共查询到20条相似文献,搜索用时 593 毫秒
1.
We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D(1) and D(2), representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar. 相似文献
2.
Lie-Poisson structure of the Lorenz’63 system gives a physical insight on its dynamical and statistical behavior considering
the evolution of the associated Casimir functions. We study the invariant density and other recurrence features of a Markov
expanding Lorenz-like map of the interval arising in the analysis of the predictability of the extreme values reached by particular
physical observables evolving in time under the Lorenz’63 dynamics with the classical set of parameters. Moreover, we prove
the statistical stability of such an invariant measure. This will allow us to further characterize the SRB measure of the
system. 相似文献
3.
Rudolf FriedrichJoachim Peinke Muhammad SahimiM. Reza Rahimi Tabar 《Physics Reports》2011,506(5):87-162
This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions. 相似文献
4.
The construction of an Ito model for geoelectrical signals 总被引:3,自引:0,他引:3
Zbigniew Czechowski 《Physica A》2011,390(13):2511-2519
The Ito stochastic differential equation governs the one-dimensional diffusive Markov process. Geoelectrical signals measured in seismic areas can be considered as the result of competitive and collective interactions among system elements. The Ito equation may constitute a good macroscopic model of such a phenomenon in which microscopic interactions are adequately averaged. The present study shows how to construct an Ito model for a geoelectrical time series measured in a seismic area of southern Italy. Our results reveal that the Ito model describes the whole time series quite well, but it performs better when one considers fragments of the data set with lower variability range (absent or rare large fluctuations). Our findings show that generally detrended geoelectrical time series can be considered as approximations of Markov diffusion processes. 相似文献
5.
The influence of fluctuations on the kinetic processes of Brownian motion is investigated. We consider fluctuations for which the correlation time is comparable with the relaxation time of the distribution function. Taking such large scale fluctuations into account is shown to lead to a change of the diffusion coefficient and to the appearance of additional correlations in the motions of Brownian particles. An expression is obtained for the correlation function of a Langevin source in the diffusion equation taking into account the contribution of large scale fluctuations. 相似文献
6.
V. I. Shishov 《Waves in Random and Complex Media》1995,5(4):497-507
Fluctuations of the interferometric response, averaged partly with an integration time much greater than the temporal scale of the diffraction scintillations and less than the temporal scale of the refraction scintillations, are discussed. The second moments of the interferometric response are obtained using a perturbation series for the partly-averaged coherence function. The correlations between the fluctuations of the partly-averaged flux and the coherence-length estimates are also obtained. The variances of these values are determined. 相似文献
7.
8.
We consider the scattering problem for absorptive interactions within the framework of phase-function method. A Green’s function
approach is used to derive the phase equation. As a case study we apply the algorithm presented on a shallow α-α potential,
the real and imaginary parts of which have been deduced from experimental data. The real and imaginary parts of theS-wave phase shift are found to vary smoothly with energy while those forD andG waves show some fluctuations in the low-energy region. It is shown that studies in spatial behaviour of the phase function
provide a plausible explanation for the dynamical origin of these fluctuations. 相似文献
9.
《Physica A》2006,369(2):655-678
Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients. 相似文献
10.
Many theoretical models have recently been proposed to understand the structure of cellular systems composed of various types of elements (e.g., proteins, metabolites and genes) and their interactions. However, the cell is a highly dynamic system with thousands of functional elements fluctuating across temporal states. Therefore, structural analysis alone is not sufficient to reproduce the cell's observed behavior.In this article, we analyze the gene expression dynamics (i.e., how the amount of mRNA molecules in cell fluctuate in time) by using a new constructive approach, which reveals a symmetry embedded in gene expression fluctuations and characterizes the dynamical equation of gene expression (i.e., a specific stochastic differential equation). First, by using experimental data of human and yeast gene expression time series, we found a symmetry in short-time transition probability from time t to time t+1. We call it self-similarity symmetry (i.e., the gene expression short-time fluctuations contain a repeating pattern of smaller and smaller parts that are like the whole, but different in size). Secondly, we reconstruct the global behavior of the observed distribution of gene expression (i.e., scaling-law) and the local behavior of the power-law tail of this distribution. This approach may represent a step forward toward an integrated image of the basic elements of the whole cell. 相似文献
11.
It is shown that the experimentally investigated structural ion-sound plasma turbulence is a self-similar stationary random
process. The self-similarity parameter is determined by two temporal laws: the nonrandom character of the appearance of nonlinear
structures (nonlinear ion-sound solitons) in the plasma, and the nonlinear interaction between them. As the distance from
the threshold of the ion-sound current instability increases, the self-similar random process approaches a Gaussian random
process, but this limit has not been attained experimentally. The possibility of recording superlong time series of the fluctuations
of the signal of the plasma process and processing of the time series by the R/S analysis method has made it possible to prove self-similarity of the plasma structural turbulence.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 203–208 (10 August 1999) 相似文献
12.
Electron density fluctuations as well as current density correlations are considered for excited nano plasmas. Calculations are performed by classical MD simulations at high temperatures for expanding nearly spherical clusters of laser irradiated sodium atoms. The resonance structures observed in the frequency spectrum of the bi‐local correlation functions are analyzed. Mie modes and volume plasmon type excitations are observed as well as breathing modes. We investigate the relation between the bi‐local correlation functions of the electron density fluctuations and current density via the equation of continuity.The collective excitations are of significance for the dielectric function and further properties such as the photo absorption coefficients. Results are presented for an exemplarily taken set of parameter values of the nano plasma (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
The silo discharge process is studied by molecular
dynamics simulations. The development of the velocity profile and
the probability density function for the displacements in the
horizontal and vertical axis are obtained. The PDFs obtained at
the beginning of the discharge reveal non-Gaussian statistics and
superdiffusive behaviors. When the stationary flow is developed,
the PDFs at shorter temporal scales are non-Gaussian too. For big
orifices a well-defined transition between ballistic and diffusive
regime is observed. In the case of a small outlet orifice, no
well-defined transition is observed. We use a nonlinear diffusion
equation introduced in the framework of non-extensive
thermodynamics in order to describe the movements of the grains.
The solution of this equation gives a well-defined relationship
(γ= 2/(3-q)) between the anomalous diffusion exponent
γ and the entropic parameter q introduced by the
non-extensive formalism to fit the PDF of the fluctuations. 相似文献
14.
R. Taranko P. Parafiniuk 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,84(1):89-97
We consider the electron transport through one-level quantum dot, out of the Kondo
regime, under the influence of the external microwave fields. The influence of the
intra-dot Coulomb electron-electron interaction is studied using the equation of motion
method for appropriate correlation functions. The formula for the current and the closed
set of the integro-differential equations for the expectation values of the quantum dot
charge states are given. The most characteristic feature of these time-averaged
expectation values is an appearance of the additional structure (sidebands) on the curves
of the derivatives of the expectation values with respect to the gate voltage. The
sidebands structure formed on both sides of the ‘ionization’ and ‘affinity’ quantum dot
levels are also found on the current and differential conductance curves. 相似文献
15.
Noel Corngold 《Journal of statistical physics》2005,120(3-4):521-541
We consider particle transport in a spatially random medium, the transport governed by the traditional, linear, time- and
space-dependent transport equation for “host and guest.” The scattering is elastic and isotropic; there is no absorption.
If the host medium has uniform density we know that an initial burst will, in time, approach the solution to the time-dependent
diffusion equation. In the case of random medium we find that for a large class of such media the asymptotic behavior is unchanged
by the stochasticity; there is neither renormalization of the equation nor the diffusion co-efficient.The nature of the correlation
between fluctuations of density at large separation plays an important role in the analysis. 相似文献
16.
Detailed analysis is presented of the well-known Tatarskii’s formula, which describes sound wave scattering in a turbulent
atmosphere. The adiabaticity of the acoustic fluctuations and incompressibility of the turbulent fluctuations are assumed
only. This yields to additional 1 terms in the classical formula (probably, small in the inertial range of turbulence). We
show the change of Obukhov’s formula, which describes the connection between turbulent fluctuations of pressure and velocities
in a compressible atmosphere, and also demonstrate the effect of the independence of fluctuations of the potential and thermodynamic
temperatures. By analogy with the formula for small-scale isotropic temperature fluctuations, which was also obtained by Obukhov,
we derive a formula for the fluctuations of entropy and potential density as function of entropy, which describes spatial
distribution of the probability density of identical “fluid particles” in the turbulent media. 相似文献
17.
《Waves in Random and Complex Media》2013,23(4):497-507
Abstract Fluctuations of the interferometric response, averaged partly with an integration time much greater than the temporal scale of the diffraction scintillations and less than the temporal scale of the refraction scintillations, are discussed. The second moments of the interferometric response are obtained using a perturbation series for the partly-averaged coherence function. The correlations between the fluctuations of the partly-averaged flux and the coherence-length estimates are also obtained. The variances of these values are determined. 相似文献
18.
Ovidiu Buhucianu Marina-Aura Dariescu Ciprian Dariescu 《International Journal of Theoretical Physics》2012,51(2):526-535
In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field
and a static magnetic induction, both directed along the normal to the sample’s plane. The Klein–Gordon equation describing
the relativistic bosons leads to a Mathieu’s type equation for the temporal part of the wave functions. It follows that, for
the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions
are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic
stationary amplitude behavior. 相似文献
19.
To model chirped fiber Bragg gratings (FBGs) for dispersion compensation in optical fibers a novel method of single expression
(MSE) is used. The reformulation of Helmholtz’s equation in the MSE to the full set of first-order differential equations
leads to dealing with the electric field amplitude, its derivative, power flow density and phase distributions in any aperiodic
media. The phase derivative obtained numerically permits to compute the dispersion slope in the time delay of investigated
chirped gratings. Reflective and time delay spectra of linearly chirped gratings of different lengths and chirp coefficients
are computed. A self-similarity law for the gratings of the same strength but different lengths and chirp coefficients is
revealed. The apodization of gratings is applied to reduce sidelobes in gratings’ reflection spectra and eliminate oscillations
in the time delay characteristics. 相似文献
20.
E. Minguzzi 《Communications in Mathematical Physics》2010,298(3):855-868
Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion
of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the
causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog
in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to
the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K
+ relation (Seifert’s relation). By exploiting this analogy, we are able to import some mathematical results, most notably
Peleg’s and Levin’s theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover
the K
+ (or Seifert) relation which indeed turns out to be the intersection of the time or temporal orderings. This result tells
us in which circumstances it is possible to recover the chronological or causal relation starting from the set of time or
temporal functions allowed by the spacetime. Moreover, it is proved that a chronological spacetime in which the closure of
the causal relation is transitive (for instance a reflective spacetime) admits a semi-time function. Along the way a new proof
avoiding smoothing techniques is given that the existence of a time function implies stable causality, and a new short proof
of the equivalence between K-causality and stable causality is given which takes advantage of Levin’s theorem and smoothing techniques. 相似文献