematical models for nonperiodic tilings of a plane proposed by Penrose and Ammann in the 1970s. Due to the missing translational symmetry of quasicrystals, till today only finite, relatively small systems or periodic approximants have been investigated by means of numerical calculations and theoretical results have mainly been obtained for one-dimensional systems. In this thesis we study d-dimensional quasiperiodic models, so-called labyrinth tilings, with separable Hamiltonians in the tight-binding approach. This method paves the way to study higher-dimensional, quantum mechanical solutions, which can be directly derived from the one-dimensional results. This allows the investigation of very large systems in two and three dimensions with up to 10^10 sites. In particular, we contemplate the class of metallic-mean sequences. Based on this model we focus on the electronic properties of quasicrystals with a special interest on the connection of the spectral and dynamical properties of the Hamiltonian. Hence, we investigate the characteristics of the eigenstates and wave functions and compare these with the wave-packet dynamics in the labyrinth tilings by numerical calculations and by a renormalization group approach in connection with perturbation theory. It turns out that many properties show a qualitatively similar behavior in different dimensions or are even independent of the dimension as e.g. the scaling behavior of the participation numbers and the mean square displacement of a wave packet. Further, we show that the structure of the labyrinth tilings and their transport properties are connected and obtain that certain moments of the spectral dimensions are related to the wave-packet dynamics. Besides this also the photonic properties are studied for one-dimensional quasiperiodic multilayer systems for oblique incidence of light, and we show that the characteristics of the transmission bands are related to the quasiperiodic structure
Eine der elementaren Fragen der Physik kondensierter Materie beschäftigt sich mit dem Zusammenhang zwischen der atomaren Struktur und den physikalischen Eigenschaften von Materialien. Eine Forschungslinie in diesem Kontext begann mit der Entdeckung der Quasikristalle durch Shechtman et al. 1982. Es stellte sich bald heraus, dass diese Materialien mit ihren laut der klassischen Kristallographie verbotenen 5-, 8-, 10- oder 12-zähligen Rotationssymmetrien durch mathematische Modelle für die aperiodische Pflasterung der Ebene beschrieben werden können, die durch Penrose und Ammann in den 1970er Jahren vorgeschlagen wurden. Aufgrund der fehlenden Translationssymmetrie in Quasikristallen sind bis heute nur endliche, relativ kleine Systeme oder periodische Approximanten durch numerische Berechnungen untersucht worden und theoretische Ergebnisse wurden hauptsächlich für eindimensionale Systeme gewonnen. In dieser Arbeit werden d-dimensionale quasiperiodische Modelle, sogenannte Labyrinth-Pflasterungen, mit separablem Hamilton-Operator im Modell starker Bindung betrachtet. Diese Methode erlaubt es, quantenmechanische Lösungen in höheren Dimensionen direkt aus den eindimensionalen Ergebnissen abzuleiten und ermöglicht somit die Untersuchung von sehr großen Systemen in zwei und drei Dimensionen mit bis zu 10^10 Gitterpunkten. Insbesondere betrachten wir dabei quasiperiodische Folgen mit metallischem Schnitt. Basierend auf diesem Modell befassen wir uns im Speziellen mit den elektronischen Eigenschaften der Quasikristalle im Hinblick auf die Verbindung der spektralen und dynamischen Eigenschaften des Hamilton-Operators. Hierfür untersuchen wir die Eigenschaften der Eigenzustände und Wellenfunktionen und vergleichen diese mit der Dynamik von Wellenpaketen in den Labyrinth-Pflasterungen basierend auf numerischen Berechnungen und einem Renormierungsgruppen-Ansatz in Verbindung mit Störungstheorie. Dabei stellt sich heraus, dass viele Eigenschaften wie etwa das Skalenverhalten der Partizipationszahlen und der mittleren quadratischen Abweichung eines Wellenpakets für verschiedene Dimensionen ein qualitativ gleiches Verhalten zeigen oder sogar unabhängig von der Dimension sind. Zudem zeigen wir, dass die Struktur der Labyrinth-Pflasterungen und deren Transporteigenschaften sowie bestimmte Momente der spektralen Dimensionen und die Dynamik der Wellenpakete in Beziehung zueinander stehen. Darüber hinaus werden auch die photonischen Eigenschaften für eindimensionale quasiperiodische Mehrschichtsysteme für beliebige Einfallswinkel untersucht und der Verlauf der Transmissionsbänder mit der quasiperiodischen Struktur in Zusammenhang gebracht

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4

Thiem, Stefanie [Verfasser], Michael [Akademischer Betreuer] Schreiber, Michael [Gutachter] Schreiber, and Uwe [Gutachter] Grimm. "Electronic and Photonic Properties of Metallic-Mean Quasiperiodic Systems / Stefanie Thiem ; Gutachter: Michael Schreiber, Uwe Grimm ; Betreuer: Michael Schreiber." Chemnitz : Universitätsbibliothek Chemnitz, 2012. http://d-nb.info/1214009794/34.

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5

Leguil, Martin. "Cocycle dynamics and problems of ergodicity." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC159/document.

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Le travail qui suit comporte quatre chapitres : le premier est centré autour de la propriété de mélange faible pour les échanges d'intervalles et flots de translation. On y présente des résultats obtenus avec Artur Avila qui renforcent des résultats précédents dus à Artur Avila et Giovanni Forni. Le deuxième chapitre est consacré à un travail en commun avec Zhiyuan Zhang et concerne les propriétés d'ergodicité et d'accessibilité stables pour des systèmes partiellement hyperboliques de dimension centrale au moins égale à deux. On montre que sous des hypothèses de cohérence dynamique, center bunching et pincement fort, la propriété d'accessibilité stable est dense en topologie C^r, r>1, et même prévalente au sens de Kolmogorov. Dans le troisième chapitre, on expose les résultats d'un travail réalisé en collaboration avec Julie Déserti, consacré à l'étude d'une famille à un paramètre d'automorphismes polynomiaux de C^3 ; on montre que de nouveaux phénomènes apparaissent par rapport à ce qui était connu dans le cas de la dimension deux. En particulier, on étudie les vitesses d'échappement à l'infini, en montrant qu'une transition s'opère pour une certaine valeur du paramètre. Le dernier chapitre est issu d'un travail en collaboration avec Jiangong You, Zhiyan Zhao et Qi Zhou ; on s'intéresse à des estimées asymptotiques sur la taille des trous spectraux des opérateurs de Schrödinger quasi-périodiques dans le cadre analytique. On obtient des bornes supérieures exponentielles dans le régime sous-critique, ce qui renforce un résultat précédent de Sana Ben Hadj Amor. Dans le cas particulier des opérateurs presque Mathieu, on montre également des bornes inférieures exponentielles, qui donnent des estimées quantitatives en lien avec le problème dit "des dix Martinis". Comme conséquences de nos résultats, on présente des applications à l'homogénéité du spectre de tels opérateurs ainsi qu'à la conjecture de Deift
The following work contains four chapters: the first one is centered around the weak mixing property for interval exchange transformations and translation flows. It is based on the results obtained together with Artur Avila which strengthen previous results due to Artur Avila and Giovanni Forni. The second chapter is dedicated to a joint work with Zhiyuan Zhang, in which we study the properties of stable ergodicity and accessibility for partially hyperbolic systems with center dimension at least two. We show that for dynamically coherent partially hyperbolic diffeomorphisms and under certain assumptions of center bunching and strong pinching, the property of stable accessibility is dense in C^r topology, r>1, and even prevalent in the sense of Kolmogorov. In the third chapter, we explain the results obtained together with Julie Déserti on the properties of a one-parameter family of polynomial automorphisms of C^3; we show that new behaviours can be observed in comparison with the two-dimensional case. In particular, we study the escape speed of points to infinity and show that a transition exists for a certain value of the parameter. The last chapter is based on a joint work with Jiangong You, Zhiyan Zhao and Qi Zhou; we get asymptotic estimates on the size of spectral gaps for quasi-periodic Schrödinger operators in the analytic case. We obtain exponential upper bounds in the subcritical regime, which strengthens a previous result due to Sana Ben Hadj Amor. In the particular case of almost Mathieu operators, we also show exponential lower bounds, which provides quantitative estimates in connection with the so-called "Dry ten Martinis problem". As consequences of our results, we show applications to the homogeneity of the spectrum of such operators, and to Deift's conjecture

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6

Maranhão, Isis Albuquerque de Souza. "Localização eletrônica de sistemas aperiódicos em uma dimensão." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=8688.

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Desde a descoberta do estado quasicristalino por Daniel Shechtman et al. em 1984 e da fabricação por Roberto Merlin et al. de uma superrede artificial de GaAs/ AlAs em 1985 com características da sequência de Fibonacci, um grande número de trabalhos teóricos e experimentais tem relatado uma variedade de propriedades interessantes no comportamento de sistemas aperiódicos. Do ponto de vista teórico, é bem sabido que a cadeia de Fibonacci em uma dimensão se constitui em um protótipo de sucesso para a descrição do estado quasicristalino de um sólido. Dependendo da regra de inflação, diferentes tipos de estruturas aperiódicas podem ser obtidas. Esta diversidade originou as chamadas regras metálicas e devido à possibilidade de tratamento analítico rigoroso este modelo tem sido amplamente estudado. Neste trabalho, propriedades de localização em uma dimensão são analisadas considerando-se um conjunto de regras metálicas e o modelo de ligações fortes de banda única. Considerando-se o Hamiltoniano de ligações fortes com um orbital por sítio obtemos um conjunto de transformações relativas aos parâmetros de dizimação, o que nos permitiu calcular as densidades de estados (DOS) para todas as configurações estudadas. O estudo detalhado da densidade de estados integrada (IDOS) para estes casos, mostra o surgimento de plateaux na curva do número de ocupação explicitando o aparecimento da chamada escada do diabo" e também o caráter fractal destas estruturas. Estudando o comportamento da variação da energia em função da variação da energia de hopping, construímos padrões do tipo borboletas de Hofstadter, que simulam o efeito de um campo magnético atuando sobre o sistema. A natureza eletrônica dos auto estados é analisada a partir do expoente de Lyapunov (γ), que está relacionado com a evolução da função de onda eletrônica ao longo da cadeia unidimensional. O expoente de Lyapunov está relacionado com o inverso do comprimento de localização (ξ= 1 /γ), sendo nulo para os estados estendidos e positivo para estados localizados. Isto define claramente as posições dos principais gaps de energia do sistema. Desta forma, foi possível analisar o comportamento autossimilar de cadeias com diferentes regras de formação. Analisando-se o espectro de energia em função do número de geração de cadeias que seguem as regras de ouro e prata foi feito, obtemos conjuntos do tipo-Cantor, que nos permitiu estudar o perfil do calor específico de uma cadeia e Fibonacci unidimensional para diversas gerações
Since the discovery of a quasicrystalline state by Daniel Shechtman et al. in 1984 and the growth of artificial GaAs/AlAs superlattices on nonperiodic Fibonacci sequence by Roberto Merlin et al., a number of theoretical and experimental works have reported a variety of interesting physical properties of aperiodic systems. Theoretically, it is well known that in one dimension, the Fibonacci chain is a successful prototype to describe a quasicrystalline state. Depending on the in ation rule, different kinds of aperiodic structures can be obtained. This diversity originates the called metallic means, and due to the possibility of analytical and rigorous mathematical treatments the Fibonacci model has been applied by several authors. In this work, electronic localization properties are studied, taking into account a set of metallic means in one dimension. Considering a single band tight-binding Hamiltonian, a set of decimation transformations is obtained allowing the calculation of the Density of States (DOS) for all configurations. The detailed study of the Integrated Density of States (IDOS), shows the appearance of plateaux in the occupation number curve exhibiting the so-called "devil's staircase"indicating the fractal nature of the structures. Studying the behavior of the energy as a function of the hopping we derive Hofstadter butter y type patters, which simulate the effect of a magnetic field acting on the system. The electronic nature of the eigenstate is analyzed by looking at the Lyapunov exponent which is related to the evolution of the electronic wave unction along the one dimensional chain. Since it is zero for an extended state and positive for a localized one, defining the main gaps positions, it is related to the inverse of the localization length. Through a careful analysis of the Lyapunov curves it was also possible to obtain the perfect self-similarity structures for all chains. In particular,for the chains that follow the golden and silver rules, the study of the energy behavior was done by analyzing the energy spectrum as a function of the generation number of each one of the chains. The results yield Cantor-like sets, which allowed us to calculate the specific heat profile for several generations of the one-dimensional Fibonacci chain.

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7

Zou, Yong [Verfasser]. "Exploring recurrences in quasiperiodic systems / von Yong Zou." 2007. http://d-nb.info/987730541/34.

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8

Thiem, Stefanie. "Electronic and Photonic Properties of Metallic-Mean Quasiperiodic Systems." Doctoral thesis, 2011. https://monarch.qucosa.de/id/qucosa%3A19673.

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Understanding the connection of the atomic structure and the physical properties of materials remains one of the elementary questions of condensed-matter physics. One research line in this quest started with the discovery of quasicrystals by Shechtman et al. in 1982. It soon became clear that these materials with their 5-, 8-, 10- or 12-fold rotational symmetries, which are forbidden according to classical crystallography, can be described in terms of mathematical models for nonperiodic tilings of a plane proposed by Penrose and Ammann in the 1970s. Due to the missing translational symmetry of quasicrystals, till today only finite, relatively small systems or periodic approximants have been investigated by means of numerical calculations and theoretical results have mainly been obtained for one-dimensional systems. In this thesis we study d-dimensional quasiperiodic models, so-called labyrinth tilings, with separable Hamiltonians in the tight-binding approach. This method paves the way to study higher-dimensional, quantum mechanical solutions, which can be directly derived from the one-dimensional results. This allows the investigation of very large systems in two and three dimensions with up to 10^10 sites. In particular, we contemplate the class of metallic-mean sequences. Based on this model we focus on the electronic properties of quasicrystals with a special interest on the connection of the spectral and dynamical properties of the Hamiltonian. Hence, we investigate the characteristics of the eigenstates and wave functions and compare these with the wave-packet dynamics in the labyrinth tilings by numerical calculations and by a renormalization group approach in connection with perturbation theory. It turns out that many properties show a qualitatively similar behavior in different dimensions or are even independent of the dimension as e.g. the scaling behavior of the participation numbers and the mean square displacement of a wave packet. Further, we show that the structure of the labyrinth tilings and their transport properties are connected and obtain that certain moments of the spectral dimensions are related to the wave-packet dynamics. Besides this also the photonic properties are studied for one-dimensional quasiperiodic multilayer systems for oblique incidence of light, and we show that the characteristics of the transmission bands are related to the quasiperiodic structure.
Eine der elementaren Fragen der Physik kondensierter Materie beschäftigt sich mit dem Zusammenhang zwischen der atomaren Struktur und den physikalischen Eigenschaften von Materialien. Eine Forschungslinie in diesem Kontext begann mit der Entdeckung der Quasikristalle durch Shechtman et al. 1982. Es stellte sich bald heraus, dass diese Materialien mit ihren laut der klassischen Kristallographie verbotenen 5-, 8-, 10- oder 12-zähligen Rotationssymmetrien durch mathematische Modelle für die aperiodische Pflasterung der Ebene beschrieben werden können, die durch Penrose und Ammann in den 1970er Jahren vorgeschlagen wurden. Aufgrund der fehlenden Translationssymmetrie in Quasikristallen sind bis heute nur endliche, relativ kleine Systeme oder periodische Approximanten durch numerische Berechnungen untersucht worden und theoretische Ergebnisse wurden hauptsächlich für eindimensionale Systeme gewonnen. In dieser Arbeit werden d-dimensionale quasiperiodische Modelle, sogenannte Labyrinth-Pflasterungen, mit separablem Hamilton-Operator im Modell starker Bindung betrachtet. Diese Methode erlaubt es, quantenmechanische Lösungen in höheren Dimensionen direkt aus den eindimensionalen Ergebnissen abzuleiten und ermöglicht somit die Untersuchung von sehr großen Systemen in zwei und drei Dimensionen mit bis zu 10^10 Gitterpunkten. Insbesondere betrachten wir dabei quasiperiodische Folgen mit metallischem Schnitt. Basierend auf diesem Modell befassen wir uns im Speziellen mit den elektronischen Eigenschaften der Quasikristalle im Hinblick auf die Verbindung der spektralen und dynamischen Eigenschaften des Hamilton-Operators. Hierfür untersuchen wir die Eigenschaften der Eigenzustände und Wellenfunktionen und vergleichen diese mit der Dynamik von Wellenpaketen in den Labyrinth-Pflasterungen basierend auf numerischen Berechnungen und einem Renormierungsgruppen-Ansatz in Verbindung mit Störungstheorie. Dabei stellt sich heraus, dass viele Eigenschaften wie etwa das Skalenverhalten der Partizipationszahlen und der mittleren quadratischen Abweichung eines Wellenpakets für verschiedene Dimensionen ein qualitativ gleiches Verhalten zeigen oder sogar unabhängig von der Dimension sind. Zudem zeigen wir, dass die Struktur der Labyrinth-Pflasterungen und deren Transporteigenschaften sowie bestimmte Momente der spektralen Dimensionen und die Dynamik der Wellenpakete in Beziehung zueinander stehen. Darüber hinaus werden auch die photonischen Eigenschaften für eindimensionale quasiperiodische Mehrschichtsysteme für beliebige Einfallswinkel untersucht und der Verlauf der Transmissionsbänder mit der quasiperiodischen Struktur in Zusammenhang gebracht.

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Books on the topic "Quasiperiodic systems"

1

Mitropolʹskiĭ, I͡U A. Systems of evolution equations with periodic and quasiperiodic coefficients. Dordrecht: Kluwer Academic, 1993.

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2

Mitropolsky, Yu A., A. M. Samoilenko, and D. I. Martinyuk. Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2728-8.

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3

D, Coca, ed. Nonlinear system identification and analysis of quasiperiodic oscillations in reflected light measurements of vasomotion. Sheffield: University of Sheffield, Dept. Of Automatic Control and Systems Engineering, 1998.

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Mitropolsky, Yuri A., Anatolii M. Samoilenko, and D. I. Martinyuk. Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients. Springer, 2012.

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Mitropolsky, Yuri A. Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients. Springer, 2012.

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6

Samoilenko, A. M., Yuri A. Mitropolsky, and D. I. Martinyuk. Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients (Mathematics and its Applications). Springer, 1992.

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Janssen, Ted, Gervais Chapuis, and Marc de Boissieu. Other topics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198824442.003.0007.

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The law of rational indices to describe crystal faces was one of the most fundamental law of crystallography and is strongly linked to the three-dimensional periodicity of solids. This chapter describes how this fundamental law has to be revised and generalized in order to include the structures of aperiodic crystals. The generalization consists in using for each face a number of integers, with the number corresponding to the rank of the structure, that is, the number of integer indices necessary to characterize each of the diffracted intensities generated by the aperiodic system. A series of examples including incommensurate multiferroics, icosahedral crystals, and decagonal quaiscrystals illustrates this topic. Aperiodicity is also encountered in surfaces where the same generalization can be applied. The chapter discusses aperiodic crystal morphology, including icosahedral quasicrystal morphology, decagonal quasicrystal morphology, and aperiodic crystal surfaces; magnetic quasiperiodic systems; aperiodic photonic crystals; mesoscopic quasicrystals, and the mineral calaverite.

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Janssen, Ted, Gervais Chapuis, and Marc de Boissieu. Description and symmetry of aperiodic crystals. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198824442.003.0002.

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This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

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Book chapters on the topic "Quasiperiodic systems"

1

Anishchenko, Vadim S., Tatyana E. Vadivasova, and Galina I. Strelkova. "Quasiperiodic Oscillator with Two Independent Frequencies." In Deterministic Nonlinear Systems, 203–15. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06871-8_12.

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Hiramoto, H. "Localization in One-Dimensional Quasiperiodic Systems." In Springer Series in Solid-State Sciences, 169–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84253-5_18.

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Janssen, T. "From Quasiperiodic to More Complex Systems." In Beyond Quasicrystals, 75–140. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-662-03130-8_5.

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Tokihiro, T. "Quasiperiodic Systems with Long-Range Hierarchical Interactions." In Springer Series in Solid-State Sciences, 179–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84253-5_19.

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Koukiou, Flora, Dimitri Petritis, and Miloš Zahradník. "Low Temperature Phase Transitions on Quasiperiodic Lattices." In Cellular Automata and Cooperative Systems, 375–86. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1691-6_29.

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Delshams, Amadeu, Àngel Jorba, Tere M. Seara, and Vassili Gelfreich. "Splitting of Separatrices for (Fast) Quasiperiodic Forcing." In Hamiltonian Systems with Three or More Degrees of Freedom, 367–71. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4673-9_40.

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Mitropolsky, Yu A., A. M. Samoilenko, and D. I. Martinyuk. "Quasiperiodic Solutions of Systems with Lag. Bubnov-Galerkin’s Method." In Mathematics and its Applications, 107–34. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2728-8_3.

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Heidari, Alireza, and Mohammadali Ghorbani. "RETRACTED CHAPTER: Lempel–Ziv Model of Dynamical-Chaotic and Fibonacci-Quasiperiodic Systems." In Chaos and Complex Systems, 11–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33914-1_2.

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Kohmoto, M. "Multifractal Method for Spectra and Wave Functions of Quasiperiodic Systems." In Springer Series in Solid-State Sciences, 158–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84253-5_17.

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Mitropolsky, Yu A., A. M. Samoilenko, and D. I. Martinyuk. "Reducibility of Linear Systems of Difference Equations with Quasiperiodic Coefficients." In Mathematics and its Applications, 201–22. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2728-8_5.

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Conference papers on the topic "Quasiperiodic systems"

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DUMAS, H. SCOTT, and JAMES A. ELLISON. "AVERAGING FOR QUASIPERIODIC SYSTEMS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0121.

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Redkar, Sangram, and S. C. Sinha. "Order Reduction of Nonlinear Systems With Periodic-Quasiperiodic Coefficients." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85306.

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In this work, some techniques for order reduction of nonlinear systems involving periodic/quasiperiodic coefficients are presented. The periodicity of the linear terms is assumed non-commensurate with the periodicity of either the nonlinear terms or the forcing vector. The dynamical evolution equations are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the nonlinear parts and forcing take the form of quasiperiodic functions. The techniques proposed here construct a reduced order equivalent system by expressing the non-dominant states as time-modulated functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states. Three methods are proposed to carry out this model order reduction (MOR). First type of MOR technique is a linear method similar to the ‘Guyan reduction’, the second technique is a nonlinear projection method based on singular perturbation while the third method utilizes the concept of ‘quasiperiodic invariant manifold’. Order reduction approach based on invariant manifold technique yields a unique ‘generalized reducibility condition’. If this ‘reducibility condition’ is satisfied only then an accurate order reduction via invariant manifold is possible. Next, the proposed methodologies are extended to solve the forced problem. All order reduction approaches except the invariant manifold technique can be applied in a straightforward way. The invariant manifold formulation is modified to take into account the effects of forcing and nonlinear coupling. This approach not only yields accurate reduced order models but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover all ‘resonance conditions’ obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems.

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Tkachenko, Viktor. "On reducibility of linear quasiperiodic systems with bounded solutions." In The 6'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 1999. http://dx.doi.org/10.14232/ejqtde.1999.5.29.

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Stépán, G., and G. Haller. "Stable and Unstable Quasiperiodic Oscillations in Robot Dynamics." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0115.

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Abstract Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.

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Feldman, Michael. "Time-Varying and Non-Linear Dynamical System Identification Using the Hilbert Transform." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84644.

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The objective of the paper is to explain a modern Hilbert transform method for analysis and identification of mechanical non-linear vibration structures in the case of quasiperiodic signals. This special kind of periodicity arises in experimental vibration signals. The method is based on the Hilbert transform of input and output signals in a time domain to extract the instantaneous dynamic structure characteristics. The paper focuses on the dynamic analysis and identification of three groups of dynamics systems: • Forced vibrations of linear and non-linear SDOF systems excited with quasiperiodic force signal. • Combined forced vibrations of quasiperiodic time varying linear and non-linear SDOF systems excited with harmonic signal. • Combined self-excited and forced vibrations of non-linear SDOF systems excited with harmonic signal. The study focuses on signal processing techniques for nonlinear system investigation, which enable us to estimate instantaneous system dynamic parameters (natural frequencies, damping characteristics and their dependencies on a vibration amplitude and frequency) for different kinds of system excitation.

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Chu, Shih-I. "Quasiperiodic and chaotic motions in intense field multiphoton processes." In International Laser Science Conference. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/ils.1986.thb2.

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The question of the behavior of quantum systems in time-dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many-mode Floquet theory1 that the autocorrelation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible.2 In particular, for an N-level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2 – 1)-dimensional coherence vector S in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and chaotic behavior is observed as the coherence vector Sevolves from an initially (N2 – 1)-dimensional space to a lower-dimensional space. The recurrence and chaotic phenomena are illustrated for two- and three-level quantum systems driven by intense bichromatic laser fields.2

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Rand, Richard, Kamar Guennoun, and Mohamed Belhaq. "2:2:1 Resonance in the Quasiperiodic Mathieu Equation." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48563.

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In this work, we investigate regions of stability in the vicinity of 2:2:1 resonance in the quasiperiodic Mathieu equation: d2xdt2+(δ+εcost+εμcos(1+εΔ)t)x=0, using two successive perturbation methods. The parameters ε and μ are assumed to be small. The parameter ε serves for deriving the corresponding slow flow differential system and μ serves to implement a second perturbation analysis on the slow flow system near its proper resonance. This strategy allows us to obtain analytical expressions for the transition curves in the resonant quasiperiodic Mathieu equation. We compare the analytical results with those of direct numerical integration. This work has application to parametrically excited systems in which there are two periodic drivers, each with frequency close to twice the frequency of the unforced system.

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Isaeva, O. B., D. V. Savin, E. P. Seleznev, and N. V. Stankevich. "Hyperbolic chaos and quasiperiodic dynamics in experimental nonautonomous systems of coupled oscillators." In 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS). IEEE, 2017. http://dx.doi.org/10.1109/piers.2017.8262291.

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Boucher, Yann G., Emmanuel Drouard, Ludovic Escoubas, and Francois Flory. "One-dimensional transfer matrix formalism with localized losses for fast designing of quasiperiodic waveguide filters." In Optical Systems Design, edited by Laurent Mazuray, Philip J. Rogers, and Rolf Wartmann. SPIE, 2004. http://dx.doi.org/10.1117/12.512980.

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Rahman, Lutfur, and Herbert G. Winful. "Fractal Transmission Properties of a Quasiperiodic Sequence of Directional Couplers." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/nlgwp.1989.fc3.

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Quasi-periodic structures, structures which are intermediate between the periodic and disordered systems, have been a subject of considerable theoretical interest in recent years1–3. It has been shown theoretically that such structures display exotic behavior such as weak localization and scaling. Experimental realization of such structures and identification of these exotic features is needed. One potentially simple experiment towards this end has recently been proposed2 where a stack of dielectric layers is constructed using two types of dielectric layers arranged in a Fibonacci sequence. The transmission coefficient, as a function of the wavelength of incident light, was demonstrated to be multifractal and displayed scaling. Our work is concerned with a quasi-periodic optical system consisting of waveguide directional couplers which under certain resonant conditions displays localization and scaling. The energy exchange between the guides is codirectional as opposed to the contradirectional energy exchange of Ref. 2.

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