Journal articles: 'One dimensional quasi periodic systems'

1

Geng, Jiansheng, Jiangong You, and Zhiyan Zhao. "Localization in One-dimensional Quasi-periodic Nonlinear Systems." Geometric and Functional Analysis 24, no. 1 (January 28, 2014): 116–58. http://dx.doi.org/10.1007/s00039-014-0256-9.

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Basu, C., A. Mookerjee, A. K. Sen, and P. K. Thakur. "Metal-insulator transition in one-dimensional quasi-periodic systems." Journal of Physics: Condensed Matter 3, no. 32 (August 12, 1991): 6041–53. http://dx.doi.org/10.1088/0953-8984/3/32/011.

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Ma, Hong-ru, and Chien-Hua Tsai. "On the energy spectra of one-dimensional quasi-periodic systems." Journal of Physics C: Solid State Physics 21, no. 23 (August 20, 1988): 4311–24. http://dx.doi.org/10.1088/0022-3719/21/23/014.

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Cohen, J., and Y. Avishai. "Scattering of edge states in quasi-one-dimensional periodic systems." Physica B: Condensed Matter 202, no. 1-2 (September 1994): 91–103. http://dx.doi.org/10.1016/0921-4526(94)00149-9.

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McDermott, Danielle, Cynthia J. Olson Reichhardt, and Charles Reichhardt. "Stripe systems with competing interactions on quasi-one dimensional periodic substrates." Soft Matter 10, no. 33 (July 4, 2014): 6332. http://dx.doi.org/10.1039/c4sm01341g.

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Pérez-Maldonado, M. T., G. Monsivais, V. Velasco, R. Rodríguez-Ramos, and C. Stern. "Electronic spectra of one-dimensional nano-quasi-periodic systems under bias." Superlattices and Microstructures 47, no. 6 (June 2010): 661–75. http://dx.doi.org/10.1016/j.spmi.2010.04.005.

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GENTILE, GUIDO. "Quasi-periodic motions in strongly dissipative forced systems." Ergodic Theory and Dynamical Systems 30, no. 5 (August 3, 2009): 1457–69. http://dx.doi.org/10.1017/s0143385709000583.

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AbstractWe consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing.

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Otto, P. "Calculation of the polarizability and hyperpolarizabilities of periodic quasi-one-dimensional systems." Physical Review B 45, no. 19 (May 15, 1992): 10876–85. http://dx.doi.org/10.1103/physrevb.45.10876.

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Evangelou, S. N., and E. N. Economou. "Spectral density correlations and eigenfunction fluctuations in one-dimensional quasi-periodic systems." Journal of Physics: Condensed Matter 3, no. 29 (July 22, 1991): 5499–513. http://dx.doi.org/10.1088/0953-8984/3/29/005.

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CORSI, LIVIA, and GUIDO GENTILE. "Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems." Ergodic Theory and Dynamical Systems 35, no. 4 (February 26, 2014): 1079–140. http://dx.doi.org/10.1017/etds.2013.92.

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AbstractWe consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the perturbation. We assume that the unperturbed system is locally integrable and anisochronous, and that the frequency vector of the perturbation satisfies the Bryuno condition. Existence of resonant solutions is related to the zeros of a suitable function, called the Melnikov function—by analogy with the periodic case. We show that, if the Melnikov function has a zero of odd order and under some further condition on the sign of the perturbation parameter, then there exists at least one resonant solution which continues an unperturbed solution. If the Melnikov function is identically zero then one can push perturbation theory up to the order where a counterpart of Melnikov function appears and does not vanish identically: if such a function has a zero of odd order and a suitable positiveness condition is met, again the same persistence result is obtained. If the system is Hamiltonian, then the procedure can be indefinitely iterated and no positiveness condition must be required: as a byproduct, the result follows that at least one resonant quasi-periodic solution always exists with no assumption on the perturbation. Such a solution can be interpreted as a (parabolic) lower-dimensional torus.

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11

Varga, I. "Evidence for Power Law Localization At the Metal-Insulator Transition in One-Dimensional Quasi-Periodic Systems." Europhysics Letters (EPL) 20, no. 6 (November 15, 1992): 529–33. http://dx.doi.org/10.1209/0295-5075/20/6/010.

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12

Timorian, S., G. Petrone, S. De Rosa, F. Franco, M. Ouisse, and N. Bouhaddi. "Spectral analysis and structural response of periodic and quasi-periodic beams." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 23-24 (November 28, 2019): 7498–512. http://dx.doi.org/10.1177/0954406219888948.

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Periodic structures have found a big interest in engineering applications because they introduce frequency band effects, due to the impedance mismatch generated by periodic discontinuities in the geometry, material, or boundary conditions, which can improve the vibroacoustic performances. However, the presence of defects or irregularity in the structure leads to a partial lost of regular periodicity (called quasi-periodic structure) that can have a noticeable impact on the vibrational and/or acoustic behavior of the elastic structure. The irregularity can be tailored to have impact on dynamical behavior. In the present paper, numerical studies on the vibrational analysis of one-dimensional finite, periodic, and quasi-periodic structures are presented. The contents deal with the finite element models of beams focused on the spectral analysis and the damped forced responses. The quasi-periodicity is defined by invoking the Fibonacci sequence for building the assigned variations (geometry and material) along the span of finite element model. Similarly, the same span is used as a super unit cell with Floquet–Bloch conditions waves for analyzing the infinite periodic systems. Considering both longitudinal and flexural elastic waves, the frequency ranges corresponding to band gaps are investigated. The wave characteristics in quasi-periodic beams, present some elements of novelty and could be considered for designing structural filters and controlling the properties of elastic waves.

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13

Bouazzi, Y., and M. Kanzari. "Comparative study of optical properties of the one-dimensional multilayer Period-Doubling and Thue-Morse quasi-periodic photonic crystals." Advanced Electromagnetics 1, no. 3 (October 14, 2012): 1. http://dx.doi.org/10.7716/aem.v1i3.49.

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The last decades have witnessed the growing interest in the use of photonic crystal as a new material that can be used to control electromagnetic wave. Actually, not only the periodic structures but also the quasi-periodic systems have become significant structures of photonic crystals. This work deals with optical properties of dielectric Thue-Morse multilayer and Period-Doubling multilayer. We use the so-called Transfer Matrix Method (TMM) to determine the transmission spectra of the structures. Based on the representation of the transmittance spectra in the visible range a comparative analysis depending on the iteration number, number of layers and incidence angle is presented.

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14

Teplinsky, Yu. "ON APPROXIMATION OF ALMOST-PERIODIC SOLUTIONS FOR A NON-LINEAR COUNTABLE SYSTEM OF DIFFERENTIAL EQUATIONS BY QUASI-PERIODIC SOLUTIONS FOR SOME LINEAR SYSTEM." Bukovinian Mathematical Journal 9, no. 2 (2021): 111–23. http://dx.doi.org/10.31861/bmj2021.02.09.

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It is well-known that many applied problems in diﬀerent areas of mathematics, physics, and technology require research into questions of existence of oscillating solutions for diﬀerential systems, which are their mathematical models. This is especially true for the problems of celestial mechanics. Novadays, by oscillatory motions in dynamical systems, according to V. V. Nemitsky, we call their recurrent motions. As it is known from Birkhoﬀ theorem, trajectories of such motions contain minimal compact sets of dynamical systems. The class of recurrent motions contains, in particular, both quasi-periodic and almost-periodic motions. There are renowned fundamental theorems by Amerio and Favard related to existence of almost-periodic solutions for linear and non-linear systems. It is also of interest to research the behavior of a dynamical system’s motions in a neighborhood of a recurrent trajectory. It became understood later, that the question of existence of such trajectories is closely related to existence of invariant tori in such systems, and the method of Green-Samoilenko function is useful for constructing such tori. Here we consider a non-linear system of diﬀerential equations deﬁned on Cartesian product of the inﬁnite-dimensional torus T∞ and the space of bounded number sequences m. The problem is to ﬁnd suﬃcient conditions for the given system of equations to possess a family of almost-periodic in the sense of Bohr solutions, dependent on the parameter ψ ∈ T∞, every one of which can be approximated by a quasi-periodic solution of some linear system of equations deﬁned on a ﬁnite-dimensional torus.

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15

JING, ZHUJUN, and JIANPING YANG. "COMPLEX DYNAMICS IN PENDULUM EQUATION WITH PARAMETRIC AND EXTERNAL EXCITATIONS II." International Journal of Bifurcation and Chaos 16, no. 10 (October 2006): 3053–78. http://dx.doi.org/10.1142/s0218127406016653.

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This paper (II) is a continuation of "Complex dynamics in pendulum equation with parametric and external excitations (I)." By applying second-order averaging method and Melnikov's method, we obtain the criterion of existence of chaos in an averaged system under quasi-periodic perturbation for Ω = nω + ∊ν, n = 1, 2, 4 and cannot prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for Ω = nω + ∊ν, n = 3, 5–15 by Melnikov's method, where ν is not rational to ω. However, we show the occurrence of chaos in the averaged and original systems under quasi-periodic perturbation for Ω = nω + ∊ν, n = 3, 5 by numerical simulation. The numerical simulations, include the bifurcation diagram of fixed points, bifurcation diagrams in three- and two-dimensional spaces, homoclinic bifurcation surface, maximum Lyapunov exponent, phase portraits, Poincaré map, are plotted to illustrate theoretical analysis, and to expose the complex dynamical behaviors, including period-3 orbits in different chaotic regions, interleaving occurrence of chaotic behaviors and quasi-periodic behaviors, a different kind of interior crisis, jumping behavior of quasi-periodic sets, different nice quasi-periodic attractors, nonchaotic attractors and chaotic attractors, coexistence of three quasi-periodic sets, onset of chaos which occurs more than once for a given external frequency or amplitudes, and quasi-periodic route to chaos. We do not find the period-doubling cascade. The dynamical behaviors under quasi-periodic perturbation are different from that of periodic perturbation.

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Gentile, Guido, Alessandro Mazzoccoli, and Faenia Vaia. "Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension." Communications in Contemporary Mathematics 21, no. 07 (October 10, 2019): 1850064. http://dx.doi.org/10.1142/s0219199718500645.

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We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term, in the case of large dissipation. We assume the system to be conservative in the absence of dissipation, so that the forcing term is — up to the sign — the gradient of a potential energy, and both the mass and damping matrices to be symmetric and positive definite. Further, we assume a non-degeneracy condition on the forcing term, essentially that the time-average of the potential energy has a strict local minimum. On the contrary, no condition is assumed on the forcing frequency; in particular, we do not require any Diophantine condition. We prove that, under the assumptions above, a response solution always exists provided the dissipation is strong enough. This extends results previously available in the literature in the one-dimensional case.

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17

Murzin, Serguei P. "Formation of ZnO/CuO Heterostructures Based on Quasi-One-Dimensional Nanomaterials." Applied Sciences 13, no. 1 (December 30, 2022): 488. http://dx.doi.org/10.3390/app13010488.

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Nanostructured metal oxides are of great interest both for advanced research and for a wide range of applications that contribute to the increasing demands of electronics, photonics, catalysis, sensorics, and other high-tech industries and are being actively researched and developed. One-dimensional nanocrystal arrays of copper and zinc oxides have become prominent in optoelectronic devices and energy conversion systems. However, although desirable improved properties have been demonstrated, the morphology of materials containing copper and zinc oxide nanowires is extremely sensitive to synthesis conditions and difficult to control. Studies focused on the morphology control of such quasi-one-dimensional materials are not numerous, so the consideration of this issue is still relevant. The characteristics of devices based on such oxide materials can be improved by taking advantage of nanoheterojunctions. A special feature is the possibility of forming a polycrystalline heterojunction in a system of semiconductors belonging to different crystalline syngonies. Currently, much attention is devoted to developing reliable methods of obtaining such nanomaterials, including those, based on processes exploiting novel physical effects. Possibilities of synthesis by pulse-periodic laser irradiation of arrays of quasi-one-dimensional ZnO nanostructures with varying micromorphology on metallic substrates, as well as the creation of ZnO/CuO heterostructures based on ZnO nanowires, were considered. The main distinguishing feature of this approach was the use of laser-induced vibrations to intensify diffusion processes in the solid phase of metallic materials as compared to the simple effects of laser beam heating. Expanding the area of application of the advanced method of creating oxide heterostructures requires a detailed and comprehensive study of new possibilities used to form structures with improved physical properties.

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18

MOROZOV, ALBERT D. "ON THE STRUCTURE OF RESONANCE ZONES AND CHAOS IN NONLINEAR PARAMETRIC SYSTEMS." International Journal of Bifurcation and Chaos 04, no. 02 (April 1994): 401–10. http://dx.doi.org/10.1142/s0218127494000265.

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Periodic-in-time systems close to two-dimensional nonlinear Hamiltonian ones are analyzed in the case when a perturbation contains nonlinear parametric terms and it is nonconservative. The existence of new regimes in the resonance zone, regular two-frequency regimes and non-regular “quasi-attractors,” is determined. The problem of transition from a resonance case to a nonresonance one for a changing detuning is solved on the basis of the analysis of shortened auto-oscillatory systems that determine the topology of the resonance zones. The theoretical results of this investigation are illustrated on a computer for a specific example. In the quasi-conservative case the numerical and analytical results are in good agreement.

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19

Martinez, A. "Non-linear optical properties of quasi-one-dimensional periodic systems: consistent theoretical treatment within the crystal orbital method." Chemical Physics Letters 327, no. 5-6 (September 2000): 389–96. http://dx.doi.org/10.1016/s0009-2614(00)00871-x.

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20

Dushkin, Volodymyr, and Stanislav Zhuchenko. "NUMERICAL MODELLING OF ELECTROMAGNETIC WAVE SCATTERING ON GRATINGS WITH ONE-DIMENSIONAL QUASI-FRACTAL PERIOD STRUCTURE." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1 (August 1, 2023): 110–15. http://dx.doi.org/10.20998/2222-0631.2023.01.16.

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Numerical modelling of the properties of E-polarised and H-polarised waves scattered on periodic screened quasi-fractal gratings is carried out. The location of the band system at each period is determined by the principle of constructing a generalized symmetric Cantor set at a certain step of the algorithm. A mathematical model of the problems based on systems of boundary singular integral equations of the first kind was used in the study. These systems of equations were obtained using the method of parametric representations of singular and hypersingular integral operators. The systems of singular integral equations were solved numerically using the computational schemes of the method of discrete singularities. The solutions of these equations are used to obtain the main characteristics of the electric and magnetic fields. This experiment proved the possibility of using the MDS computational scheme to analyse systems containing 8 – 16 bands at different distances from each other. Graphs of the dependence of harmonic amplitudes on the wavenumber, point plots of absolute values of all non-zero harmonics at resonant wavenumber values, and maps of electric and magnetic field components in the region above the grating were obtained. It is confirmed that the overall field structure in the case of normal incidence is significantly influenced by all harmonics with absolute numbers from 0 to 50. The harmonics had a large number of resonances that were observed at different values of the wavenumber. This led to a complex structure of the isolines of absolute values of the scattered electric and magnetic field amplitudes in the region above the structure, and a significant difference in amplitude values with small changes in coordinates. In the future, it is planned to carry out computer simulations for imperfectly conducting structures and compare the results with the numerical results for the ideal case considered in this paper. The proposed structure may be of interest for the design of multimode broadband antennas.

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Martinez, A., P. Otto, and J. Ladik. "Coupled-perturbed Hartree-Fock theory for quasi-one-dimensional periodic systems: Calculation of static and dynamic nonlinear optical properties of model systems." International Journal of Quantum Chemistry 94, no. 5 (2003): 251–68. http://dx.doi.org/10.1002/qua.10750.

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Дзюба, Ж. В., and В. Н. Удодов. "Критический индекс восприимчивости 1D-изинговского ферромагнетика, замкнутого в кольцо." Физика твердого тела 60, no. 7 (2018): 1318. http://dx.doi.org/10.21883/ftt.2018.07.46115.238.

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AbstractUsing the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН_3)_3NH] · FeCl_3 · 2H_2O and with the magnitude of the exchange interaction J/k _B = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown that values of the susceptibility exponent for the one-dimensional Ising model with periodic boundary conditions are considerably less than the known values of the exponents for three-dimensional systems. The critical susceptibility exponent strongly depends on energy parameters; namely, it decreases with an increase in them.

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Liu, Licai, Chuanhong Du, Lixiu Liang, and Xiefu Zhang. "A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit." Entropy 21, no. 10 (October 22, 2019): 1026. http://dx.doi.org/10.3390/e21101026.

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As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.

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Li, He, Ji Dan Wen, Jie Zhang, and Bang Chun Wen. "Research on Characteristics of Chaotic Motion Based on the Wavelet Ridge." Advanced Engineering Forum 2-3 (December 2011): 765–68. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.765.

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The wavelet ridge method to analyze chaos is described, and the wavelet ridge method is applied to analysis of the nonlinear vibration of blooming mill which exists chaos. The results show that the wavelet ridge can tell the periodic motion, quasi-periodic motion or chaotic motion by analysising the time history of one component of the system state variables. Compared to the other researching methods, such as the Poincaré sections or the phase diagram, we can find the wavelet ridge is more suitable to high dimensional chaotic systems and the clutter of instantaneous frequency which is represented by the wavelet ridge can distinguish between strong and week chaos motion. And it can provide more accurate partial details and features of chaotic motion.

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25

MARTÍNEZ, GENARO J., ANDREW ADAMATZKY, CHRISTOPHER R. STEPHENS, and ALEJANDRO F. HOEFLICH. "CELLULAR AUTOMATON SUPERCOLLIDERS." International Journal of Modern Physics C 22, no. 04 (April 2011): 419–39. http://dx.doi.org/10.1142/s0129183111016348.

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Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular automaton analogous of localizations or quasi-local collective excitations traveling in a spatially extended nonlinear medium. They can be considered as binary strings or symbols traveling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyze what types of interaction occur between gliders traveling on a cellular automaton "cyclotron" and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in nonlinear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analyzed via implementation of cyclic tag systems.

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Baesens, C., and R. S. Mackay. "Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family." Journal of Fluid Mechanics 241 (August 1992): 333–47. http://dx.doi.org/10.1017/s0022112092002064.

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Numerical work of many people on the bifurcations of uniformly travelling water waves (two-dimensional irrotational gravity waves on inviscid fluid of infinite depth) suggests that uniformly travelling water waves have a reversible Hamiltonian formulation, where the role of time is played by horizontal position in the wave frame. In this paper such a formulation is presented. Based on this viewpoint, some insights are given into bifurcations from Stokes’ family of periodic waves. It is demonstrated numerically that there is a ‘fold point’ at amplitude A0 ≈ 0.40222. Assuming non-degeneracy of the fold and existence of an associated centre manifold, this explains why a sequence of p/q-bifurcations occurs on one side of A0, with 0 < p/q [les ] ½, in the order of the rationals. Secondly, it explains why no symmetry-breaking bifurcation is observed at A0, contrary to the expectations of some. Thirdly, it explains why the bifurcation tree for periodic uniformly travelling waves looks so much like that for the area-preserving Hénon map. Fourthly, it leads to predictions of a rich variety of spatially quasi-periodic, heteroclinic and chaotic waves.

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MAZROUI, M'HAMMED, and YAHIA BOUGHALEB. "SURFACE DIFFUSION IN SYSTEMS OF INTERACTING BROWNIAN PARTICLES." International Journal of Modern Physics B 15, no. 16 (June 30, 2001): 2193–247. http://dx.doi.org/10.1142/s0217979201001649.

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The paper reviews recent results on diffusive phenomena in two-dimensional periodic potential. Specifically, static and dynamic properties are investigated by calculating different correlation functions. Diffusion process is first studied for one-dimensional system by using the Fokker–Planck equation which is solved numerically by the matrix continued fraction method in the case of bistable potential. The transition from hopping to liquid-like diffusion induced by variation of some parameters is discussed. This study will therefore serve to demonstrate the influence of this form of potential. Further, an analytical approximation for the dc-conductivity is derived for a wide damping range in the framework of the Linear Response Theory. On the basis of this expression, calculations of the ac conductivity of two-dimensional system with Frenkel–Kontorova pair interaction in the intermediate friction regime is performed by using the continued fraction expansion method. The dc-conductivity expression is used to determine the rest of the development. By varying the density of mobile ions we discuss commensurability effects. To get information about the diffusion mechanism, the full width at half maximum λω(q), of the quasi-elastic line of the dynamical structure factor S(q,ω) is computed. The calculations are extended up to large values of q covering several Brillouin zones. The analysis of λω(q) with different parameters shows that the most probable diffusion process in good two-dimensional superionic conductors consists of a competition between a back correlated hopping in one direction and forward correlated hopping in addition to liquid-like motions in the other direction.

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Li, Jibin, Fengjuan Chen, and A. S. Tchakoutio-Nguetcho. "Bifurcations and Exact Solutions in a Model of Hydrogen-Bonded-Chains." International Journal of Bifurcation and Chaos 25, no. 04 (April 2015): 1550062. http://dx.doi.org/10.1142/s0218127415500625.

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A model of dynamics of protons in hydrogen-bonded quasi-one-dimensional networks was derived, which is a singular system of the second kind with three parameters and two singular straight lines. In this paper, we use the method of dynamical systems to discuss the bifurcations of phase portraits of the vector fields defined by the singular system. Corresponding to the phase orbits of the system in different parameter conditions, we compute all possible exact parametric representations of solutions. It is shown that in given parameter conditions, there exist solitary wave solutions, kink wave solutions and periodic wave solutions. The mentioned system has no peakon solution.

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BRAUN, HANS-BENJAMIN, and DANIEL LOSS. "CHIRALITY CORRELATION OF SPIN SOLITONS: BLOCH WALLS, SPIN-½ SOLITONS AND HOLES IN A 2D ANTIFERROMAGNETIC BACKGROUND." International Journal of Modern Physics B 10, no. 02 (January 20, 1996): 219–34. http://dx.doi.org/10.1142/s021797929600009x.

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We consider the quantum dynamics of spin solitons in a variety of low-dimensional magnetic systems in the semiclassical and the extreme quantum limit. Introducing the concept of chirality of the soliton we derive the dispersion of spin solitons moving through a periodic pinning potential and show that for half-odd integer spin the topological part of the Berry phase induces a halving of the Brillouin zone as well as chirality correlations between subsequent band minima. We demonstrate that these chirality and spin parity effects are universal by considering quasi-one-dimensional ferromagnets and antiferromagnets with local anisotropies and large spins, as well as spin-½ ferromagnetic and antiferromagnetic Heisenberg chains in the Ising limit. For large spin systems, the tunneling rate between states of opposite chiralities is derived and shown to provide a novel scenario for macroscopic quantum phenomena. The results are extended to solitons moving as holes in a two-dimensional antiferromagnetic background, leading to a hole spectrum which is in remarkable agreement with recent ARPES measurements on high-Tc compounds.

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BRAUN, OLEG M., IRINA I. ZELENSKAYA, and YURI S. KIVSHAR. "DIFFUSION IN THE FRENKEL–KONTOROVA MODEL WITH ANHARMONIC INTERATOMIC INTERACTIONS." International Journal of Modern Physics B 08, no. 17 (July 30, 1994): 2353–89. http://dx.doi.org/10.1142/s0217979294000968.

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Low-temperature diffusion and transport properties of the generalized Frenkel–Kontorova model are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weaklyinteracting quasiparticles (kinks). The model takes into account realistic (anharmonic) interaction of particles subjected into a periodic substrate potential, and such a generalization leads to a series of novel effects which we expect are related to the experimentally-observed phenomena in several quasi-one-dimensional systems. Analysing the concentration dependences in the framework of the kink phenomenology, we use the renormalization procedure when the atomic structure with a complex unit cell is treated as (more simple) periodic structure of kinks. Using phenomenology of the ideal kink gas, the low-temperature states of the chain are described as those consisting of "residual" kinks supplemented by thermally-excited kinks. This approach allows us to describe the ground states of the chain as a hierarchy of "melted" kink lattices. Dynamical and diffusion properties of the system are then described in terms of the kink dynamics and kink diffusion. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. Susceptibility, conductivity, self-diffusion and chemical diffusion coefficients of the chain are calculated as functions of the kink diffusion coefficient. In this way, we qualitatively analyze, for the first time to our knowledge, dependence of the different diffusion coefficients on the concentration of atoms in the chain. The results are applied to describe peculiarities in conductivity and diffusion coefficients of quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces which were earlier investigated experimentally.

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Kashinath, Karthik, Iain C. Waugh, and Matthew P. Juniper. "Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos." Journal of Fluid Mechanics 761 (November 25, 2014): 399–430. http://dx.doi.org/10.1017/jfm.2014.601.

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AbstractThermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized two-dimensional premixed flame in a duct via numerical simulations of a $G$-equation flame coupled with duct acoustics. We examine the bifurcations and routes to chaos for three control parameters: (i) the flame position in the duct, (ii) the length of the duct and (iii) the mean flow velocity. We observe period-1, period-2, quasi-periodic and chaotic oscillations. For certain parameter ranges, more than one stable state exists, so mode switching is possible. At intermediate times, the system is attracted to and repelled from unstable states, which are also identified. Two routes to chaos are established for this system: the period-doubling route and the Ruelle–Takens–Newhouse route. These are corroborated by analyses of the power spectra of the acoustic velocity. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch-off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and aperiodic oscillations. This study complements recent experiments by providing a reduced-order model of a system with approximately 5000 degrees of freedom that captures much of the elaborate nonlinear behaviour of ducted premixed flames observed in the laboratory.

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Zhang, Tingting, Hans True, and Huanyun Dai. "The Lateral Dynamics of a Nonsmooth Railway Wheelset Model." International Journal of Bifurcation and Chaos 28, no. 08 (July 2018): 1850095. http://dx.doi.org/10.1142/s0218127418500955.

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In this paper, we investigate the lateral dynamics of a railway wheelset suspended under a moving car with linear springs and dry friction dampers. Both theoretical and numerical methods are used to complement each other. The car runs on an ideal, straight and perfect track with a constant speed. A nonlinear relation between the creepages and the creep forces is used in this paper. The nonsmoothness of this model is due to the dry friction dampers. The speed is selected as the bifurcation parameter. The one-dimensional bifurcation diagram, which gives a general view of the dynamics of the system, is presented. Both symmetric and asymmetric periodic motions, quasi-periodic motions and chaotic motions are found. In addition to bifurcations that can exist in both smooth and nonsmooth systems, a kind of sliding bifurcations that are unique to nonsmooth systems is found. Bifurcation diagrams, phase portraits, Poincaré sections and Lyapunov exponents are presented to ensure that no contradictory results are given. The influence of the conicity of the wheel tread on the Hopf bifurcation type is examined.

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Zolfaghari-Nejad, Maryam, Hossein Hassanpoor, and Mostafa Charmi. "Numerical Analysis of a Novel 3D Chaotic System with Period-Subtracting Structures." International Journal of Bifurcation and Chaos 31, no. 11 (September 2, 2021): 2150169. http://dx.doi.org/10.1142/s0218127421501698.

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In this work, we present a novel three-dimensional chaotic system with only two cubic nonlinear terms. Dynamical behavior of the system reveals a period-subtracting bifurcation structure containing all [Formula: see text]th-order ([Formula: see text]) periods that are found in the dynamical evolution of the novel system concerning different values of parameters. The new system could be evolved into different states such as point attractor, limit cycle, strange attractor and butterfly strange attractor by changing the parameters. Also, the system is multistable, which implies another feature of a chaotic system known as the coexistence of numerous spiral attractors with one limit cycle under different initial values. Furthermore, bifurcation analysis reveals interesting phenomena such as period-doubling route to chaos, antimonotonicity, periodic solutions, and quasi-periodic motion. In the meantime, the existence of periodic solutions is confirmed via constructed Poincaré return maps. In addition, by studying the influence of system parameters on complexity, it is confirmed that the chaotic system has high spectral entropy. Numerical analysis indicates that the system has a wide variety of strong dynamics. Finally, a message coding application of the proposed system is developed based on periodic solutions, which indicates the importance of studying periodic solutions in dynamical systems.

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Koley, Arpita, Santanu K. Maiti, Laura M. Pérez, Judith Helena Ojeda Silva, and David Laroze. "Possible Routes to Obtain Enhanced Magnetoresistance in a Driven Quantum Heterostructure with a Quasi-Periodic Spacer." Micromachines 12, no. 9 (August 27, 2021): 1021. http://dx.doi.org/10.3390/mi12091021.

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In this work, we perform a numerical study of magnetoresistance in a one-dimensional quantum heterostructure, where the change in electrical resistance is measured between parallel and antiparallel configurations of magnetic layers. This layered structure also incorporates a non-magnetic spacer, subjected to quasi-periodic potentials, which is centrally clamped between two ferromagnetic layers. The efficiency of the magnetoresistance is further tuned by injecting unpolarized light on top of the two sided magnetic layers. Modulating the characteristic properties of different layers, the value of magnetoresistance can be enhanced significantly. The site energies of the spacer is modified through the well-known Aubry–André and Harper (AAH) potential, and the hopping parameter of magnetic layers is renormalized due to light irradiation. We describe the Hamiltonian of the layered structure within a tight-binding (TB) framework and investigate the transport properties through this nanojunction following Green’s function formalism. The Floquet–Bloch (FB) anstaz within the minimal coupling scheme is introduced to incorporate the effect of light irradiation in TB Hamiltonian. Several interesting features of magnetotransport properties are represented considering the interplay between cosine modulated site energies of the central region and the hopping integral of the magnetic regions that are subjected to light irradiation. Finally, the effect of temperature on magnetoresistance is also investigated to make the model more realistic and suitable for device designing. Our analysis is purely a numerical one, and it leads to some fundamental prescriptions of obtaining enhanced magnetoresistance in multilayered systems.

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Walgraef, Daniel. "Laser-Induced Deformation Patterns in Thin Films and Surfaces." Journal of Engineering Materials and Technology 121, no. 2 (April 1, 1999): 182–88. http://dx.doi.org/10.1115/1.2812365.

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The coupling between surface deformation and defect motion may be at the origin of deformation patterns in thin films under laser irradiation. We analyze the dynamics of laser-induced vacancy densities and deformation fields and show how it triggers deformational instabilities, in the case of uniform and focused laser irradiation. Pattern selection analysis is performed, through linear, nonlinear, and numerical methods. In irradiation with extended beams, we show that, according to the relative importance of nonlinearities arising from the defect or from the bending dynamics, square, hexagonal or even quasi-periodic patterns are selected. It appears, furthermore, that one-dimensional gratings are always unstable in isotropic systems. In irradiation with focused laser beams, rose deformation patterns, with petal number increasing with laser intensity, naturally arise in this model, in qualitative agreement with experimental observations. These results claim for more systematic and quantitative experimental investigations of deformational pattern formation under laser irradiation.

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Briggeman, Megan, Jianan Li, Mengchen Huang, Hyungwoo Lee, Jung-Woo Lee, Kitae Eom, Chang-Beom Eom, Patrick Irvin, and Jeremy Levy. "Engineered spin-orbit interactions in LaAlO3/SrTiO3-based 1D serpentine electron waveguides." Science Advances 6, no. 48 (November 2020): eaba6337. http://dx.doi.org/10.1126/sciadv.aba6337.

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The quest to understand, design, and synthesize new forms of quantum matter guides much of contemporary research in condensed matter physics. One-dimensional (1D) electronic systems form the basis for some of the most interesting and exotic phases of quantum matter. Here, we describe a family of quasi-1D nanostructures, based on LaAlO3/SrTiO3 electron waveguides, in which a sinusoidal transverse spatial modulation is imposed. These devices display unique dispersive features in the subband spectra, namely, a sizeable shift (∼7 T) in the spin-dependent subband minima, and fractional conductance plateaus. The first property can be understood as an engineered spin-orbit interaction associated with the periodic acceleration of electrons as they undulate through the nanowire (ballistically), while the second property signifies the presence of enhanced electron-electron scattering in this system. The ability to engineer these interactions in quantum wires contributes to the tool set of a 1D solid-state quantum simulation platform.

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Zhong, Qi, Lars Melchior, Jichang Peng, Qiushi Huang, Zhanshan Wang, and Tim Salditt. "Reconstruction of the near-field distribution in an X-ray waveguide array." Journal of Applied Crystallography 50, no. 3 (May 16, 2017): 701–11. http://dx.doi.org/10.1107/s1600576717004630.

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Iterative phase retrieval has been used to reconstruct the near-field distribution behind tailored X-ray waveguide arrays, by inversion of the measured far-field pattern recorded under fully coherent conditions. It is thereby shown that multi-waveguide interference can be exploited to control the near-field distribution behind the waveguide exit. This can, for example, serve to create a secondary quasi-focal spot outside the waveguide structure. For this proof of concept, an array of seven planar Ni/C waveguides are used, with precisely varied guiding layer thickness and cladding layer thickness, as fabricated by high-precision magnetron sputtering systems. The controlled thickness variations in the range of 0.2 nm results in a desired phase shift of the different waveguide beams. Two kinds of samples, a one-dimensional waveguide array and periodic waveguide multilayers, were fabricated, each consisting of seven C layers as guiding layers and eight Ni layers as cladding layers. These are shown to yield distinctly different near-field patterns.

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Tarnai, Tibor, Patrick W. Fowler, Simon D. Guest, and Flórián Kovács. "Equiauxetic Hinged Archimedean Tilings." Symmetry 14, no. 2 (January 25, 2022): 232. http://dx.doi.org/10.3390/sym14020232.

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There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An equiauxetic framework has a unique mechanism of expansion (an equiauxetic mode) where the symmetry forces a Poisson’s ratio of −1. Hinged tilings offer opportunities for the design of auxetic and equiauxetic frameworks in 2D, and generic auxetic behaviour can often be detected using a symmetry extension of the scalar counting rule for mobility of periodic body-bar systems. Hinged frameworks based on Archimedean tilings of the plane are considered here. It is known that the regular hexagonal tiling, {63}, leads to an equiauxetic framework for both single-link and double-link connections between the tiles. For single-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found here to be equiauxetic: these are {3.122}, {4.6.12}, and {4.82}. For double-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found to be equiauxetic: these are {34.6}, {32.4.3.4}, and {3.6.3.6}.

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Huang, Lizhong, Jiayou Du, and Zefei Zhu. "Neutrally Buoyant Particle Migration in Poiseuille Flow Driven by Pulsatile Velocity." Micromachines 12, no. 9 (September 6, 2021): 1075. http://dx.doi.org/10.3390/mi12091075.

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A neutrally buoyant circular particle migration in two-dimensional (2D) Poiseuille channel flow driven by pulsatile velocity is numerical studied by using immersed boundary-lattice Boltzmann method (IB-LBM). The effects of Reynolds number (25≤Re≤200) and blockage ratio (0.15≤k≤0.40) on particle migration driven by pulsatile and non-pulsatile velocity are all numerically investigated for comparison. The results show that, different from non-pulsatile cases, the particle will migrate back to channel centerline with underdamped oscillation during the time period with zero-velocity in pulsatile cases. The maximum lateral travel distance of the particle in one cycle of periodic motion will increase with increasing Re, while k has little impact. The quasi frequency of such oscillation has almost no business with Re and k. Moreover, Re plays an essential role in the damping ratio. Pulsatile flow field is ubiquitous in aorta and other arteries. This article is conducive to understanding nanoparticle migration in those arteries.

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Khouider, Boualem, and Mitchell W. Moncrieff. "Organized Convection Parameterization for the ITCZ*." Journal of the Atmospheric Sciences 72, no. 8 (August 1, 2015): 3073–96. http://dx.doi.org/10.1175/jas-d-15-0006.1.

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Abstract Mesoscale convective systems (MCSs) are of fundamental importance in the dynamics of the atmospheric circulation and the climate system. They are often observed to develop over significant terrain in ambient shear flows in midlatitudes and embedded within the Madden–Julian oscillation (MJO) and convectively coupled equatorial wave (CCEW) envelopes, as well as in the intertropical convergence zone (ITCZ). Yet general circulation models (GCMs) fail to resolve these systems, and their underlying convective parameterizations are not directed to represent organized circulations. Shear-parallel MCSs, which are common in the ITCZ, have a three-dimensional structure and, as such, present a serious modeling challenge. Here, a previously developed multicloud model (MCM) is modified to parameterize MCSs. One of the main modifications is the parameterization of stratiform condensation to capture extended stratiform outflows, which characterize MCSs, resulting from strong upper-level jets. Linear analysis shows that, under the influence of a typical double African and equatorial jet shear flow, this modification results in an additional new scale-selective instability peaking at the mesoalpha scale of roughly 400 km. Nonlinear simulations conducted with the modified MCM on a 400 km × 400 km doubly periodic domain, without rotation, resulted in the spontaneous transition from a quasi-two-dimensional shear-perpendicular convective system, consistent with linear theory, to a fully three-dimensional flow structure. The simulation is characterized by shear-parallel bands of convection, moving slowly eastward, embedded in stratiform systems that expand perpendicularly and propagate westward with the upper-level jet. The mean circulation and the implications for the domain-averaged vertical transport of momentum and potential temperature are discussed.

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Xie, Hua, Xiaoliang Xu, Linjun Wang, and Wei Zhuang. "Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model." Journal of Chemical Physics 156, no. 15 (April 21, 2022): 154116. http://dx.doi.org/10.1063/5.0085759.

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We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron–phonon couplings, are calculated with density-functional theory and density-functional perturbation theory and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k points and the number of phonon q points plays an important role in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched–compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We, therefore, provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems.

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ANTONOPOULOS, CHRIS, VASILEIOS BASIOS, JACQUES DEMONGEOT, PASQUALE NARDONE, and RENÉ THOMAS. "LINEAR AND NONLINEAR ARABESQUES: A STUDY OF CLOSED CHAINS OF NEGATIVE 2-ELEMENT CIRCUITS." International Journal of Bifurcation and Chaos 23, no. 09 (September 2013): 1330033. http://dx.doi.org/10.1142/s0218127413300334.

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In this paper we consider a family of dynamical systems that we call "arabesques", defined as closed chains of 2-element negative circuits. An n-dimensional arabesque system has n 2-element circuits, but in addition, it displays by construction, two n-element circuits which are both positive versus one positive and one negative, depending on the parity (even or odd) of the dimension n. In view of the absence of diagonal terms in their Jacobian matrices, all these dynamical systems are conservative and consequently, they cannot possess any attractor. First, we analyze a linear variant of them which we call "arabesque 0" or for short "A0". For increasing dimensions, the trajectories are increasingly complex open tori. Next, we inserted a single cubic nonlinearity that does not affect the signs of its circuits (that we call "arabesque 1" or for short "A1"). These systems have three steady states, whatever be the dimension, in agreement with the order of the nonlinearity. All three are unstable, as there cannot be any attractor in their state-space. The 3D variant (that we call for short "A1_3D") has been analyzed in some detail and found to display a complex mixed set of quasi-periodic and chaotic trajectories. Inserting n cubic nonlinearities (one per equation) in the same way as above, we generate systems "A2_nD". A2_3D behaves essentially as A1_3D, in agreement with the fact that the signs of the circuits remain identical. A2_4D, as well as other arabesque systems with even dimension, has two positive n-circuits and nine steady states. Finally, we investigate and compare the complex dynamics of this family of systems in terms of their symmetries.

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Mukhin, S. I., and S. I. Matveenko. "Stripe Phase: Analytical Results for Weakly Coupled Repulsive Hubbard Model." International Journal of Modern Physics B 17, no. 21 (August 20, 2003): 3749–83. http://dx.doi.org/10.1142/s0217979203022726.

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Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high Tc cuprates is discussed.

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Mishra, Bhupendra, Wlodek Kluźniak, and P. Chris Fragile. "Relativistic, axisymmetric, viscous, radiation hydrodynamic simulations of geometrically thin discs. II. Disc variability." Monthly Notices of the Royal Astronomical Society 497, no. 1 (June 30, 2020): 1066–79. http://dx.doi.org/10.1093/mnras/staa1848.

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ABSTRACT An analysis of two-dimensional viscous, radiation hydrodynamic numerical simulations of thin α-discs around a stellar mass black hole reveals multiple robust, coherent oscillations. Our disc models are initialized on both the gas- and radiation-pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates between $\dot{M} = 0.01 L_\mathrm{Edd}/c^2$ and $10\, L_\mathrm{Edd}/c^2$. In the initially radiation-pressure-dominated disc, we confirm the presence of global inertial–acoustic oscillations of frequency slightly above the maximum radial epicyclic one. In the gas-pressure-dominated Schwarzschild-metric models, we find a velocity oscillation occurring at the maximum value of the radial epicyclic frequency, $3.5\times 10^{-3}\, t_\mathrm{g}^{-1}$, which is most likely a trapped fundamental g-mode. For the Kerr-metric, gas-pressure-dominated disc with dimensionless black hole spin parameter a* = 0.5, the mode frequency is well below the epicyclic frequency maximum, thus confirming that this oscillation is a trapped g-mode. Additionally, the total pressure fluctuations in the discs strongly suggest standing-wave p-modes with frequencies below the apparent g-mode frequency, some trapped in the inner disc close to the innermost stable circular orbit (ISCO), others present in the middle/outer parts of the disc. The strongest oscillations occur at the breathing oscillation frequency and are present in all the numerical models we report here, as are weaker velocity oscillations at the vertical epicyclic frequencies. The vertical oscillations show a 3:2 frequency ratio with oscillations occurring approximately at the radial epicyclic frequency, which could be of astrophysical importance in systems with observed twin peak, high-frequency quasi-periodic oscillations.

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Su, Xifeng, and Rafael de la Llave. "KAM Theory for Quasi-periodic Equilibria in One-Dimensional Quasi-periodic Media." SIAM Journal on Mathematical Analysis 44, no. 6 (January 2012): 3901–27. http://dx.doi.org/10.1137/12087160x.

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Fujita, M., and K. Machida. "Electrons on one-dimensional quasi-periodic lattices." Synthetic Metals 19, no. 1-3 (March 1987): 39–44. http://dx.doi.org/10.1016/0379-6779(87)90328-6.

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Antipov, A. E., V. Yu Zitserman, Yu A. Makhnovskii, and S. M. Aldoshin. "Diffusion in quasi-one-dimensional periodic structures." Doklady Physical Chemistry 454, no. 2 (February 2014): 32–35. http://dx.doi.org/10.1134/s0012501614020031.

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Mugassabi, S., and A. Vourdas. "Almost periodic one-dimensional systems." Journal of Physics A: Mathematical and Theoretical 42, no. 20 (April 30, 2009): 202001. http://dx.doi.org/10.1088/1751-8113/42/20/202001.

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Geng, Jiansheng, and Zhiyan Zhao. "Reducibility of one-dimensional quasi-periodic Schrödinger equations." Journal de Mathématiques Pures et Appliquées 104, no. 3 (September 2015): 436–53. http://dx.doi.org/10.1016/j.matpur.2015.03.004.

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Tang, Xiao-Yan, and Sen-Yue Lou. "Quasi-periodic and Non-periodic Waves in (2+1)-Dimensional Nonlinear Systems." Communications in Theoretical Physics 44, no. 4 (October 2005): 583–88. http://dx.doi.org/10.1088/6102/44/4/583.

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Journal articles on the topic 'One dimensional quasi periodic systems'

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