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Статті в журналах з теми "Disordered and aperiodic systems"

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Автор: Grafiati

Опубліковано: 7 липня 2024

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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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10

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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11

BEZUGLYI, S., J. KWIATKOWSKI, and K. MEDYNETS. "Aperiodic substitution systems and their Bratteli diagrams." Ergodic Theory and Dynamical Systems 29, no. 1 (February 2009): 37–72. http://dx.doi.org/10.1017/s0143385708000230.

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AbstractWe study aperiodic substitution dynamical systems arising from non-primitive substitutions. We prove that the Vershik homeomorphism φ of a stationary ordered Bratteli diagram is topologically conjugate to an aperiodic substitution system if and only if no restriction of φ to a minimal component is conjugate to an odometer. We also show that every aperiodic substitution system generated by a substitution with nesting property is conjugate to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitution system is recognizable. The classes of m-primitive substitutions and derivative substitutions associated with them are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.

12

Igloi, F. "Critical behaviour in aperiodic systems." Journal of Physics A: Mathematical and General 26, no. 15 (August 7, 1993): L703—L709. http://dx.doi.org/10.1088/0305-4470/26/15/016.

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13

Tao, Ruibao. "Extended states in aperiodic systems." Journal of Physics A: Mathematical and General 27, no. 15 (August 7, 1994): 5069–77. http://dx.doi.org/10.1088/0305-4470/27/15/008.

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14

Nagy, Endre. "Modelling of aperiodic sampling systems." IFAC Proceedings Volumes 32, no. 2 (July 1999): 3950–55. http://dx.doi.org/10.1016/s1474-6670(17)56674-4.

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15

Timotijević, Dejan V., Jadranka M. Vasiljević, and Dragana M. Jović Savić. "Numerical methods for generation and characterization of disordered aperiodic photonic lattices." Optics Express 30, no. 5 (February 17, 2022): 7210. http://dx.doi.org/10.1364/oe.447572.

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16

Meekel, Emily G., Ella M. Schmidt, Lisa J. Cameron, A. David Dharma, Hunter J. Windsor, Samuel G. Duyker, Arianna Minelli, et al. "Truchet-tile structure of a topologically aperiodic metal–organic framework." Science 379, no. 6630 (January 27, 2023): 357–61. http://dx.doi.org/10.1126/science.ade5239.

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When tiles decorated to lower their symmetry are joined together, they can form aperiodic and labyrinthine patterns. Such Truchet tilings offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. We show that the crystalline metal–organic framework [OZn 4 ][1,3-benzenedicarboxylate] 3 (TRUMOF-1) is an atomic-scale realization of a complex three-dimensional Truchet tiling. Its crystal structure consists of a periodically arranged assembly of identical zinc-containing clusters connected uniformly in a well-defined but disordered fashion to give a topologically aperiodic microporous network. We suggest that this unusual structure emerges as a consequence of geometric frustration in the chemical building units from which it is assembled.

17

Hertz, John. "Disordered Systems." Physica Scripta T10 (January 1, 1985): 1–43. http://dx.doi.org/10.1088/0031-8949/1985/t10/001.

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18

Baake, Michael, Uwe Grimm, and Carmelo Pisani. "Partition function zeros for aperiodic systems." Journal of Statistical Physics 78, no. 1-2 (January 1995): 285–97. http://dx.doi.org/10.1007/bf02183349.

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19

Medynets, Konstantin. "Cantor aperiodic systems and Bratteli diagrams." Comptes Rendus Mathematique 342, no. 1 (January 2006): 43–46. http://dx.doi.org/10.1016/j.crma.2005.10.024.

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20

Collins, J. J., Carson C. Chow, and Thomas T. Imhoff. "Aperiodic stochastic resonance in excitable systems." Physical Review E 52, no. 4 (October 1, 1995): R3321—R3324. http://dx.doi.org/10.1103/physreve.52.r3321.

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21

Takens, Floris, and Evgeny Verbitskiy. "Rényi entropies of aperiodic dynamical systems." Israel Journal of Mathematics 127, no. 1 (December 2002): 279–302. http://dx.doi.org/10.1007/bf02784535.

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22

Pavlenko, Ivan, Justyna Trojanowska, Vitalii Ivanov, Svetlana Radchenko, Jozef Husár, and Jana Mižáková. "Signal Decomposition for Monitoring Systems of Processes." Processes 12, no. 6 (June 9, 2024): 1188. http://dx.doi.org/10.3390/pr12061188.

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This article is devoted to the problem of signal decomposition into periodic and aperiodic components. According to the proposed approach, there is no need to evaluate the aperiodic component as a difference between the total signal of its periodic components. This research aims to create a general analytical approach that combines the Fourier and Maclaurin series methodologies into a single comprehensive series. As a result, analytical expressions for determining deposition coefficients were established for an aperiodic signal with a monoharmonic overlay. Recurrence relations were established to determine the coefficients of this series. These relations allow direct integrations of the obtained values of integrals to be avoided. The evaluated numerical values of the coefficients are also presented graphically and tabulated. It was proven that the values of these coefficients are universal numbers since they do not depend on the period/frequency of oscillations. The reliability of the proposed approach was confirmed by the fact that the evaluated coefficients are equal to the Fourier series coefficients in the case of a periodic signal. Also, for an aperiodic signal, these coefficients were reduced to the coefficients of the Maclaurin series. The usability of the proposed generalized analytical approach for signal decomposition is for control and monitoring systems of processes.

23

Thornton, Fabian, Michael Döllinger, Stefan Kniesburges, David Berry, Christoph Alexiou, and Anne Schützenberger. "Impact of Subharmonic and Aperiodic Laryngeal Dynamics on the Phonatory Process Analyzed in Ex Vivo Rabbit Models." Applied Sciences 9, no. 9 (May 13, 2019): 1963. http://dx.doi.org/10.3390/app9091963.

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Normal voice is characterized by periodic oscillations of the vocal folds. On the other hand, disordered voice dynamics (e.g., subharmonic and aperiodic oscillations) are often associated with voice pathologies and dysphonia. Unfortunately, not all investigations may be conducted on human subjects; hence animal laryngeal studies have been performed for many years to better understand human phonation. The rabbit larynx has been shown to be a potential model of the human larynx. Despite this fact, only a few studies regarding the phonatory parameters of rabbit larynges have been performed. Further, to the best of our knowledge, no ex vivo study has systematically investigated phonatory parameters from high-speed, audio and subglottal pressure data with irregular oscillations. To remedy this, the present study analyzes experiments with sustained phonation in 11 ex vivo rabbit larynges for 51 conditions of disordered vocal fold dynamics. (1) The results of this study support previous findings on non-disordered data, that the stronger the glottal closure insufficiency is during phonation, the worse the phonatory characteristics are; (2) aperiodic oscillations showed worse phonatory results than subharmonic oscillations; (3) in the presence of both types of irregular vibrations, the voice quality (i.e., cepstral peak prominence) of the audio and subglottal signal greatly deteriorated compared to normal/periodic vibrations. In summary, our results suggest that the presence of both types of irregular vibration have a major impact on voice quality and should be considered along with glottal closure measures in medical diagnosis and treatment.

24

El Osta, Rola, Maryline Chetto, and Hussein El Ghor. "Optimal Slack Stealing Servicing for Real-Time Energy Harvesting Systems." Computer Journal 63, no. 10 (July 7, 2020): 1537–46. http://dx.doi.org/10.1093/comjnl/bxaa047.

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Abstract We consider the problem of real-time scheduling in uniprocessor devices powered by energy harvesters. In particular, we focus on mixed sets of tasks with time and energy constraints: hard deadline periodic tasks and soft aperiodic tasks without deadlines. We present an optimal aperiodic servicing algorithm that minimizes the response times of aperiodic tasks without compromising the schedulability of hard deadline periodic tasks. The server, called Slack Stealing with energy Preserving (SSP), is designed based on a slack stealing mechanism that profits whenever possible from available spare processing time and energy. We analytically establish the optimality of SSP. Our simulation results validate our theoretical analysis.

25

Bi, Jing Cun, Qi Li, Wei Jun Yang, and Yan Fei Liu. "Feedback Controlled Adaptive Bandwidth Server Scheduling and its Application in NCS." Applied Mechanics and Materials 631-632 (September 2014): 761–65. http://dx.doi.org/10.4028/www.scientific.net/amm.631-632.761.

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As for the aperiodic tasks of node in network control systems, the FC-ABS (Feedback Controlled Adaptive Bandwidth Server) scheduling algorithm is designed. The different scheduling methods are used according to time characteristics of aperiodic tasks, and feedback scheduling is used to mitigate the effect of aperiodic tasks on periodic tasks. The simulation results show that the method is effective. Keyword: Network Control Systems; Server Scheduling; Feedback Scheduling; FC-ABS.

26

Wu, Jian Lang, Jing Kai Shi, and Yi Bin Wang. "Analysis on Scheduling Algorithms of Real-Time Hybrid Tasks." Applied Mechanics and Materials 644-650 (September 2014): 2253–57. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.2253.

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In real-time systems, periodic tasks and aperiodic tasks exist simultaneously. In a uniprocessor system, mainly there are Deferrable Server algorithm (DS) [1], Slack Stealing algorithm (SSA) [2] and their extended version for software/hardware hybrid real-time task scheduling. DS algorithm sets a high priority periodic task server to provide services for aperiodic tasks, while SSA algorithm computes tasks unoccupied time offline, and then schedule aperiodic tasks during the unoccupied period. The two algorithms are both proposed for soft real-time tasks, reducing the response time of the real-time tasks, but cannot guarantee that these aperiodic real-time tasks received can meet deadlines. In this paper, through combination of DS algorithm and EDF (Earliest Deadline First) algorithm [6], a new algorithm called DS-EDF is introduced, which can scheduling hard real-time aperiodic tasks on the DS server. This algorithm is not only suitable for uniprocessor systems, but also has the ability to extend to multiprocessor systems.

27

LAI, YING-CHENG, ZONGHUA LIU, ARJE NACHMAN, and LIQIANG ZHU. "SUPPRESSION OF JAMMING IN EXCITABLE SYSTEMS BY APERIODIC STOCHASTIC RESONANCE." International Journal of Bifurcation and Chaos 14, no. 10 (October 2004): 3519–39. http://dx.doi.org/10.1142/s0218127404011454.

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To suppress undesirable noise (jamming) associated with signals is important for many applications. Here we explore the idea of jamming suppression with realistic, aperiodic signals by stochastic resonance. In particular, we consider weak amplitude-modulated (AM), frequency-modulated (FM), and chaotic signals with strong, broad-band or narrow-band jamming, and show that aperiodic stochastic resonance occurring in an array of excitable dynamical systems can be effective to counter jamming. We provide formulas for quantitative measures characterizing the resonance. As excitability is ubiquitous in biological systems, our work suggests that aperiodic stochastic resonance may be a universal and effective mechanism for reducing noise associated with input signals for transmitting and processing information.

28

Duan, Fabing, François Chapeau-Blondeau, and Derek Abbott. "Noise-enhanced transmission efficacy of aperiodic signals in nonlinear systems." International Journal of Modern Physics: Conference Series 33 (January 2014): 1460356. http://dx.doi.org/10.1142/s2010194514603561.

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We study the aperiodic signal transmission in a static nonlinearity in the context of aperiodic stochastic resonance. The performance of a nonlinearity over that of the linear system is defined as the transmission efficacy. The theoretical and numerical results demonstrate that the noise-enhanced transmission efficacy effects occur for different signal strengths in various noise scenarios.

29

Muramatsu, Hisayoshi, and Seiichiro Katsura. "Periodic/Aperiodic Motion Control Using Periodic/Aperiodic Separation Filter." IEEE Transactions on Industrial Electronics 67, no. 9 (September 2020): 7649–58. http://dx.doi.org/10.1109/tie.2019.2942535.

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30

Li, Tao, Shihao Li, Yuanmei Wang, Yingwen Hui, and Jing Han. "Bipartite Formation Control of Nonlinear Multi-Agent Systems with Fixed and Switching Topologies under Aperiodic DoS Attacks." Electronics 13, no. 4 (February 8, 2024): 696. http://dx.doi.org/10.3390/electronics13040696.

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This paper concentrates on bipartite formation control for nonlinear leader-following multi-agent systems (MASs) with fixed and switching topologies under aperiodic Denial-of-Service (DoS) attacks. Firstly, distributed control protocols are proposed under the aperiodic DoS attacks based on fixed and switching topologies. Then, considering control gains, as well as attack frequency and attack length ratio of the aperiodic DoS attacks, using algebraic graph theory and the Lyapunov stability method, some criteria are acquired to ensure that the nonlinear leader-following MASs with either fixed or switching topologies can realize bipartite formation under aperiodic DoS attacks. Finally, numerical simulations are carried out to validate the correctness of the theoretical results.

31

Chai, Shan, Can Chang Liu, and Hong Yan Li. "A Harmonic Analysis for the Steady Analysis of Non-Linear Systems." Advanced Materials Research 433-440 (January 2012): 5536–41. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.5536.

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A numerical analysis is used to investigate the response of non-linear systems under aperiodic excitations based on the harmonic response analysis method. An idea of fine discretization is proposed to turn the aperiodic excitations into the superposition of a series of periodic excitations in a tiny time interval. The method of perturbation is employed to transform the non-linear governing equation into a series of linear differential equations. Harmonic response analysis can be applied in the solution of aperiodic steady response. The algebraic algorithm of direct steady-state analysis can improve computational efficiency. The defect that the steady-state solution can be gotten out until the free vibration attenuates is avoided. The examples show that the numerical results match well with the analytic data.

32

Haddad, T. A. S., Angsula Ghosh, and S. R. Salinas. "Tricritical behavior in deterministic aperiodic Ising systems." Physical Review E 62, no. 6 (December 1, 2000): 7773–77. http://dx.doi.org/10.1103/physreve.62.7773.

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33

Berche, P. E., B. Berche, and L. Turban. "Marginal Anisotropy in Layered Aperiodic Ising Systems." Journal de Physique I 6, no. 5 (May 1996): 621–40. http://dx.doi.org/10.1051/jp1:1996233.

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34

Mahmoud, Magdi S., and Azhar M. Memon. "Aperiodic triggering mechanisms for networked control systems." Information Sciences 296 (March 2015): 282–306. http://dx.doi.org/10.1016/j.ins.2014.11.004.

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35

Spuri, Marco, and Giorgio Buttazzo. "Scheduling aperiodic tasks in dynamic priority systems." Real-Time Systems 10, no. 2 (March 1996): 179–210. http://dx.doi.org/10.1007/bf00360340.

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36

Berche, B., P. E. Berche, M. Henkel, F. Igloi, P. Lajko, S. Morgan, and L. Turban. "Anisotropic scaling in layered aperiodic Ising systems." Journal of Physics A: Mathematical and General 28, no. 5 (March 7, 1995): L165—L171. http://dx.doi.org/10.1088/0305-4470/28/5/004.

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37

Garakhin, S. A., S. Yu Zuev, R. S. Pleshkov, V. N. Polkovnikov, N. N. Salashchenko, and N. I. Chkhalo. "Aperiodic Mirrors Based on Multilayer Beryllium Systems." Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques 13, no. 2 (March 2019): 267–71. http://dx.doi.org/10.1134/s1027451019020290.

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38

Min Wu, Baogang Xu, Weihua Cao, and Jinhua She. "Aperiodic Disturbance Rejection in Repetitive-Control Systems." IEEE Transactions on Control Systems Technology 22, no. 3 (May 2014): 1044–51. http://dx.doi.org/10.1109/tcst.2013.2272637.

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39

Lumpkin, G. R., and R. C. Ewing. "Alpha-decay damage and the aperiodic structure of pyrochlore." Proceedings, annual meeting, Electron Microscopy Society of America 46 (1988): 470–71. http://dx.doi.org/10.1017/s0424820100104418.

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Alpha-decay damage in minerals which contain U and Th involves two separate damage processes: a high energy (4-5 MeV) alpha particle with a range of 10,000 nm displaces several hundred atoms creating Frenkel defects near the end of die track; and a recoil atom (0.1 MeV) with a range of 10 nm produces several thousand atomic displacements creating “tracks” of disordered material. Pyrochlore group minerals are suitable for the study of alpha-decay damage because they contain variable amounts of U and Th such that the accumulated dose spans the transition from the crystalline to the fully aperiodic, “metamict” state.More than 50 natural pyrochlores were characterized by a number of experimental techniques. Electron microprobe analyses were obtained using a JEOL 733 Superprobe operated at 15 KV and 20 nA. X-ray diffraction studies were completed using an automated Scintag powder diffractometer.

40

Lee, Patrick A., and T. V. Ramakrishnan. "Disordered electronic systems." Reviews of Modern Physics 57, no. 2 (April 1, 1985): 287–337. http://dx.doi.org/10.1103/revmodphys.57.287.

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41

Al'tshuler, Boris L., and Patrick A. Lee. "Disordered Electronic Systems." Physics Today 41, no. 12 (December 1988): 36–44. http://dx.doi.org/10.1063/1.881139.

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42

Liu, Can Chang, Shan Chai, Lu Liu, and Hong Yan Li. "Neural Element Harmonic Response Analysis for the Aperiodic Steady Response of Non-Linear Systems." Advanced Materials Research 433-440 (January 2012): 871–75. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.871.

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A novel numerical analysis was used to investigate the response of non-linear systems undergoing aperiodic excitations based on the Neural Harmonic Response Analysis method (NNHRAM). A numerical method of neural element discretization was proposed to turn the aperiodic excitations into superposition of a series of periodic excitations. The method of perturbation was applied to transform the non-linear governing equation into a series of linear differential equations. The method of NNHRAM could be used to solve the aperiodic steady response. The algebraic algorithm of direct steady-state analysis can improve the computational efficiency. The examples showed that the numerical results match well with the analytic solution.

43

Jeon, Wonbo, Wonsop Kim, Heoncheol Lee, and Cheol-Hoon Lee. "Online Slack-Stealing Scheduling with Modified laEDF in Real-Time Systems." Electronics 8, no. 11 (November 5, 2019): 1286. http://dx.doi.org/10.3390/electronics8111286.

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In hard real-time task systems where periodic and aperiodic tasks coexist, the object of task scheduling is to reduce the response time of the aperiodic tasks while meeting the deadline of periodic tasks. Total bandwidth server (TBS) and advanced TBS (ATBS) are used in dynamic priority systems. However, these methods are not optimal solutions because they use the worst-case execution time (WCET) or the estimation value of the actual execution time of the aperiodic tasks. This paper presents an online slack-stealing algorithm called SSML that can make significant response time reducing by modification of look-ahead earliest deadline first (laEDF) algorithm as the slack computation method. While the conventional slack-stealing method has a disadvantage that the slack amount of each frame must be calculated in advance, SSML calculates the slack when aperiodic tasks arrive. Our simulation results show that SSML outperforms the existing TBS based algorithms when the periodic task utilization is higher than 60%. Compared to ATBS with virtual release advancing (VRA), the proposed algorithm can reduce the response time up to about 75%. The performance advantage becomes much larger as the utilization increases. Moreover, it shows a small performance variation of response time for various task environments.

44

Grimm, Uwe. "Aperiodic crystals and beyond." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 71, no. 3 (May 29, 2015): 258–74. http://dx.doi.org/10.1107/s2052520615008409.

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Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order, encompassing both periodic and aperiodic crystals. The current definition of crystals rests on their essentially point-like diffraction. Considering a number of recently investigated toy systems, with particular emphasis on non-crystalline ordered structures, the limits of the current definition are explored.

45

Stankiewicz, Jacek Maciej, and Agnieszka Choroszucho. "Efficiency of the Wireless Power Transfer System with Planar Coils in the Periodic and Aperiodic Systems." Energies 15, no. 1 (December 24, 2021): 115. http://dx.doi.org/10.3390/en15010115.

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This article presents the results of the proposed numerical and analytical analysis of the Wireless Power Transfer System (WPT). The system consists of a transmitting surface and a receiving surface, where each of them is composed of planar spiral coils. Two WPT systems were analysed (periodic and aperiodic) considering two types of coils (circular and square). In the aperiodic system, the adjacent coils were wound in the opposite direction. The influence of the type of coils, the winding direction, the number of turns, and the distance between the coils on the efficiency of the WPT system was compared. In periodic models, higher efficiency was obtained with circular rather than square coils. The results obtained with both proposed methods were consistent, which confirmed the correctness of the adopted assumptions. In aperiodic models, for a smaller radius of the coil, the efficiency of the system was higher in the square coil models than in the circular coil models. On the other hand, with a larger radius of the coil, the efficiency of the system was comparable regardless of the coil type. When comparing both systems (periodic and aperiodic), for both circular and square coils, aperiodic models show higher efficiency values (the difference is even 57%). The proposed system can be used for simultaneous charging of many sensors (located in, e.g., walls, floors).

46

Chen, Kai, Matthew Weiner, Mengyao Li, Xiang Ni, Andrea Alù, and Alexander B. Khanikaev. "Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries." Proceedings of the National Academy of Sciences 118, no. 34 (August 19, 2021): e2100691118. http://dx.doi.org/10.1073/pnas.2100691118.

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The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA—the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.

47

Pyragas, K. "Stabilization of Unstable Periodic and Aperiodic Orbits of Chaotic Systems by Self-Controlling Feedback." Zeitschrift für Naturforschung A 48, no. 5-6 (June 1, 1993): 629–32. http://dx.doi.org/10.1515/zna-1993-5-605.

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Abstract The methods of stabilization of unstable periodic and aperiodic orbits of a strange attractor with the help of a small time-continuous perturbation are discussed. The perturbation is applied to the system in such a way that the desired periopdic or aperiodic orbits remain unperturbed. An experimental application of the methods can be carried out by a purely analogous technique without use of any computer.

48

Coates, Sam, and Ryuji Tamura. "High Dimensional Approach to Antiferromagnetic Aperiodic Spin Systems." MATERIALS TRANSACTIONS 62, no. 3 (March 1, 2021): 307–11. http://dx.doi.org/10.2320/matertrans.mt-mb2020010.

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49

FUSTER, A., and J. M. GUILLEN. "New modelling technique for aperiodic-sampling linear systems." International Journal of Control 45, no. 3 (March 1987): 951–68. http://dx.doi.org/10.1080/00207178708933780.

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50

Kao, Chung-Yao, and Hisaya Fujioka. "On Stability of Systems With Aperiodic Sampling Devices." IEEE Transactions on Automatic Control 58, no. 8 (August 2013): 2085–90. http://dx.doi.org/10.1109/tac.2013.2246491.

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