Relevant bibliographies by topics / Disordered and aperiodic systems

Academic literature on the topic 'Disordered and aperiodic systems'

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Published: 7 July 2024

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Disordered and aperiodic systems":

1

RIKLUND, ROLF, MATTIAS SEVERIN, and YOUYAN LIU. "THE THUE-MORSE APERIODIC CRYSTAL, A LINK BETWEEN THE FIBONACCI QUASICRYSTAL AND THE PERIODIC CRYSTAL." International Journal of Modern Physics B 01, no. 01 (April 1987): 121–32. http://dx.doi.org/10.1142/s0217979287000104.

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The electronic spectrum and eigenstates of a one-dimensional aperiodic Thue-Morse crystal isstudied with an on-site tight-binding model. The relation between the constructing elements andthe hierarchical splitting of the bands into subbands is analysed. The eigenstates are shown to be much more similar to those of a periodic crystal than those of a Fibonacci quasicrystal. We thus claim that the Thue-Morse aperiodic crystal is a link between the Fibonacci quasicrystal and theperiodic crystal, and that the study of non-Fibonaccian aperiodic crystals is a promising steptowards the desired unified theory of disordered, aperiodic and periodic systems. Since the experimentally studied MBE-grown aperiodic crystals typically has 5% fluctuation in layer thickness, we also investigate the density of states and eigenstates for a model system withfluctuating site-energies.
2

De Oliveira, Mário J., and Alberto Petri. "Density of States and Localization Lengths in One-dimensional Linear Chains." International Journal of Modern Physics B 11, no. 18 (July 20, 1997): 2195–205. http://dx.doi.org/10.1142/s0217979297001131.

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The integral equation for computing the density of states of a disordered linear chain of harmonic oscillators is interpreted as describing a stochastic Markov process, and its solution is determined by means of Monte Carlo simulation of the process. It is also shown that, in addition to the localization lengths of the eigenstates, the method allows the computation of the generalized Ljapunov exponents. Many different examples of application, ranging from systems with uncorrelated disorder to deterministic aperiodic chains, are reported.
3

Chakraborty, Srija, and Santanu K. Maiti. "Localization phenomena in a one-dimensional phononic lattice with finite mass modulation: Beyond nearest-neighbor interaction." Journal of Physics: Conference Series 2349, no. 1 (September 1, 2022): 012009. http://dx.doi.org/10.1088/1742-6596/2349/1/012009.

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One-dimensional phononic systems beyond conventional nearest-neighbor interaction have not been well explored, to the best of our knowledge. In this work, we critically investigate the localization properties of a 1D phononic lattice in presence of second-neighbor interaction along with the nearest-neighbor one. A finite modulation in masses is incorporated following the well known Aubry-Andre-Harper (AAH) form to make the system a correlated disordered one. Solving the motion equations we determine the phonon frequency spectrum, and characterize the localization properties of the individual phononic states by calculating inverse participation ratio (IPR). The key aspect of our analysis is that, in the presence of second-neighbor interaction, the phonon eigenstates exhibit frequency dependent transition from sliding to the pinned phase upon the variation of the modulation strength, exhibiting a mobility edge. This is completely in contrast to the nearest-neighbor interaction case, where all the states get localized beyond a particular modulation strength, and thus, no mobility edge appears. Our analysis can be utilized in many aspects to regulate phonon transmission through similar kind of aperiodic lattices that are described beyond the usual nearest-neighbor interaction.
4

Lory, Pierre-François, Marc de Boissieu, Peter Gille, Mark Johnson, Marek Mihalkovic, and Helmut Schober. "Lattice dynamics and macroscopic properties in complex metallic alloys." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C399. http://dx.doi.org/10.1107/s2053273314096004.

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Complex metallic alloys are long-range ordered materials, characterized by large unit cells, comprising several tens to thousands of atoms [1]. These complex alloys often consist of characteristic, cluster building blocks, which in many cases show icosahedral symmetry. Numerous complex phases are known, that can be described in a rather simple way as the periodic or quasi-periodic packing of such atomic clusters. The lattice dynamics of CMAs has been the subject of both theoretical and experimental investigations in view of their interesting macroscopic properties such as low thermal conductivity. In aperiodic crystals in the higher wave-vector regime, theory predicts that the lattice modes are critical: they are neither extended as in simple crystals nor localized as in disordered systems [2]. Experimentally phonons have been studied in different CMAs systems like clathrates, approximant-crystals and quasicrystals. For all of them, acoustic modes are well-defined for wave-vectors close to Brillouin zone centres, but then broaden rapidly as the result of coupling with other excitations [3]. We will present a combined experimental and atomistic simulation study of the lattice dynamics of the complex metallic alloy Al13Co4 phase [4], which is a periodic approximant of the decagonal phase. Particular attention will be paid to the differences between the periodic and `quasiperiodic' directions. Inelastic neutron scattering measurements carried out on a large, single grain on a triple-axis spectrometer will be compared to simulations, focussing on the dispersion relations and the intensity distribution of the S(Q,ω) scattering function, which is a very sensitive test of the model [3]. Simulations are performed with DFT methods and empirical, oscillating, pair potentials [5]. In addition, thermal conductivity calculations, based on the Green-Kubo method, will be compared with measurements, which show a weak anisotropy [6-7]. In this way, the structure-dynamics-properties relation for CMAs is thoroughly explored.
5

Vasiljević, Jadranka M., Dejan V. Timotijević, and Dragana M. Jović Savić. "Light propagation in disordered aperiodic Mathieu photonic lattices." EPJ Web of Conferences 266 (2022): 08015. http://dx.doi.org/10.1051/epjconf/202226608015.

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We present the numerical modeling of two different randomization methods of photonic lattices. We compare the results of light propagation in disordered aperiodic and disordered periodic lattices. In disordered aperiodic lattice disorder always enhances light transport for both methods, contrary to the disordered periodic lattice. For the highest disorder levels, we detect Anderson localization for both methods and both disordered lattices. More pronounced localization is observed for disordered aperiodic lattice.
6

Hart, A. G., T. C. Hansen, and W. F. Kuhs. "A Markov theoretic description of stacking-disordered aperiodic crystals including ice and opaline silica." Acta Crystallographica Section A Foundations and Advances 74, no. 4 (July 1, 2018): 357–72. http://dx.doi.org/10.1107/s2053273318006083.

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This article reviews the Markov theoretic description of one-dimensional aperiodic crystals, describing the stacking-faulted crystal polytype as a special case of an aperiodic crystal. Under this description the centrosymmetric unit cell underlying a topologically centrosymmetric crystal is generalized to a reversible Markov chain underlying a reversible aperiodic crystal. It is shown that for the close-packed structure almost all stackings are irreversible when the interaction reichweite s > 4. Moreover, the article presents an analytic expression of the scattering cross section of a large class of stacking-disordered aperiodic crystals, lacking translational symmetry of their layers, including ice and opaline silica (opal CT). The observed stackings and their underlying reichweite are then related to the physics of various nucleation and growth processes of disordered ice. The article discusses how the derived expressions of scattering cross sections could significantly improve implementations of Rietveld's refinement scheme and compares this Q-space approach with the pair-distribution function analysis of stacking-disordered materials.
7

Bahov, V. A., E. A. Nazderkin, A. S. Mazinov, and L. D. Pisarenko. "Effect of structural heterogeneity on conductivity semiconductor materials." Electronics and Communications 16, no. 4 (March 31, 2011): 11–14. http://dx.doi.org/10.20535/2312-1807.2011.16.4.242709.

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Complexity in understanding of the processes spotting the electrical properties of structured materials is considered from the side of the quantum representation of aperiodic structure. Determination of each of the view disordered aperiodic matrixes by means of statistical and energy parameters have allowed to describe the temperature dependences of the electroconductivity of the hydrogenated silicon amorphous films
8

SCHROEDER, VIKTOR, and STEFFEN WEIL. "Aperiodic sequences and aperiodic geodesics." Ergodic Theory and Dynamical Systems 34, no. 5 (March 14, 2013): 1699–723. http://dx.doi.org/10.1017/etds.2013.2.

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AbstractWe introduce a quantitative condition on orbits of dynamical systems, which measures their aperiodicity. We show the existence of sequences in the Bernoulli shift and geodesics on closed hyperbolic manifolds which are as aperiodic as possible with respect to this condition.
9

Vasiljević, Jadranka M., Alessandro Zannotti, Dejan V. Timotijević, Cornelia Denz, and Dragana M. Jović Savić. "Light transport and localization in disordered aperiodic Mathieu lattices." Optics Letters 47, no. 3 (January 31, 2022): 702. http://dx.doi.org/10.1364/ol.445779.

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Shamblin, Jacob, Cameron L. Tracy, Raul I. Palomares, Eric C. O'Quinn, Rodney C. Ewing, Joerg Neuefeind, Mikhail Feygenson, Jason Behrens, Christina Trautmann, and Maik Lang. "Similar local order in disordered fluorite and aperiodic pyrochlore structures." Acta Materialia 144 (February 2018): 60–67. http://dx.doi.org/10.1016/j.actamat.2017.10.044.

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You might also be interested in the extended bibliographies on the topic 'Disordered and aperiodic systems' for particular source types:
Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Disordered and aperiodic systems":

1

Karevski, Dragi. "Ising Quantum Chains." Habilitation à diriger des recherches, Université Henri Poincaré - Nancy I, 2005. http://tel.archives-ouvertes.fr/hal-00113500.

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The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular, a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.
2

Vieira, Andre de Pinho. "Efeitos de desordem ou aperiodicidade sobre o comportamento de sistemas magnéticos." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-23022012-155648/.

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Consideramos os efeitos de desordem ou aperiodicidade sobre três sistemas magnéticos distintos. Inicialmente, apresentamos um modelo fenomenológico para descrever a dependência térmica da magnetização remanente induzida por diluição numa classe de antiferromagnetos quase-unidimensionais. O modelo trata exatamente as correlações ao longo da direção dominante, levando em conta as demais interações por meio de um campo efetivo. Em seguida, utilizamos uma aproximação autoconsistente de Bethe-Peierls para avaliar os efeitos de um campo cristalino aleatório sobre os diagramas de fases de um modelo de Ising de spins mistos. Mostramos que a desordem é capaz de modificar a natureza dos pontos multicríticos existentes no limite uniforme do modelo. Finalmente, estudamos os efeitos de interações aleatórias ou aperiódicas sobre o comportamento da cadeia XX quântica em baixas temperaturas, através de câlculos numéricos baseados no mapeamento do sistema em um modelo de férmions livres. Apontamos evidências de que, em temperatura zero, existe um único ponto fixo universal, característico de uma fase de singleto aleatório, que governa o comportamento do modelo na presença de interações desordenadas. No caso de interações aperiódicas,obtemos resultados consistentes com previsões de grupo de renormalização, indicando, para uma certa classe de seqüências de substituição, um comportamento semelhante àquele associado à desordem.
We consider effects of disorder or aperiodicity on three different magnetic systems. First, we present a phenomenological model to describe the thermal dependence of the dilution-induced remanent magnetization in a class of quasi-one-dimensional antiferromagnets. The model treats correlations along the dominant direction in an exact way, while including the remaining inte-. i ractions via an effective field. Then, we use a self-consistent Bethe-Peierls ~ j .. approximation to gauge the effects of a random crystal field on the phase diagram of a mixed-spin Ising mode!. We show that disorder may have profound effects on the multicritical behavior associated with the uniform limit of the mo de!. Finally, we study effects of random or aperiodic interactions on the behavior of the quantum XX chain at low temperatures, by performing numerical calculations based on a mapping of the system onto a free-fermion mo de!. . We present evidence that, at zero temperature, there exists a single, universal fixed-point, associated with a random-singlet phase, which governs the behavior of the model in the presence of disordered interactions. In the case of aperiodic interactions, our results are consistent with renormalizationgroup predictions, indicating, for a certain class of substitution sequences, a behavior similar to the one induced by disorder.
3

Bishnani, Zahir. "Safety criteria for aperiodic dynamical systems." Thesis, University of Warwick, 1997. http://wrap.warwick.ac.uk/57617/.

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The use of dynamical system models is commonplace in many areas of science and engineering. One is often interested in whether the attracting solutions in these models are robust to perturbations of the equations of motion. This question is extremely important in situations where it is undesirable to have a large response to perturbations for reasons of safety. An especially interesting case occurs when the perturbations are aperiodic and their exact form is unknown. Unfortunately, there is a lack of theory in the literature that deals with this situation. It would be extremely useful to have a practical technique that provides an upper bound on the size of the response for an arbitrary perturbation of given size. Estimates of this form would allow the simple determination of safety criteria that guarantee the response falls within some pre-specified safety limits. An excellent area of application for this technique would be engineering systems. Here one is frequently faced with the problem of obtaining safety criteria for systems that in operational use are subject to unknown, aperiodic perturbations. In this thesis I show that such safety criteria are easy to obtain by using the concept of persistence of hyperbolicity. This persistence result is well known in the theory of dynamical systems. The formulation I give is functional analytic in nature and this has the advantage that it is easy to generalise and is especially suited to the problem of unknown, aperiodic perturbations. The proof I give of the persistence theorem provides a technique for obtaining the safety estimates we want and the main part of this thesis is an investigation into how this can be practically done. The usefulness of the technique is illustrated through two example systems, both of which are forced oscillators. Firstly, I consider the case where the unforced oscillator has an asymptotically stable equilibrium. A good application of this is the problem of ship stability. The model is called the escape equation and has been argued to capture the relevant dynamics of a ship at sea. The problem is to find practical criteria that guarantee the ship does not capsize or go through large motions when there are external influences like wind and waves. I show how to provide good criteria which ensure a safe response when the external forcing is an arbitrary, bounded function of time. I also consider in some detail the phased-locked loop. This is a periodically forced oscillator which has an attracting periodic solution that is synchronised (or phase-locked) with the external forcing. It is interesting to consider the effect of small aperiodic variations in the external forcing. For hyperbolic solutions I show that the phase-locking persists and I give a method by which one can find an upperbound on the maximum size of the response.
4

Lenz, Daniel. "Aspects of aperiodic order: spectral theory via dynamical systems." Doctoral thesis, [S.l.] : [s.n.], 2005. http://archiv.tu-chemnitz.de/pub/2005/0079.

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5

Gao, Yulong. "Stochastic Invariance and Aperiodic Control for Uncertain Constrained Systems." Licentiate thesis, KTH, Reglerteknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-236072.

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Uncertainties and constraints are present in most control systems. For example, robot motion planning and building climate regulation can be modeled as uncertain constrained systems. In this thesis, we develop mathematical and computational tools to analyze and synthesize controllers for such systems. As our first contribution, we characterize when a set is a probabilistic controlled invariant set and we develop tools to compute such sets. A probabilistic controlled invariantset is a set within which the controller is able to keep the system state with a certainprobability. It is a natural complement to the existing notion of robust controlled invariantsets. We provide iterative algorithms to compute a probabilistic controlled invariantset within a given set based on stochastic backward reachability. We prove that thesealgorithms are computationally tractable and converge in a finite number of iterations. The computational tools are demonstrated on examples of motion planning, climate regulation, and model predictive control. As our second contribution, we address the control design problem for uncertain constrained systems with aperiodic sensing and actuation. Firstly, we propose a stochastic self-triggered model predictive control algorithm for linear systems subject to exogenous disturbances and probabilistic constraints. We prove that probabilistic constraint satisfaction, recursive feasibility, and closed-loop stability can be guaranteed. The control algorithm is computationally tractable as we are able to reformulate the problem into a quadratic program. Secondly, we develop a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. In the particular case when there is no uncertainty, the design leads to a control system requiring minimum number of samples over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as mixed integer linear programs. The method is applied to a motion planning problem with temporal constraints.

QC 20181016

6

Motakpalli, Sankalpanand. "Aperiodic Job Handling in Cache-Based Real-Time Systems." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1474.

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Real-time systems require a-priori temporal guarantees. While most of the normal operation in such a system is modeled using time-driven, hard-deadline sporadic tasks, event-driven behavior is modeled using aperiodic jobs with soft or no deadlines. To provide good Quality-of- Service for aperiodic jobs in the presence of sporadic tasks, aperiodic servers were introduced. Aperiodic servers act as a sporadic task and reserve a quota periodically to serve aperiodic jobs. The use of aperiodic servers in systems with caches is unsafe because aperiodic servers do not take into account, the indirect cache-related preemption delays that the execution of aperiodic jobs might impose on the lower-priority sporadic tasks, thus jeopardizing their safety. To solve this problem, we propose an enhancement to the aperiodic server that we call a Cache Delay Server. Here, each lower-priority sporadic task is assigned a delay quota to accommodate the cache-related preemption delay imposed by the execution of aperiodic jobs. Aperiodic jobs are allowed to execute at their assigned server priority only when all the active lower-priority sporadic tasks have a sufficient delay quota to accommodate it. Simulation results demonstrate that a Cache Delay Server ensures the safety of sporadic tasks while providing acceptable Quality-of-Service for aperiodic jobs. We propose a Integer Linear Program based approach to calculate delay quotas for sporadic tasks within a task set where Cache Delay Servers have been pre-assigned. We then propose algorithms to determine Cache Delay Server characteristics for a given sporadic task set. Finally, we extend the Cache Delay Server concept to multi-core architectures and propose approaches to schedule aperiodic jobs on appropriate Cache Delay Servers. Simulation results demonstrate the effectiveness of all our proposed algorithms in improving aperiodic job response times while maintaining the safety of sporadic task execution.
7

Vispa, Alessandro. "Dynamics of disordered systems." Doctoral thesis, Universitat Politècnica de Catalunya, 2016. http://hdl.handle.net/10803/404444.

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Disordered systems are ubiquitous in nature and their study is complicated and often leads to controversial results. In any case, the important role of such systems in science and technological applications should not be ignored. The characteristic properties of such systems seem to be driven by a fundamental feature, the degrees of freedom. Although many problems still remain matter of debate, the challenge posed in recent decades in the understanding of the impact of disorder in the physical behavior of materials is of considerable scientic interest. An exact description of a disordered phase is not possible since it is a many-body problem hard to model. However, for some materials it is possible, upon cooling, to preserve the disordered liquid-like structure having a state of high regularity. Therefore, for the so-called glass formers, it is possible to freeze some degrees of freedom obtaining a glass that presents the irregularity of a liquid with the high viscosity of a solid below the melting temperature Tm. The aim of the present PhD thesis is to present our understanding of disorder in related experimental approaches using three different pure compounds: two plastic crystals (1-Chloroadamantane and Freon113) and a liquid (Glycerol). To understand the behavior of these kinds of materials neutron scattering and dielectric spectroscopy have been used. These two powerful techniques allow us to investigate the dynamics of disordered phases on a picosecond time scale. Furthermore, given the complexity of these disordered phases, data analysis and model selection have been performed with a Bayesian approach that provides a solid statistical ground bases on probability distribution functions. Such methods have been applied to study of the above mentioned compounds dynamics in order to give an explanation of some open questions: the microscopic origin of the plastic-plastic transition in 1-chloroadamantane (C10H15Cl), the high fragility and the correlation between kinetic and thermodynamic fragility in freon113 (Cl2FC-CClF2) and the dynamics, accompanied by a robust model selection, of one of the most studied glass former compound, glycerol (C3H8O3). In addition, a brief overview of the theoretical background for neutron scattering and dielectric spectroscopy, as well as a description of the experimental setup and the consequent data treatment and analysis, are given to deliver a comprehensive and consistent view of the topic under consideration. The results, presented in this work of thesis, represent a small step in a deeper understanding of disordered phases dynamics, giving a base for further investigations.
Los sistemas desordenados son ubicuos en la naturaleza y su estudio es complicado y con frecuencia conduce a resultados controvertidos. En cualquier caso, el papel importante de este tipo de sistemas en aplicaciones científicas y tecnológicas no debe ser ignorada. Las propiedades características de tales sistemas parecen estar impulsadas por una característica fundamental, los grados de libertad. Aunque muchos problemas siguen siendo materia de debate, el desafío planteado en las últimas décadas en el entendimiento del impacto del desorden en el comportamiento físico de los materiales es de considerable interés científico. Una descripción exacta de una fase desordenada no es posible, ya que es un problema de muchos cuerpos difícil de modelar. Sin embargo, para algunos materiales, es posible, tras el enfriamiento, conservar la estructura desordenada del líquido con un estado de alta regularidad. Por lo tanto, para los denominados glass-formers, es posible congelar algunos grados de libertad obteniendo un vidrio que presenta la irregularidad de un líquido con la alta viscosidad de un sólido por debajo de la temperatura de fusión Tm. El objetivo de la presente tesis doctoral es presentar nuestra comprensión del desorden en los enfoques experimentales relacionados utilizando tres diferentes compuestos puros: dos cristales de plástico (1-Chloroadamantane y Freon113) y un líquido (Glycerol). Para entender el comportamiento de este tipo de materiales se han utilizado scattering de neutrones y espectroscopía dieléctrica. Estas dos técnicas nos permiten investigar la dinámica de las fases desordenadas en una escala de tiempo de picosegundos. Por otra parte, dada la complejidad de estas fases desordenadas, análisis de datos y la selección del modelo se han realizado con un enfoque bayesiano que proporciona una sólida base estadística basada sobre las funciones de distribución de probabilidad. Tales métodos se han aplicado al estudio de la dinámica de los compuestos antes mencionados con el fin de dar una explicación de algunas preguntas abiertas: el origen microscópico de la transición plástico-plástico en 1-chloroadamantane (C10H15Cl), la alta fragilidad y la correlación entre la fragilidad cinética y termodinámica en freon113 (Cl2FC-CClF2) y la dinámica, acompañada por una robusta selección de modelo, de uno de los compuestos más estudiados, glycerol (C3H8O3). Los resultados, presentados en este trabajo de tesis, representan un pequeño paso para una comprensión más profunda de la dinámica de las fases desordenadas, dando una base para futuras investigaciones.
8

Gorokhov, Denis A. "Dynamics of disordered systems /." [S.l.] : [s.n.], 1999. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13070.

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9

Hashimoto, Kazumune. "Distributed Aperiodic Model Predictive Control for perturbed multi-agent systems." Thesis, KTH, Reglerteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-138441.

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In this master thesis we propose an aperiodic formulation of Model Predictive Control for distributed agents with additive bounded disturbances. In this control method, each agent solves an optimal control problem only when certain control performances are not guaranteed according to several triggering rules. This may lead not only to the dramatic reduction of energy expenditures but also to the alleviation of communication loads among them. The problem will be considered to be general and practical; it handles the non-linearity of the each agent which is perturbed by additive bounded disturbances, where the triggering rule is derived from several robust stability criterion. The triggering rule will be addressed for event-based control and self-triggered control, which are the two main different aperiodic control approaches. Finally some simulation results verify our proposal.
10

Romanini, Michela. "Relaxation dynamics in disordered systems." Doctoral thesis, Universitat Politècnica de Catalunya, 2015. http://hdl.handle.net/10803/317384.

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The nature of the glass transition and of the glassy state is a fundamental and still unsolved problem of condensed matter physics. Many liquids can be supercooled below their melting point without crystallizing, that is, without acquiring translational and orientational order. As the temperature of a supercooled liquid is lowered, the characteristic timescale of moleuclar motions, called relaxation time, increases until it becomes comparable to the timescale of human experimentation. This takes place at the glass transition temperature and leads to a non-equilibrium state of matter, called a ¿structural glass¿, in which a liquid-like lack of order is combined with solid-like elastic properties. Glass transitions are also observed in systems where there is only orientational disorder, such as orientationally disordered (OD) crystals or plastic crystals, which are translationally ordered solids in which the constituent molecules display reorientational motions about their centres of mass. Upon supercooling an OD crystal, the orientational disorder can ¿freeze¿, yielding a so-called ¿orientational glass¿. In molecular materials forming structural or orientational glasses, the most important molecular dynamics process is the cooperative motion of the molecules, referred to as primary relaxation, whose freezing marks the transition to the glass state characterized by static disorder. The main difference between orientational and structural glasses is that in the former the freezing involves exclusively the rotational degrees of freedom of the molecules, while in the latter all six molecular degrees of freedom (i.e., both orientational and translational ones) are frozen. Orientational glasses are therefore systems with fewer degrees of freedom than structural glasses. This simplification, together with the fact that many OD phases are characterized by a crystal lattice with high symmetry, makes OD phases a model playground to investigate the nature of the glass transition. Other than the primary relaxation, there can be also so-called ¿secondary relaxations¿, usually characterized by shorter relaxation time than the primary process. Secondary relaxations may have different origins; for example, they can be due to conformational fluctuations or intramolecular vibrations; in many cases a special kind of secondary relaxation is observed, which is the single-molecule precursor process of the primary relaxation. This thesis focuses on the effect of pressure and temperature on the dynamics of several pure compounds and binary mixtures forming structural or orientational glasses. We present a comparative study between two structural glass formers (ternidazole and the mixture of m-fluoroaniline with m-xylene), a plastic binary mixed crystal (neopenthyl alchol and neopentyl glycol), and two materials displaying statistical orientational disorder (2-adamantanone and pentachloronitrobenzene). In all cases a primary relaxation is present, associated with the collective motion of the molecules, and in most cases also secondary relaxations are observed. For each material, we analyse the temperature- and pressure-dependence of the various molecular relaxation and discuss the origin of secondary processes. One of the most important results of the thesis is the presence of secondary relaxations also in systems with low-dimensional disorder that behave similarly to the secondary relaxations observed in structural glasses.
La naturaleza de la transición vítrea es un problema fundamental y aún no resuelto de la física de la materia condensada. Muchos líquidos pueden ser superenfriados por debajo de su temperatura de fusión sin que cristalicen, es decir, sin que adquieran orden traslacional y orientacional. Cuando la temperatura de un líquido superenfriado baja, el tiempo característico de los movimientos moleculares, llamado tiempo de relajación, aumenta hasta llegar a tiempos comparables con el tiempo característico de los experimentos y de la observación humana. Esto ocurre a una temperatura llamada temperatura de transición vítrea y lleva a un estado de non-equilibrio del material llamado ¿vidrio estructural¿, en el que la ausencia de orden de largo alcance típica del estado líquido se combina con las propiedades elásticas propias de un sólido ordenado. Las transiciones vítreas se pueden observar también en sistemas caracterizados por desorden exclusivamente orientacional, como en los cristales orientacionalmente desordenados (OD) o cristales plásticos. Estos son sólidos traslacionalmente ordenados en los que las moléculas tienen movimientos de reorientación alrededor de sus centros de masa, que están fijos. Superenfriando un cristal OD se obtiene un ¿vidrio orientacional¿ en el cual este desorden orientacional está congelado. El proceso dinámico más importante que caracteriza los materiales moleculares que forman vidrios estructurales u orientacionales es el movimiento cooperativo de las moléculas conocido como relajación primaria. Su congelamiento marca la transición al estado vítreo caracterizado por un desorden estático. La diferencia principal entre los vidrios orientacionales y estructurales es que en los primeros el congelamiento involucra sólo los grados de libertad de rotación, mientras que en los segundos todos los seis grados de libertad moleculares (orientacionales y traslacionales) están congelados. Por tanto, los vidrios orientacionales son sistemas con menos grados de libertad respecto los vidrios estructurales y pueden considerarse como sistemas modelo para investigar la transición vítrea, ya que además muchas fases OD están caracterizadas por redes cristalinas de alta simetría. Además de la relajación primaria, existen también relajaciones secundarias caracterizadas por tiempos de relajación más cortos con respecto al proceso primario. Estas relajaciones secundarias pueden tener diferentes orígenes: por ejemplo, pueden ser debidas a fluctuaciones de la conformación molecular o a vibraciones de enlaces intramoleculares; en muchos casos se observa una relajación secundaria que es considerada como la precursora del proceso primario (relajación Johari-Goldstein). Esta tesis está enfocada en el estudio de los efectos de la presión y de la temperatura sobre la dinámica de algunos compuestos puros y mezclas binarias, los cuales forman vidrios estructurales u orientacionales. Se presenta un estudio comparativo entre dos vidrios estructurales (ternidazole y la mezcla de m-fluoroanilina con m-xileno), un cristal plástico binario (formado por neopenthyl alcohol y neopentyl glycol), y dos materiales que presentan desorden estadístico (2-adamantanona y pentacloronitrobenceno). En todos los casos se observa una relajación primaria asociada a los movimientos colectivos de las moléculas y en la mayoría de los casos se observa también relajaciones secundarias. Para cada material se analiza la dependencia de diferentes relajaciones con la temperatura y con la presión y se discute el origen de los procesos secundarios. Uno de los resultados importantes de la tesis es que en sistemas con desorden de baja dimensionalidad, pueden aparecer relajaciones secundarias que obecen a patrones similares a las encontradas en vidrios estructurales
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Books on the topic "Disordered and aperiodic systems":

1

Hertz, John. Disordered systems. Stockholm, Sweden: Royal Academy of Sciences, 1985.

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Schmid, Siegbert. Aperiodic Crystals. Dordrecht: Springer Netherlands, 2013.

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1947-, Bunde Armin, and Havlin Shlomo, eds. Fractals and disordered systems. 2nd ed. Berlin: Springer, 1996.

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Newman, Charles M. Topics in Disordered Systems. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8912-4.

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Bunde, Armin, and Shlomo Havlin, eds. Fractals and Disordered Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-51435-7.

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Bunde, Armin, and Shlomo Havlin, eds. Fractals and Disordered Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-84868-1.

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Newman, Charles M. Topics in disordered systems. Basel: Birkhäuser Verlag, 1997.

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Bunde, Armin. Fractals and Disordered Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991.

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1947-, Bunde Armin, and Havlin Shlomo, eds. Fractals and disordered systems. Berlin: Springer-Verlag, 1991.

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Bunde, Armin. Fractals and Disordered Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996.

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Book chapters on the topic "Disordered and aperiodic systems":

1

Buttazzo, Giorgio C. "Aperiodic Task Scheduling." In Hard Real-Time Computing Systems, 53–78. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4614-0676-1_3.

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Buttazzo, Giorgio. "Aperiodic Task Scheduling." In Hard Real-Time Computing Systems, 45–67. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-45410-3_3.

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Sólyom, Jenő. "Disordered Systems." In Fundamentals of the Physics of Solids, 531–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04518-9_9.

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Crisanti, Andrea, Giovanni Paladin, and Angelo Vulpiani. "Disordered Systems." In Springer Series in Solid-State Sciences, 59–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-84942-8_4.

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Wegner, Franz. "Disordered Systems." In Supermathematics and its Applications in Statistical Physics, 29–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49170-6_4.

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Stankovic, John A., Marco Spuri, Krithi Ramamritham, and Giorgio C. Buttazzo. "Aperiodic Task Scheduling." In Deadline Scheduling for Real-Time Systems, 169–96. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5535-3_8.

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Mizutani, U., M. Inukai, H. Sato, and E. S. Zijlstra. "Hume–Rothery Stabilization Mechanism in Low-Temperature Phase Zn6Sc Approximant and e/a Determination of Sc and Y in M–Sc and M–Y (M=Zn, Cd and Al) Alloy Systems." In Aperiodic Crystals, 109–15. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6431-6_15.

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Elias, Hans-Georg. "Disordered Condensed Systems." In Macromolecules, 173–90. D-69451 Weinheim, Germany: Wiley-VCH Verlag GmbH, 2014. http://dx.doi.org/10.1002/9783527627233.ch6.

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Tanaka, H., and T. Fujiwara. "Electronic Structure in Aperiodic Systems." In Structure and Properties of Aperiodic Materials, 1–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-10116-2_1.

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Ovshinsky, Stanford R. "Amorphous Materials as Interactive Systems." In Disordered Materials, 269–74. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-8745-9_52.

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Conference papers on the topic "Disordered and aperiodic systems":

1

Cazzulani, Gabriele, Emanuele Riva, Edoardo Belloni, and Francesco Braghin. "Design of Disordered Periodic Structures for Mode Localization." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3876.

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Abstract:
Periodic structures are the repetition of unit cells in space, that provide a filtering behavior for wave propagation. In particular, it is possible to tailor the geometrical, physical and elastic properties of the unit cells, in order to attenuate certain frequency bands, called band-gaps or stop-bands. Having each element characterized with the same parameters, the filtering behavior of the system can be described through the wave propagation properties of the unit cell. This is technologically impossible to obtain, therefore the Lyapunov factor is used, in order to define the mean attenuation of a quasi-periodic structure. Tailoring Gaussian unit cell properties potentially allows to extend the stop-bands width in the frequency domain. A drawback is that some unexpected resonance peaks may lie in the neighborhood of the extended regions. However, the correspondent mode-shapes are localized in a particular region of the structure, and they partially decrease the global attenuating behavior. In this paper, the aperiodicity introduced in the otherwise perfect repetition is investigated, providing an explanation for the mode-localization problem and for the stop-bands extension. Then, the proposed approach is applied to a passive quasi-periodic beam, characterized from a localized peak within a designed band-gap. The geometrical properties of its aperiodic parts are changed in order to deterministically move the localization peak in the frequency response. Numerical and experimental results are compared.
2

Klar, Paul Benjamin, Gotzon Madariaga, and Iñigo Etxebarria. "DFT of incommensurate, disordered structures:ordering phenomena in mullite." In Aperiodic 2018 ("9th Conference on Aperiodic Crystals"). Iowa State University, Digital Press, 2018. http://dx.doi.org/10.31274/aperiodic2018-180810-19.

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Wang, Shaoyun, Zhou Hu, Qian Wu, Rui Zhu, and Guoliang Huang. "Smart Patterning for Topological Pumping of Elastic Surface Waves." In ASME 2023 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/imece2023-115083.

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Abstract Topological pumping supplies a robust mechanism to steer waves across a sample without being affected by disorders and defects. For the first time, we demonstrate the pumping of elastic surface waves, achieved by a smart patterning of a surface that creates a synthetic dimension, which is explored by the wave as it is launched perpendicularly to the steering direction. Specifically, we design and fabricate an elastic medium decorated with arrays of pillar-type resonators whose eigenmodes are located below the sound cone, together with coupling bridges edged according to a specific algorithm. We establish a connection between the collective dynamics of the pillars and that of electrons in a magnetic field by deriving an accurate tight-binding model and developing a WKB-type analysis suitable for such discrete aperiodic systems with spatially slow-varying couplings. This enables us to predict topological pumping pattern, which is numerically and experimentally demonstrated by steering waves from one edge of the system to the other. Finally, the immune character of the topologically pumped surface waves against disorder and defects is evidenced. The principle of surface patterning together with the WKB-analysis could provide a powerful new platform for surface wave control and exploration of topological matter in higher dimensions.
4

Vasiljević, Jadranka, Dejan V. Timotijević, and Dragana M. Jović Savić. "Light propagation in disordered aperiodic Mathieu lattices generated with two different randomization methods." In Nonlinear Optics and its Applications 2022, edited by Anna C. Peacock, Neil G. R. Broderick, and John M. Dudley. SPIE, 2022. http://dx.doi.org/10.1117/12.2621228.

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Socolar, Joshua E. S. "Limit-periodic systems: structure formation and structure functions." In Aperiodic 2018 ("9th Conference on Aperiodic Crystals"). Iowa State University, Digital Press, 2018. http://dx.doi.org/10.31274/aperiodic2018-180810-39.

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Baz, A. "Active Control of Periodic Structures." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1734.

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Abstract Conventional passive periodic structures exhibit unique dynamic characteristics that make them act as mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called the “Pass Bands” and wave propagation is completely blocked within other frequency bands called the “Stop Bands”. In this paper, the emphasis is placed on providing the passive structures with active control capabilities in order to tune the spectral width and location of the pass and stop bands in response to the structural vibration. Apart from their unique filtering characteristics, the ability of periodic structures to transmit waves, from one location to another, within the pass bands can be greatly reduced when the ideal periodicity is disrupted resulting in the well-known phenomenon of “Localization”. In the case of passive structures, the aperiodicity (or the disorder) can result from unintentional material, geometric and manufacturing variability. However, in the case of active periodic structures the aperiodicity is intentionally introduced by proper tuning of the controllers of the individual substructure or cell. The theory governing the operation of this class of Active Periodic structures is introduced and numerical examples are presented to illustrate their tunable filtering and localization characteristics. The examples considered include periodic/aperiodic spring-mass systems controlled by piezoelectric actuators. The presented results emphasize the unique potential of the active periodic structures in controlling the wave propagation both in the spectral and spatial domains in an attempt to stop/confine the propagation of undesirable disturbances.
7

Loss, Daniel. "Mesoscopic and Disordered Systems." In Proceedings of the 24th Solvay Conference on Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304474_0002.

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Murthy, K. P. N., S. Rajasekar, and K. W. Kehr. "Diffusion in disordered systems." In Ordering disorder: Prospect and retrospect in condensed matter physics. AIP, 1992. http://dx.doi.org/10.1063/1.44727.

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9

Wan, Bo, Xi Li, Haizhao Luo, Beilei Sun, Chao Wang, Xianglan Chen, and Xuehai Zhou. "Exploiting Aperiodic Server to Improve Aperiodic Responsiveness for LET-Based Real-Time Systems." In 2017 IEEE International Symposium on Parallel and Distributed Processing with Applications and 2017 IEEE International Conference on Ubiquitous Computing and Communications (ISPA/IUCC). IEEE, 2017. http://dx.doi.org/10.1109/ispa/iucc.2017.00094.

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Bastug, Mert, Mihaly Petreczky, and Laurentiu Hetel. "Minimality of aperiodic sampled data systems." In 2017 American Control Conference (ACC). IEEE, 2017. http://dx.doi.org/10.23919/acc.2017.7963851.

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Reports on the topic "Disordered and aperiodic systems":

1

Bensen, Daniel, Michael Welge, Alfred Huebler, and Norman Packard. Characterization of Complex Systems by Aperiodic Driving Forces. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada245832.

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2

Kopidakis, Georgios. Dynamical studies of periodic and disordered systems. Office of Scientific and Technical Information (OSTI), October 1995. http://dx.doi.org/10.2172/130662.

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3

Yen, W. M. Optical studies of dynamical processes in disordered systems. Progress report. Office of Scientific and Technical Information (OSTI), May 1994. http://dx.doi.org/10.2172/10150077.

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4

Yen, W. Optical studies of dynamical processes in disordered systems. [Annual] progress report. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10124369.

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5

Yen, W. M. Optical studies of dynamical processes in disordered systems. Progress report, 1993--1994. Office of Scientific and Technical Information (OSTI), May 1994. http://dx.doi.org/10.2172/10151261.

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6

Report on DOE Proposal ''Electronic Transport in Disordered Two Dimensional Electron Systems''. Office of Scientific and Technical Information (OSTI), March 2004. http://dx.doi.org/10.2172/825011.

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