Characteristic Exponents Research Articles

Kinetic roughening and nontrivial scaling in the Kardar–Parisi–Zhang growth with long-range temporal correlations

Long-range spatiotemporal correlations may play important roles in non-equilibrium surface growth processes. In order to explore the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we carry out extensive numerical simulations of the (1 + 1)- and (2 + 1)-dimensional Kardar–Parisi–Zhang (KPZ) growth system in the presence of temporally correlated noise, and compare our results with previous theoretical predictions and numerical simulations. We find that surface morphologies are obviously affected with long-range temporal correlations, and as the temporal correlation exponent increases, the KPZ surfaces develop gradually faceted patterns in the saturated growth regimes. Our results show that the temporal correlated KPZ system displays evidently nontrivial dynamic properties when 0 < θ < 0.5, the characteristic roughness exponents satisfy α < α s, and α loc exhibits non-universal scaling within local window sizes, which differs with the existing dynamic scaling hypotheses, both in the (1 + 1)- and (2 + 1)-dimensions.

Magnetic ground state and crystal structure of the giant dielectric constant material Ba(Fe1/2Nb1/2)O3

The room temperature crystal structure as well as the magnetic ground state of Ba(Fe1/2Nb1/2)O3 (BFN) are controversial. The results of Rietveld refinements using high-resolution synchrotron x-ray powder diffraction (SXRPD) data are presented to show that BFN belongs to cubic perovskite structure in the Pm3¯m space group and not in the cubic Fm3¯m or monoclinic symmetries, proposed by some earlier workers based on the analysis of the laboratory source XRD data. The temperature dependent specific heat measurements in the 1.8 to 300 K range on well characterized BFN samples are presented to show the absence of any long-range ordered (LRO) antiferromagnetic (AFM) transition, proposed by some earlier workers based on the observation of a peak in the temperature dependence of zero-field cooled (ZFC) DC magnetization around 25 to 32 K. Results of temperature dependent magnetization measurements during warming cycle on ZFC and field cooled (FC) BFN samples reveal history dependent bifurcation with a peak in the ZFC M (T) curve at Tf ~ 29 K, in agreement with some previous results where it was attributed to a spin-glass transition even though such an irreversibility can result from superparamagnetic (SPM) blocking as well. The appearance of a short plateau in our FC M (T) curve below Tf suggests a cluster spin-glass phase of BFN below Tf. This was confirmed by us through the ac susceptibility χ' (T, ω) studies which reveal divergence of spin dynamics at the spin-glass transition temperature TSG ~ (28 ± 1) K with a large characteristic spin relaxation time τ0 ~ 10−6 s following Vogel-Fulcher as well as power-law type critical dynamics. The existence of the magnetic glassy state in BFN is further supported by the observation of (1) magnetic field dependent shift of Tf with increasing magnetic field along the de Almeida-Thouless line in the T-H plane with a characteristic exponent of m = 2/3, (2) weak remanent magnetization Mr below Tf with exponentially decreasing Mr on approaching Tf, (3) extremely slow decay of the thermoremanent magnetization below Tf with time as per a stretched exponential function, and (4) characteristic aging, rejuvenation and memory effects below Tf. These results provide the first unambiguous confirmation of the cluster spin-glass state of BFN and settle the existing controversies related to its magnetic ground state.

Electronic and heat transport phenomena in the nanogranular thiospinelFe3S4

The iron sulphide ${\mathrm{Fe}}_{3}{\mathrm{S}}_{4}$ (greigite) is similar to its oxide counterpart ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ (magnetite) as to the crystal structure and ferrimagnetic order, but differs in electronic states. The ab initio calculations have evidenced $p$-type carriers at three spin-minority and three spin-majority Fermi surfaces, which is in contrast to the half-metallic character of magnetite with $n$-type carriers at three spin-minority Fermi surfaces. The transport properties including Hall and Nernst effects have been studied over the range 2--300 K by using nanogranular ceramics prepared by cold isostatic pressing of ${\mathrm{Fe}}_{3}{\mathrm{S}}_{4}$ particles with the mean crystallite size of ${d}_{\mathrm{XRD}}\ensuremath{\approx}80$ and 30 nm, respectively. The samples show metalliclike electrical resistivity with large residual value at $T$ \ensuremath{\rightarrow} 0 K. The $p$-type character of the charge carriers is reflected by the positive sign of both the thermopower and Hall effect. Temperature dependencies of the electrical resistivity, thermal conductivity, and thermopower are analyzed by considering processes of the grain boundary and defect intragrain scattering; simultaneously the role of magnons and their dynamics in electronic and heat transport is revealed. The Nernst and Hall effects show dominant contributions of anomalous type (ANE and AHE) with signs exactly opposite to those of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$, i.e., positive AHE and negative ANE in ${\mathrm{Fe}}_{3}{\mathrm{S}}_{4}$. The results are interpreted by evoking the original Callen treatment of thermoelectric and thermomagnetic phenomena using Onsager equations. Scaling between the longitudinal and transverse components of the electrical resistivity and thermoelectric conductivity tensors is checked. The analysis of the temperature dependent AHE using the relation between transverse and longitudinal resistivity ${\ensuremath{\rho}}_{yx}^{A}(T)\ensuremath{\sim}{\ensuremath{\rho}}_{xx}{(T)}^{n}$ gives the characteristic exponent $n=1.15$, which is close to the $n=1$ predicted by the skew-scattering mechanism.

An improved manson-halford model for multi-level nonlinear fatigue life prediction

The Manson-Halford (M−H) nonlinear fatigue damage model is widely used for fatigue damage analysis. It, however, does not consider the load interaction effect. This paper presents an improved M−H model with a load interaction factor defined as the ratio of the first and second stress levels. The characteristic exponent of the M−H model is modified by multiplying the load interaction factor and fatigue life ratio. The characteristic exponent can consider the load interaction effect and the load sequence effect under multi-level loading. Experimental data from five materials under two-level and multi-level stress loadings verify the accuracy of the proposed model.

Testing the flux-based statistical prediction of the three-body problem

Abstract We present an extensive comparison between the statistical properties of non-hierarchical three-body systems and the corresponding three-body theoretical predictions. We perform and analyse 1 million realizations for each different initial condition considering equal and unequal mass three-body systems to provide high accuracy statistics. We measure 4 quantities characterizing the statistical distribution of ergodic disintegrations: escape probability of each body, the characteristic exponent for escapes by a narrow margin, predicted absorptivity as a function of binary energy and binary angular momentum, and, finally, the lifetime distribution. The escape probabilities are shown to be in agreement down to the 1 per cent level with the emissivity-blind, flux-based theoretical prediction. This represents a leap in accuracy compared to previous three-body statistical theories. The characteristic exponent at the threshold for marginally unbound escapes is an emissivity-independent flux-based prediction, and the measured values are found to agree well with the prediction. We interpret both tests as strong evidence for the flux-based three-body statistical formalism. The predicted absorptivity and lifetime distributions are measured to enable future tests of statistical theories.

On the convergence of WKB approximations of the damped Mathieu equation

The form of the fundamental set of solutions of the damped Mathieu equation is determined by Floquet theory. In the limit as m → 0, we can apply WKB theory to get first order approximations of the fundamental set. WKB theory states that this approximation gets better as m → 0 and T is fixed. However, convergence of the periodic part and characteristic exponent is not addressed. We show that they converge to those predicted by WKB theory. We also provide a rate of convergence that is not dependent on T.

Equilibria, stability and chaos in photogravitational Bi-Circular restricted four-body problem

A model to investigate the influence of gravitational force and radiation pressure on interstellar dust found within the vicinities of certain stellar systems is presented in this study with the inclusion of potential due to the belt. Semi-analytic approach is adopted to examine the dynamical behaviour of the motion of a test particle in the neighbourhood of the radiating stars, namely, Wolf 630, Formalhaut, Omicron Eradani and 36 Ophiuchi respectively. The Libration points were found dependent on the mass ratios of the systems and the radiation pressure exerted by the star(s) and the motion of the dust particle around them is linearly unstable. In each of the four case studies, two Lyapunov Characteristic Exponents were seen positive which validate the chaotic nature of the system, also the Poincare Surface Section revealed the sensitivity of the dynamical system to change in initial conditions. Several scientific questions of great importance in astrophysics and astronomy; such as the motions of interstellar clouds, proto-nebulae, planetary rings and micrometeorites can be answered by engaging this model.

Power law model for subjective mental workload and validation through air traffic control human-in-the-loop simulation

We provide evidence for a power law relationship between the subjective one-dimensional Instantaneous Self Assessment workload measure (five-level ISA-WL scale) and the radio communication of air traffic controllers (ATCOs) as an objective task load variable. It corresponds to Stevens’ classical psychophysics relationship between physical stimulus and subjective response, with characteristic power law exponent γ of the order of 1. The theoretical model was validated in a human-in-the loop air traffic control simulation experiment with traffic flow as environmental stimulus that correlates positively with ATCOs frequency and duration of radio calls (task load, RC-TL) and their reported ISA-WL. The theoretical predictions together with nonlinear regression-based model parameter estimates expand previously published results that quantified the formal logistic relationship between the subjective ISA measure and simulated air traffic flow (Fürstenau et al. in Theor Issues Ergon Sci 21(6): 684–708, 2020). The present analysis refers to a psychophysics approach to mental workload suggested by (Gopher and Braune in Hum Factors 26(5): 519–532, 1984) that was recently used by (Bachelder and Godfroy-Cooper in Pilot workload esimation: synthesis of spectral requirements analysis and Weber's law, SCL Tech, San Diego, 2019) for pilot workload estimation, with a corresponding power law exponent in the typical range of Stevens’ exponents. Based on the hypothesis of cognitive resource limitation, we derived the power law by combination of the two logistic models for ISA-WL and communication TL characteristics, respectively. Despite large inter-individual variance, the theoretically predicted logistic and power law parameter values exhibit surprisingly close agreement with the regression-based estimates (for averages across participants). Significant differences between logistic ISA-WL and RC-TL scaling parameters and the corresponding Stevens exponents as ratio of these parameters quantify the TL/WL dissociation with regard to traffic flow. The sensitivity with regard to work conditions of the logistic WL-scaling parameter as well as the power law exponent was revealed by traffic scenarios with a non-nominal event: WL sensitivity increased significantly for traffic flow larger than a critical value. Initial analysis of a simultaneously measured new neurophysiological (EEG) load index (dual frequency head maps, DFHM, (Radüntz in Front Physiol 8: 1–15, 2017)) provided evidence for the power law to be applicable to the DFHM load measure as well.

Semigroup associated with a free polynomial

Let K be an algebraically closed field of characteristic zero and let KC〚x1,⋯,xe〛 be the ring of formal power series in several variables with exponents in a line free cone C. We consider irreducible polynomials f=yn+a1(x_)yn−1+⋯+an(x_) in KC〚x1,⋯,xe〛[y] whose roots are in KC〚x11n,⋯,xe1n〛. We generalize to these polynomials the theory of Abhyankar-Moh. In particular we associate with any such polynomial its set of characteristic exponents and its semigroup of values. We also prove that the set of values can be obtained using the set of approximate roots. We finally prove that polynomials of K〚x1,⋯,xe〛[y] fit in the above set for a specific line free cone (see Section 4).

Different Types of Stable Periodic Points of Diffeomorphism of a Plane with a Homoclinic Orbit

A diffeomorphism of the plane into itself with a fixed hyperbolic point is considered; it is assumed that there is a non-transversal homoclinic point. Stable and unstable manifolds are tangent to each other at the homoclinic point; there are various ways of tangency of stable and unstable manifolds. Diffeomorphisms of the plane with a non-transversal homoclinic point were analyzed in the studies of Sh. Newhouse, L.P. Shil’nikov, and other authors under the assumption that this point is a tangency point of finite order. It follows from the studies of these authors that an infinite set of stable periodic points can lie in a neighborhood of a homoclinic point; the presence of such a set depends on the properties of the hyperbolic point. In this paper, we assume that a homoclinic point is not a point at which the tangency of a stable and an unstable manifold is a tangency of finite order. There is a countable number of types of periodic points lying in the neighborhood of the homoclinic point; points belonging to the same type are called n-pass, where n is a natural number. In this paper, it is shown that, if the tangency is not finite-order, the neighborhood of a non-transversal homoclinic point can contain an infinite set of stable single-pass, two-pass, or three-pass periodic points with characteristic exponents bounded away from zero.

Energy analysis and determination of controlling mechanisms of dissociation for hydrate reservoirs via tracking of dissociation front

A number of dissociation techniques like depressurization, thermal stimulation, CO2 exchange, etc. have been reported and investigated for natural gas hydrates in literature. However, dissociation of hydrate reservoirs is a complex process that is actually governed by several parameters. Hence, when inspected closely, the dissociation characteristics are a reflection of how these parameters are interlinked with each other. The present study is designed to numerically simulate a matrix of 21 different cases, which comprises an in-depth analysis for thermal stimulation, drawdown pressure, permeability, intrinsic rate constant, and thermal conductivity. The focus of the current study is motivated by practical interest, which aims at deciphering the associated mechanisms with hydrate dissociation. Over the years, different researchers have outlined the role of mechanisms such as heat transfer (HT), fluid flow (FF), and dissociation (D). The governing mechanisms are deduced through mathematical fitting and plotting of thermodynamic parameters for deciphering associated mechanisms. A “characteristic exponent” is determined for each of the cases to identify and delineate the different mechanisms for each of the 21 cases. Further, energy conversion from hydrate and energy quantification has been described in detail. As such, this information pool about hydrate dissociation is vital and necessary for efficient energy harvesting from hydrate reservoirs from varied geological settings and composition.

Non-Debye relaxations: Smeared time evolution, memory effects, and the Laplace exponents

The non-Debye, i.e., non-exponential, behavior characterizes a large plethora of dielectric relaxation phenomena. Attempts to find their theoretical explanation are dominated either by considerations rooted in the stochastic processes methodology or by the so-called fractional dynamics based on equations involving fractional derivatives which mimic the non-local time evolution and as such may be interpreted as describing memory effects. Using the recent results coming from the stochastic approach we link memory functions with the Laplace (characteristic) exponents of infinitely divisible probability distributions and show how to relate the latter with experimentally measurable spectral functions characterizing relaxation in the frequency domain. This enables us to incorporate phenomenological knowledge into the evolution laws. To illustrate our approach we consider the standard Havriliak-Negami and Jurlewicz-Weron-Stanislavsky models for which we derive well-defined evolution equations. Merging stochastic and fractional dynamics approaches sheds also new light on the analysis of relaxation phenomena which description needs going beyond using the single evolution pattern. We determine sufficient conditions under which such description is consistent with general requirements of our approach.

Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles

We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $C^k$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $C^{k-1}$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters.

Continuous time random walks under Markovian resetting.

We investigate the effects of Markovian resetting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power-law probability density functions. We prove the existence of a nonequilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power-law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target, and the characteristic transport exponents.

Extensive numerical simulations of surface growth with temporally correlated noise.

Surface growth processes can be significantly affected by long-range temporal correlations. In this work, we perform extensive numerical simulations of a (1+1)- and (2+1)-dimensional ballistic deposition (BD) model driven by temporally correlated noise, which is regarded as the temporal correlated Kardar-Parisi-Zhang universality class. Our results are compared with the existing theoretical predictions and numerical simulations. When the temporal correlation exponent is above a certain threshold, BD surfaces develop gradually faceted patterns. We find that the temporal correlated BD system displays nontrivial dynamic properties, and the characteristic roughness exponents satisfy α≃α_{loc}<α_{s} in (1+1) dimensions, which is beyond the existing dynamic scaling classifications.

Multi-pass stable periodic points of diffeomorphism of a plane with a homoclinic orbit

A diffeomorphism of a plane into itself with a fixed hyperbolic point and a nontransversal point homoclinic to it is studied. There are various ways of touching a stable and unstable manifold at a homoclinic point. Periodic points whose trajectories do not leave the vicinity of the trajectory of a homoclinic point are divided into a countable set of types. Periodic points of the same type are called n-pass periodic points if their trajectories have n turns that lie outside a sufficiently small neighborhood of the hyperbolic point. Earlier in the articles of Sh. Newhouse, L. P. Shil’nikov, B. F. Ivanov and other authors, diffeomorphisms of the plane with a nontransversal homoclinic point were studied, it was assumed that this point is a tangency point of finite order. In these papers, it was shown that in a neighborhood of a homoclinic point there can be infinite sets of stable two-pass and three-pass periodic points. The presence of such sets depends on the properties of the hyperbolic point. In this paper, it is assumed that a homoclinic point is not a point with a finite order of tangency of a stable and unstable manifold. It is shown in the paper that for any fixed natural number n, a neighborhood of a nontransversal homolinic point can contain an infinite set of stable n-pass periodic points with characteristic exponents separated from zero.

Different types of stable periodic points of diffeomorphism of a plane with a homoclinic orbit

A diffeomorphism of the plane into itself with a fixed hyperbolic point is considered; the presence of a nontransverse homoclinic point is assumed. Stable and unstable manifolds touch each other at a homoclinic point; there are various ways of touching a stable and unstable manifold. In the works of Sh. Newhouse, L. P. Shilnikov and other authors, studied diffeomorphisms of the plane with a nontranverse homoclinic point, under the assumption that this point is a tangency point of finite order. It follows from the works of these authors that an infinite set of stable periodic points can lie in a neighborhood of a homoclinic point; the presence of such a set depends on the properties of the hyperbolic point. In this paper, it is assumed that a homoclinic point is not a point at which the tangency of a stable and unstable manifold is a tangency of finite order. Allocate a countable number of types of periodic points lying in the vicinity of a homoclinic point; points belonging to the same type are called n-pass (multi-pass), where n is a natural number. In the present paper, it is shown that if the tangency is not a tangency of finite order, the neighborhood of a nontransverse homolinic point can contain an infinite set of stable single-pass, double-pass, or three-pass periodic points with characteristic exponents separated from zero.

Average conservative chaos in quantum dusty plasmas.

We consider a hydrodynamic model of a quantum dusty plasma. We prove mathematically that the resulting dust ion-acoustic plasma waves present the property of being conservative on average. Furthermore, we test this property numerically, confirming its validity. Using standard techniques from the study of dynamical systems, as, for example, the Lyapunov characteristic exponents, we investigate the chaotic dynamics of the plasma and show numerically its existence for a wide range of parameter values. Finally, we illustrate how chaotic dynamics organizes in the parameter space for fixed values of the initial conditions, as the Mach number and the quantum diffraction parameter are continuously varied.

Minimal length effects on motion of a particle in Rindler space * *Supported in part by NSFC (11875196, 11375121, 11005016), the Fundamental Research Funds for the Central Universities, Natural Science Foundation of Chengdu University of TCM (ZRYY1729, ZRYY1921), Discipline Talent Promotion Program of /Xinglin Scholars(QNXZ2018050), the key fund project for Education Department of Sichuan (18ZA0173), the open fund of State

Various quantum theories of gravity predict the existence of a minimal measurable length. In this paper, we study effects of the minimal length on the motion of a particle in the Rindler space under a harmonic potential. This toy model captures key features of particle dynamics near a black hole horizon and allows us to make three observations. First, we find that chaotic behavior becomes stronger with increases in minimal length effects, leading predominantly to growth in the maximum Lyapunov characteristic exponents, while the KAM curves on Poincaré surfaces of a section tend to disintegrate into chaotic layers. Second, in the presence of the minimal length effects, it can take a finite amount of Rindler time for a particle to cross the Rindler horizon, which implies a shorter scrambling time of black holes. Finally, the model shows that some Lyapunov characteristic exponents can be greater than the surface gravity of the horizon, violating the recently conjectured universal upper bound. In short, our results reveal that quantum gravity effects may make black holes prone to more chaos and faster scrambling.

Dynamic Stability of Simply Supported Beams with Multi-Harmonic Parametric Excitation

Determination of the regions of dynamic instability has been an important issue for elastic structures. Under the extreme climate, the external load acting on structures is becoming more and more complicated, which can induce dynamic instability of elastic structures. In this study, we explore the dynamic instability and response characteristics of simply supported beams under multi-harmonic parametric excitation. A numerical approach for determining the instability regions under multi-harmonic parametric excitation is developed here by examining the eigenvalues of characteristic exponents of the monodromy matrix based on the Floquet theorem, and the fourth-order Runge–Kutta method is used to calculate the dynamic responses. The accuracy of the method is verified by the comparison with classical approximate boundary formulas of dynamic instability regions. The numerical results reveal that Bolotin’s approximate formulas are only applicable to the low-order instability regions with a small value of the excitation parameter of simple parametric resonance. Multi-harmonic parametric excitation can significantly change the dynamic instability regions, it may cause parametric resonance on beams for longitudinal complex periodic loads. The influence of frequency and number of multiply harmonics on the parametrically excited vibration of the beam is explored. High-order harmonics with low-frequency have positive effects on the stable response characteristics for multi-harmonic parametric excitation. This paper provides a new perspective for the vibration suppression of parametric excitation. The developed procedure can be used for multi-degree-of-freedom (MDOF) systems under complex excitation (e.g. tsunami waves and strong winds).