Showing papers on "Quasiperiodic function published in 1996"
TL;DR: In this paper, the authors present a technique for isolating climate signals in time series with a characteristic "red" noise background which arises from temporal persistence, which is estimated by a robust procedure that is largely unbiased by the presence of signals immersed in the noise.
Abstract: We present a new technique for isolating climate signals in time series with a characteristic ‘red’ noise background which arises from temporal persistence. This background is estimated by a ‘robust’ procedure that, unlike conventional techniques, is largely unbiased by the presence of signals immersed in the noise. Making use of multiple-taper spectral analysis methods, the technique further provides for a distinction between purely harmonic (periodic) signals, and broader-band (‘quasiperiodic’) signals. The effectiveness of our signal detection procedure is demonstrated with synthetic examples that simulate a variety of possible periodic and quasiperiodic signals immersed in red noise. We apply our methodology to historical climate and paleoclimate time series examples. Analysis of a ≈ 3 million year sediment core reveals significant periodic components at known astronomical forcing periodicities and a significant quasiperiodic 100 year peak. Analysis of a roughly 1500 year tree-ring reconstruction of Scandinavian summer temperatures suggests significant quasiperiodic signals on a near-century timescale, an interdecadal 16–18 year timescale, within the interannual El Nino/Southern Oscillation (ENSO) band, and on a quasibiennial timescale. Analysis of the 144 year record of Great Salt Lake monthly volume change reveals a significant broad band of significant interdecadal variability, ENSO-timescale peaks, an annual cycle and its harmonics. Focusing in detail on the historical estimated global-average surface temperature record, we find a highly significant secular trend relative to the estimated red noise background, and weakly significant quasiperiodic signals within the ENSO band. Decadal and quasibiennial signals are marginally significant in this series.
1,312 citations
TL;DR: In this paper, a metal-insulator transition was observed in icosahedral quasicrystals and magnetoresistance (MR) was found to change smoothly from weak-localization behavior in the metallic regime to anomalous features in the insulating regime.
Abstract: Metal-insulator transition was observed in icosahedral quasicrystals ${\mathrm{Al}}_{705}$${\mathrm{Pd}}_{21}$${\mathrm{Re}}_{85\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ as x changed from 5 to 0 It was found that conductivity data of the insulating samples (x\ensuremath{\leqslant}35) could be analyzed in terms of variable range hopping, ie, \ensuremath{\sigma}=${\mathrm{\ensuremath{\sigma}}}_{0}$ exp[-(${\mathit{T}}_{0}$/T${)}^{\mathit{p}}$], with p=1/2 for x=2, 25, 3, and 35 and p=1/4 for x=0, over the temperature range from 045 to 10 K The localization length was found to be of the order of intercluster distance in the quasicrystalline structure At decreasing x, magnetoresistance (MR) was found to change smoothly from weak-localization behavior in the metallic regime to anomalous features in the insulating regime which are distinctly different from those seen in other well-studied insulators The persistence of positive MR in insulating ${\mathrm{Al}}_{705}$${\mathrm{Pd}}_{21}$${\mathrm{Re}}_{85\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ alloys suggests that the backscattering effect plays an important role for localized states in quasicrystalline materials Specific heat measurement on the insulating x=2 sample yielded \ensuremath{\gamma}=038 mJ/g atom ${\mathrm{K}}^{2}$, and carrier density was found to be \ensuremath{\sim}${10}^{20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at 42 K from Hall effect measurement, which are at least as large as those of metallic Al-Cu-Fe quasicrystals The finding of spatially localized states in quasiperiodic alloys cannot be explained satisfactorily by existing theories \textcopyright{} 1996 The American Physical Society
62 citations
TL;DR: Good agreement is found between the experimental data and the results of a classical trajectory Monte Carlo simulation demonstrating that, for the times investigated, classical-quantum correspondence holds and quantum corrections are negligible.
Abstract: Wave packets comprising a superposition of very-high-lying Rydberg states have been created using a half-cycle pulse (HCP). The properties of the wave packet are probed using a second HCP that is applied following a variable time delay. The second pulse ionizes a fraction of the atoms and the survival probability exhibits pronounced oscillations that are associated with the quasiperiodic evolution of the wave packet. Good agreement is found between the experimental data and the results of a classical trajectory Monte Carlo simulation demonstrating that, for the times investigated, classical-quantum correspondence holds and quantum corrections are negligible. {copyright} {ital 1996 The American Physical Society.}
61 citations
TL;DR: In this article, an all-optical scheme based on continuous delayed optical feedback for controlling delay-induced chaotic behavior of high-speed semiconductor lasers is presented, and the successful control of continuous wave and unstable periodic or quasiperiodic dynamic states with vanishing controlling force term is demonstrated.
58 citations
TL;DR: A Fourier-domain-based recognition technique is proposed for periodic and quasiperiodic pattern recognition based on the angular correlation of the moduli of the sample and the reference Fourier spectra centered at the maximum central point.
Abstract: A Fourier-domain-based recognition technique is proposed for periodic and quasiperiodic pattern recognition. It is based on the angular correlation of the moduli of the sample and the reference Fourier spectra centered at the maximum central point. As in other correlation techniques, recognition is achieved when a high correlation peak is obtained, and this result occurs when the two spectra coincide. The angular correlation is a one-dimensional function of the rotation angle. The position of the correlation peak indicates the rotation angle between two similar patterns in the original images. Some optimizations for the discrete calculation of the Fourier-domain-based angular correlation are also proposed. Some applications of this technique to web inspection tasks, such as pattern recognition and classification, damaged web evaluation, and detection of defects, are presented and discussed.
49 citations
TL;DR: In this paper, the existence of many unstable bands of transverse wavevectors in a feedback loop with nonlinear medium has been studied by means of suitable indicators, such as the fraction of light power distributed on the first band respect to that one distributed on both.
Abstract: Recently we have observed two-dimensional periodic and quasiperiodic structures in the transverse profile of an optical beam circulating in a feedback loop which contains a nonlinear medium. The symmetries observed depend not only on the interaction between light and nonlinear medium, but also on a nonlocality due to beam rotation in the feedback loop. The linear stability analysis of our model shows the existence of many unstable bands of transverse wavevectors. Close to threshold, predictions are qualitatively and quantitatively confirmed by the experiment. When the intensity threshold values are almost the same for the two principal bands, structures with different wavenumbers arise above threshold. These modes compete with a very complex dynamics. We have started to study this behavior by means of suitable indicators. As a first indicator we have individuated the fraction of light power distributed on the first band respect to that one distributed on both.
41 citations
TL;DR: In this paper, a ray theory for the case of finite portions with periodic or quasiperiodic features has been proposed, which allows the scattered fields due to an arbitrary incident field to be constructed entirely by ray tracing.
Abstract: Many scattering configurations of interest include finite portions with periodic or quasiperiodic features. Several recent investigations have dealt with this problem for the planar two-dimensional case and have developed high-frequency asymptotic solutions that include multibeam reflections obeying the Bragg condition and Bragg-modulated edge diffractions. These constituents have been interpreted as wave objects in a generalized geometrical theory of diffraction (GTD). The present investigation adds to these previous results and formalizes them into a ray theory. This allows the scattered fields due to a finite quasiperiodic array of obstacles, excited by an arbitrary incident field, to be constructed entirely by ray tracing. Scattered ray plots and caustics for various shapings of incident fields and array parameters illustrate the variety of phenomena associated with this class of scattering environments.
36 citations
TL;DR: Theorems that predict the behavior of periodic orbits in the vicinity of an invariant surface on which the motion is conjugate to a Diophantine rotation for symplectic maps and quasiperiodic perturbations of symp eclectic maps are proved.
Abstract: The existence of an invariant surface in high-dimensional systems greatly influences the. behavior in a neighborhood of the invariant surface. We prove theorems that predict the behavior of periodic orbits in the vicinity of an invariant surface on which the motion is conjugate to a Diophantine rotation for symplectic maps and quasiperiodic perturbations of symplectic maps. Our results allow for efficient numerical algorithms that can serve as an indication for the breakdown of invariant surfaces.
30 citations
TL;DR: The model for electronic transport in quasicrystals is proposed, and a fractional multicomponent Fermi-surface model has been introduced, which explains the nearly vanishing conductivity, as well as strong temperature dependence of thermopower and related transport properties.
Abstract: The model for electronic transport in quasicrystals is proposed. Unlike all previous attempts to explain unusual electronic properties of quasicrystals by impending localization due to the lack of periodicity in defectless quasiperiodic lattices, the current theory is focused on phonon and impurity scattering in real, ``dirty'' quasicrystals. The standard scattering theory cannot be applied to quasicrystals, due to their unusual band structure, namely the fact that the Fermi surface is nearly obliterated. To solve the problem a fractional multicomponent Fermi-surface model has been introduced: the Fermi surface has been viewed as consisting of relatively large number of residual tiny electron and hole pockets, with impurity random potential scattering electrons between different components. Leaving quasiperiodicity aside, the Dyson equations for the scattering time, dc conductivity and thermopower have been solved analytically. The theory explains the nearly vanishing conductivity, as well as strong temperature dependence of thermopower and related transport properties. \textcopyright{} 1996 The American Physical Society.
30 citations
TL;DR: Certain universal aspects of the quasiperiodic route to chaos are reviewed by making use of the standard circle map with particular attention to the golden mean and silver mean with a view to comparison with experimental work.
Abstract: Numerous physical systems with two competing frequencies exhibit frequency locking and chaos associated with quasiperiodicity. In this paper we review certain universal aspects of the quasiperiodic route to chaos by making use of the standard circle map. Particular attention is paid to the golden mean and silver mean with a view to comparison with experimental work.
28 citations
TL;DR: In this paper, a general algorithm for calculating quasiperiodic lattices by the strip projection method is presented, which is applicable to any number of dimensions and to any choice of the projection space and the strip.
Abstract: A general algorithm for calculating quasiperiodic lattices by the strip projection method is presented. It is applicable to any number of dimensions and to any choice of the projection space and the strip. It is shown that, for all quasiperiodic lattices which have so far been proposed to explain experimental findings, the algorithm can be formulated in such a way that only elementary operations with integers are involved. Thus it is possible to decide exactly whether a point is inside, outside or exactly on the boundary. It is shown how points on the strip boundary must be treated in order to avoid defects in the tiling. Finally, an efficient search algorithm for finding all points in the strip within a given ‘window’ is presented.
TL;DR: In this paper, the dynamics of electrons in a two-level system under the influence of a dc-ac field is investigated, and it is shown that in the approximation of high-frequency driving, they can realize three types of localized motion: period 1, period q, and quasiperiodic ones through the choice of values of field parameters.
TL;DR: In this paper, the qualitative behavior of the flow depends in a sensitive way on the geometry of the funnel, and the flow rate reaches its maximum in this regime when the funnel opening angle is varied.
Abstract: We have investigated a granular flow consisting of a single layer of uniform balls in a two dimensional funnel. The qualitative behavior of the flow depends in a sensitive way on the geometry. For a particular configuration in which only the funnel opening angle \ensuremath{\beta} is varied, we find three regimes. When \ensuremath{\beta}g2\ifmmode^\circ\else\textdegree\fi{}, the flow is dense and steady, and the flow rate is determined by the geometry at the outlet. When 0.1\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}\ensuremath{\beta}\ensuremath{\lesssim}1\ifmmode^\circ\else\textdegree\fi{}, the flow is intermittent, consisting of quasiperiodic kinematic waves, probably shock waves, propagating against the flow. The flow rate reaches its maximum in this regime. When \ensuremath{\beta}0.05\ifmmode^\circ\else\textdegree\fi{}, the waves become stationary, and the flow rate is now determined by the geometry at the inlet. We also measure the number density fluctuations of the flow and their power spectra. For all flows, the power spectra are white at low frequencies with structures at higher frequencies resulting from the kinematic waves and short-range correlations. \textcopyright{} 1996 The American Physical Society.
Book Chapter•
1 Jan 1996
TL;DR: In this paper, the authors explore pattern evocation and the visualization of the double spherical pendulum and show that the motion in the reduced space is periodic (respectively, quasiperiodic or almost periodic).
Abstract: This paper explores pattern evocation and the visualization of orbits of the double spherical pendulum. Pattern evocation is a phenomenon where patterns emerge when the
ow of a dynamical system is viewed in a frame that rotates relative to the inertial frame. The paper begins
with a summary of the theory on pattern evocation for mechanical systems with symmetry. The result of this theory is that if the motion in the reduced space is periodic (respectively, quasiperiodic or almost periodic), then when viewed in a suitably chosen rotating frame with constant
velocity, the motion in the unreduced space is periodic (respectively, quasiperiodic or almost periodic). The motion of the system viewed in this rotating frame may have a particular pattern or symmetry. Examples of this theory are demonstrated for the double spherical pendulum. A
dierential-algebraic model is created for the double spherical pendulum and is integrated with the simulation package MEXX as well as a custom energy-momentum integrator.
TL;DR: In this paper, the authors distinguish two types of quasiperiodic behavior in peroxidase and oxidase reactions, i.e., primary and secondary quasisiperiodicity, by supercritical secondary Hopf bifurcations at one end of the relevant range of parameter values.
Abstract: Quasiperiodicity in models of the peroxidase–oxidase reaction has previously been reported in ‘‘abstract’’ or phenomenological models which sacrifice chemical realism for tractability. In the present paper, we discuss how such behavior can arise in a detailed model (BFSO) of the reaction which has previously been shown to be consistent with experimental findings. We distinguish two types of quasiperiodic behavior. Regions of what we here refer to as ‘‘primary’’ quasiperiodicity are delimited by supercritical secondary Hopf bifurcations at one end of the relevant range of parameter values and by heteroclinic transitions at the other. Regions of so‐called ‘‘secondary quasiperiodicity’’ are delimited by supercritical Hopf bifurcations at both ends of the parameter range. The existence of a quasiperiodic route to chaos in a modified version of BFSO is also described. This paper emphasizes the experimental circumstances under which quasiperiodic dynamics may be detected in the lab and offers specific prescriptions for its observation.
TL;DR: An introduction of a non-linear three-wave interaction to a growing family of paradigmatic equations which exhibit a route to turbulence via spatiotemporal intermittency is outlined in this work.
Abstract: The spatiotemporal evolution of stimulated Raman backscattering in a bounded, uniform, weakly dissipative plasma is studied. The nonlinear model of a three-wave interaction involves a quadratic coupling of slowly varying complex amplitudes of the laser pump, the backscattered and the electron plasma wave. The corresponding set of coupled partial differential equations with nonlinear phase detuning that is taken into account is solved numerically in space time with fixed nonzero source boundary conditions. The study of the above open, convective, weakly confined system reveals a quasiperiodic transition to spatiotemporal chaos via spatiotemporal intermittency. In the analysis of transitions a dual scheme borrowed from fields of nonlinear dynamics and statistical physics is applied. An introduction of a non-linear three-wave interaction to a growing family of paradigmatic equations which exhibit a route to turbulence via spatiotemporal intermittency is outlined in this work.
TL;DR: In this paper, the Anderson transition in an effective dimension $d$ ($3 \leq d \LEq 11$) for one particle propagation in a model random and quasiperiodic potential was numerically investigated.
Abstract: We numerically investigate the Anderson transition in an effective dimension $d$ ($3 \leq d \leq 11$) for one particle propagation in a model random and quasiperiodic potential. The found critical exponents are different from the standard scaling picture. We discuss possible reasons for this difference.
TL;DR: A comparative study of conditions for chaos onset in Duffing-type weakly and strongly nonlinear oscillators is carried out, and an important application of the theory is the stability analysis of parametric amplifiers.
Abstract: A comparative study of conditions for chaos onset in Duffing-type weakly and strongly nonlinear oscillators is carried out. Quasiperiodically forced oscillators with combined parametric and external excitation are considered. The concept of induced saddle states is introduced in order to illuminate reasons for chaos arising in weakly nonlinear systems. The conditions for, and the mechanisms of, the transition to chaos are investigated in detail, both analytically and numerically, for the case of weakly nonlinear oscillators. Multistability properties of the oscillators are studied as well. An important application of the theory is the stability analysis of parametric amplifiers. \textcopyright{} 1996 The American Physical Society.
TL;DR: The discussion of the resonant system concentrates on a scenario of transition to chaos consisting of an infinite sequence of ``period-doubling'' homoclinic bifurcations of stable periodic orbits, for which the left-right symmetry of the convective system plays an essential role.
Abstract: This paper describes an amplitude equation analysis of the interactions between waves with wave number ${\mathit{k}}_{1}$ (and phase speed ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$/${\mathit{k}}_{1}$) and stationary convection with wave number ${\mathit{k}}_{2}$. These two modes may bifurcate almost simultaneously from the conductive state of a two-layer B\'enard system, when the ratio of layer thicknesses is near a particular value (codimension-2 singularity). When ${\mathit{k}}_{2}$\ensuremath{
e}2${\mathit{k}}_{1}$ (nonresonant case) and the first bifurcation occurs for steady convection, a secondary bifurcation to a spatially quasiperiodic and time-periodic mixed mode is obtained when increasing the driving gradient. No stable small-amplitude solution exists when the Hopf bifurcation is the first one. The occurrence of either of these two possibilities depends on the thickness ratio. When ${\mathit{k}}_{2}$=2${\mathit{k}}_{1}$ (resonant case), the system presents a much wider variety of dynamical behaviors, including quasiperiodic relaxation oscillations and temporal chaos. The discussion of the resonant system concentrates on a scenario of transition to chaos consisting of an infinite sequence of ``period-doubling'' homoclinic bifurcations of stable periodic orbits, for which the left-right symmetry of the convective system plays an essential role. For increasing constraint, a reverse cascade is observed, for which quadratic nonlinearities in the Ginzburg-Landau equations are shown to entirely determine the dynamics (cubic and higher-order terms may be neglected near the codimension-2 point). \textcopyright{} 1996 The American Physical Society.
TL;DR: A combination of Patterson methods with the maximum-entropy method has been tested for ab initio phase determination of decagonal structures in this article, where two procedures for applying maximum entropy methods to phase extension have been derived exclusively constrained by the positions of the hyperatoms in n-dimensional space and the three-dimensional Patterson function.
Abstract: A combination of Patterson methods with the maximum-entropy method has been tested for ab initio phase determination of decagonal structures To unravel the n-dimensional Patterson function, the symmetry minimum function, an improvement of the Patterson superposition approach, is extended to the embedding dimensions This method allows the positions of the hyperatoms to be located and a first crude structure model to be derived To retrieve the shape and the chemical composition of the perpendicular space component of the hyperatoms, two procedures for applying maximum-entropy methods to phase extension have been derived exclusively constrained by the positions of the hyperatoms in n-dimensional space and the three-dimensional Patterson function These constraints enforce quasiperiodic solutions with corresponding chemical composition and correct interatomic distances Applying the maximum-entropy method in perpendicular space allows the decagonal structure to be solved, whereas the physical space approach also provides the capability of determining more complex non-periodic structures as well as deviations from the ideal quasiperiodic structure Three successful structure solutions of decagonal structures show the potential of this new development
TL;DR: The bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress ~ABC! type are studied to explore the qualitative behavior of solution branches.
Abstract: We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress ~ABC! type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasiperiodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field. @S1063-651X~96!09309-9#.
TL;DR: The structure and morphology of ultrathin epitaxial Fe films on Cu(311) is examined in situ by spot-profile analyzing low-energy electron diffraction as discussed by the authors, which is a highly asymmetrical substrate which is characterized by a troughlike surface structure composed of uniaxially arranged close-packed Cu atom rows.
Abstract: The structure and morphology of ultrathin epitaxial Fe films on Cu(311) is examined in situ by spot-profile analyzing low-energy electron diffraction. Cu(311) is a highly asymmetrical substrate which is characterized by a troughlike surface structure composed of uniaxially arranged close-packed Cu atom rows. Deposition at 140 K initially leads to the formation of pseudomorphic Fe. The constraint to lower dominant stress along the close-packed atom rows forces the formation of pseudomorphic patches with a quasiperiodic separation of 35 \AA{}. With proceeding growth, these patches act as nucleation sites for three-dimensional islands that gradually relax via a Pitsch transformation towards a strained bcc structure. Coalescence occurs at \ensuremath{\sim}5 ML and leads to a periodically faceted growth front of the overlayer. The resulting surface topography corresponds to a regular up-and-down staircase and remains unchanged for coverages g5 ML: the periodic facet separation measures 35 \AA{}; 7--8 layers contribute to the growth front. As a consequence of coalescence, the film locks into a lattice arrangement which is predominantly dictated by the substrate and is likely to correspond to an fcc-like structure. The periodic facetting of the film surface, on the other hand, allows partial relaxation towards strained bcc structure to persist in the top layers of the film. \textcopyright{} 1996 The American Physical Society.
TL;DR: The experimental results clearly reveal that the various kinds of voltage oscillations are caused by corresponding frequency-locked, quasiperiodic, or chaotic filament motions.
Abstract: Silicon multilayered devices biased with a dc voltage exhibit spontaneous voltage oscillations which are connected with spatial, pendulumlike oscillations of a current-density filament. When driven with a superimposed sinusoidal voltage, the oscillations of the device voltage show frequency locking, quasiperiodicity, and chaos. In order to correlate the global voltage oscillations with the filament motion spatially resolved measurements of the filament dynamics have been performed by using two different techniques: measurements of the recombination radiation with a streak camera and measurements of the potential on the device surface between the electrical contacts with an active potential probe. The experimental results clearly reveal that the various kinds of voltage oscillations are caused by corresponding frequency-locked, quasiperiodic, or chaotic filament motions. \textcopyright{} 1996 The American Physical Society.
TL;DR: A quasiperiodic self-dual metric of the Gibbons-Hawking type with one gravitational instanton per spacetime cell is presented, which conforms to a definition of spacetime foam given by Hawking.
Abstract: We present a quasiperiodic self-dual metric of the Gibbons-Hawking type with one gravitational instanton per spacetime cell. The solution, based on an adaptation of Weierstrassian \ensuremath{\zeta} and \ensuremath{\sigma} functions to three dimensions, conforms to a definition of spacetime foam given by Hawking. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, it was shown that linear extensions whose solutions are not almost periodic form a set of the second category inL (representable as an intersection of countably many everywhere dense open subsets).
Abstract: For a discrete dynamical system ω n =ω0+αn, where a is a constant vector with rationally independent coordinates, on thes-dimensional torus Ω we consider the setL of its linear unitary extensionsx n+1=A(ω0+αn)x n , whereA (Ω) is a continuous function on the torus Ω with values in the space ofm-dimensional unitary matrices. It is proved that linear extensions whose solutions are not almost periodic form a set of the second category inL (representable as an intersection of countably many everywhere dense open subsets). A similar assertion is true for systems of linear differential equations with quasiperiodic skew-symmetric matrices.
TL;DR: In this article, the universal finite-size-scaling functions of the Ising model are tested by Monte Carlo simulations for various lattices, including regular and quasiperiodic lattices such as the Penrose lattice.
Abstract: The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.
Keywords: Universal Finite-Size-Scaling Function; Ising Model; Order-Parameter Probability Distribution Function.
TL;DR: Godreche as mentioned in this paper proves rigorously that the structure factor of the structure intermediate between quasiperiodic and random is purely singluar continuous, apart from a delta function at zero.
Abstract: This paper proves rigorously that the structure factor of the “structure intermediate between quasiperiodic and random” introduced by Aubry. Godreche, and Luck is purely singluar continuous apart from a delta function at zero for “most” choices of the parameters. The result is based on a proof that a flow under a steep function over an irrational circle rotation is weakly mixing for “most” parameters, and on the wonderland Theorem.
TL;DR: In this paper, the universal finite-size-scaling functions of the Ising model are tested by Monte Carlo simulations for various lattices, including regular and quasiperiodic lattices such as the Penrose lattice.
Abstract: The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.
TL;DR: In this paper, the conditions necessary for the occurrence of quasiperiodicity are shown by solving the system equations using the method of harmonic balance, and it is shown that QP oscillations will occur due to the severity of magnetizing nonlinearity of the transformer core.