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Jun 30, 2018
06/18

by
B. Lehle; J. Peinke

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A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck noise $\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\eta$ is described by a Markov process in two dimensions. But even though there exists a variety of techniques for the analysis of Markov processes, it is still a challenge to estimate the process parameters solely based on a given time series of $X$. Such a partially observed 2D-process could, e.g., be analyzed in a Bayesian framework using Markov...

Topics: Physics, Data Analysis, Statistics and Probability, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1702.00032

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Sep 22, 2013
09/13

by
Ch. Renner; J. Peinke

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We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $\zeta_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of...

Source: http://arxiv.org/abs/cond-mat/0403496v1

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Sep 22, 2013
09/13

by
M. Siefert; J. Peinke

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We analyze the relationship of longitudinal and transverse increment statistics measured in isotropic small-scale turbulence. This is done by means of the theory of Markov processes leading to a phenomenological Fokker-Planck equation for the two increments from which a generalized Karman equation is derived. We discuss in detail the analysis and show that the estimated equation can describe the statistics of the turbulent cascade. A remarkably result is that the main differences between...

Source: http://arxiv.org/abs/physics/0409035v1

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Sep 22, 2013
09/13

by
M. Siefert; J. Peinke

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We address the problem of differences between longitudinal and transverse velocity increments in isotropic small scale turbulence. The relationship of these two quantities is analyzed experimentally by means of stochastic Markovian processes leading to a phenomenological Fokker- Planck equation from which a generalization of the Karman equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the difference in...

Source: http://arxiv.org/abs/physics/0309106v1

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Sep 20, 2013
09/13

by
A. P. Nawroth; J. Peinke

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A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of scales. It is possible to generate complete new time series, or to model the next steps for a given sequence of data. The method itself is based on the joint probability density which can be extracted directly from given data, thus no estimation of parameters...

Source: http://arxiv.org/abs/physics/0608069v1

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Sep 19, 2013
09/13

by
C. Renner; J. Peinke; R. Friedrich

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We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x,tau). This equation is completely determined by two coefficients...

Source: http://arxiv.org/abs/cond-mat/0102494v2

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Jul 20, 2013
07/13

by
St. Lück; J. Peinke; R. Friedrich

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The transition to fully developed turbulence of a wake behind a circular cylinder is investigated with respect to its statistics. In particular, we evaluated the probability density functions of velocity increments on different length scales $r$. Evidence is presented that the $r$-dependence of the velocity increments can be taken as Markov processes in the far field, as well as, in the near field of the cylinder wake. With the estimation of the deterministic part of these Markov processes, as...

Source: http://arxiv.org/abs/physics/9902010v1

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Sep 18, 2013
09/13

by
S. Siegert; R. Friedrich; J. Peinke

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This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the noisy data sets, and deterministic laws and fluctuating forces of the dynamics can be identified. The method is validated by the application to simulated one- and two-dimensional noisy data sets.

Source: http://arxiv.org/abs/cond-mat/9803250v1

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Sep 17, 2013
09/13

by
M. Siefert; J. Peinke; R. Friedrich

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This letter reports on a new method of analysing experimentally gained time series with respect to different types of noise involved, namely, we show that it is possible to differentiate between dynamical and measurement noise. This method does not depend on previous knowledge of model equations. For the complicated case of a chaotic dynamics spoiled at the same time by dynamical and measurement noise, we even show how to extract from data the magnitude of both types of noise. As a further...

Source: http://arxiv.org/abs/physics/0108034v2

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Sep 23, 2013
09/13

by
F. Böttcher; St. Barth; J. Peinke

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Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no matter what location is considered. The shape of these PDFs is found to be robust over a wide range of scales which seems to contradict the mathematical concept of stability where a Gaussian distribution should be the limiting one. Motivated by the...

Source: http://arxiv.org/abs/nlin/0408005v3

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Sep 22, 2013
09/13

by
T. Laubrich; F. Ghasemi; J. Peinke; H. Kantz

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We study the statistics of the horizontal component of atmospheric boundary layer wind speed. Motivated by its non-stationarity, we investigate which parameters remain constant or can be regarded as being piece-wise constant and explain how to estimate them. We will verify the picture of natural atmospheric boundary layer turbulence to be composed of successively occurring close to ideal turbulence with different parameters. The first focus is put on the fluctuation of wind speed around its...

Source: http://arxiv.org/abs/0811.3337v1

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Jun 30, 2018
06/18

by
A. Hadjihosseini; J. Peinke; N. P. Hoffmann

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This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information of multi-scale processes. In particular we show evidence of Markov properties for increment processes, which means that a three point closure for the complexity of the wave structures...

Topics: Physics, Data Analysis, Statistics and Probability, Atmospheric and Oceanic Physics

Source: http://arxiv.org/abs/1402.4366

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Sep 17, 2013
09/13

by
M. Alber; S. Lueck; C. Renner; J. Peinke

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The notion of self-similar energy cascades and multifractality has long since been connected with fully developed, homogeneous and isotropic turbulence. We introduce a number of amendments to the standard methods for analysing the multifractal properties of the energy dissipation field of a turbulent flow. We conjecture that the scaling assumption for the moments of the energy dissipation rate is valid within the transition range to dissipation introduced by Castaing et al.(Physica D (46), 177...

Source: http://arxiv.org/abs/nlin/0007014v1

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Sep 22, 2013
09/13

by
M. Waechter; F. Riess; H. Kantz; J. Peinke

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For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method was applied to different road surface profiles which were measured with high resolution. Evidence of Markov properties is...

Source: http://arxiv.org/abs/physics/0310159v1

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Sep 18, 2013
09/13

by
D. Kleinhans; R. Friedrich; A. Nawroth; J. Peinke

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A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217 (2000)], which requires sufficiently high sampling rates. The analysis is based on an iterative procedure minimizing the Kullback-Leibler distance between measured and estimated two time joint probability distributions of the process.

Source: http://arxiv.org/abs/physics/0502152v2

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Sep 18, 2013
09/13

by
S. Kriso; R. Friedrich; J. Peinke; P. Wagner

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Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow dynamics can be extracted directly from the measured data. As a result a Langevin equation for the traffic flow is obtained. From the deterministic part of the flow dynamics, stable fixed points are extracted and set into relation with common features of the...

Source: http://arxiv.org/abs/physics/0110084v1

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Sep 21, 2013
09/13

by
R. Friedrich; Ch. Renner; M. Siefert; J. Peinke

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Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"

Source: http://arxiv.org/abs/physics/0203005v1

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Sep 19, 2013
09/13

by
P. Toth; A. P. Krekhov; L. Kramer; J. Peinke

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We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical...

Source: http://arxiv.org/abs/cond-mat/9911397v1

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Sep 18, 2013
09/13

by
A. P. Nawroth; J. Peinke; D. Kleinhans; R. Friedrich

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An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimisation routine is...

Source: http://arxiv.org/abs/0705.1292v1

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Sep 20, 2013
09/13

by
Fatemeh Ghasemi; J. Peinke; M. Reza Rahimi Tabar; Muhammad Sahimi

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Statistical properties of interbeat intervals cascade are evaluated by considering the joint probability distribution $P(\Delta x_2,\tau_2;\Delta x_1,\tau_1)$ for two interbeat increments $\Delta x_1$ and $\Delta x_2$ of different time scales $\tau_1$ and $\tau_2$. We present evidence that the conditional probability distribution $P(\Delta x_2,\tau_2|\Delta x_1,\tau_1)$ may obey a Chapman-Kolmogorov equation. The corresponding Kramers-Moyal (KM) coefficients are evaluated. It is shown that...

Source: http://arxiv.org/abs/q-bio/0601051v1

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Sep 20, 2013
09/13

by
M. Waechter; F. Riess; Th. Schimmel; U. Wendt; J. Peinke

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This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of...

Source: http://arxiv.org/abs/physics/0404015v2

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Sep 23, 2013
09/13

by
J. Peinke; M. Reza Rahimi Tabar; Muhammad Sahimi; F. Ghasemi

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We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a...

Source: http://arxiv.org/abs/cond-mat/0411529v2

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Sep 22, 2013
09/13

by
F. Ghasemi; Muhammad Sahimi; J. Peinke; M. Reza Rahimi Tabar

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We describe a method for analyzing the stochasticity in the non-stationary data for the beat-to-beat fluctuations in the heart rates of healthy subjects, as well as those with congestive heart failure. The method analyzes the returns time series of the data as a Markov process, and computes the Markov time scale, i.e., the time scale over which the data are a Markov process. We also construct an effective stochastic continuum equation for the return series. We show that the drift and diffusion...

Source: http://arxiv.org/abs/physics/0603130v1

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Sep 23, 2013
09/13

by
Ch. Renner; J. Peinke; R. Friedrich; O. Chanal; B. Chabaud

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The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding...

Source: http://arxiv.org/abs/physics/0109052v1

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Sep 22, 2013
09/13

by
F. Shayeganfar; M. Holling; J. Peinke; M. Reza Rahimi Tabar

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The level crossing and inverse statistics analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, $\nu_{\alpha}^+$, where $T_{\alpha} =1/\nu_{\alpha}^+ $ is the average waiting time for observing the level $\alpha$ again. We estimate the probability $P(K, \alpha)$, which provides us the probability of observing $K$ times of the level $\alpha$ with positive slope, in time scale $T_{\alpha}$. For analyzed time series we found that...

Source: http://arxiv.org/abs/1001.4401v3

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Sep 21, 2013
09/13

by
P. Manshour; S. Saberi; Muhammad Sahimi; J. Peinke; Amalio F. Pacheco; M. Reza Rahimi Tabar

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We report on a novel stochastic analysis of seismic time series for the Earth's vertical velocity, by using methods originally developed for complex hierarchical systems, and in particular for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced change of the shapes of the probability density functions (PDF) of the series' increments. Before and close to an earthquake the shape of the PDF and the long-range correlation in the increments...

Source: http://arxiv.org/abs/0902.4331v1

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Sep 23, 2013
09/13

by
V. V. Vasconcelos; F. Raischel; M. Haase; J. Peinke; M. Wächter; P. G. Lind; D. Kleinhans

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We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf-bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of...

Source: http://arxiv.org/abs/1105.1700v2

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Sep 23, 2013
09/13

by
M. Reza Rahimi Tabar; Muhammad Sahimi; K. Kaviani; M. Allamehzadeh; J. Peinke; M. Mokhtari; M. Vesaghi; M. D. Niry; F. Ghasemi; A. Bahraminasab; S. Tabatabai; F. Fayazbakhsh

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We propose a novel method for analyzing precursory seismic data before an earthquake that treats them as a Markov process and distinguishes the background noise from real fluctuations due to an earthquake. A short time (on the order of several hours) before an earthquake the Markov time scale $t_M$ increases sharply, hence providing an alarm for an impending earthquake. To distinguish a false alarm from a reliable one, we compute a second quantity, $T_1$, based on the concept of extended...

Source: http://arxiv.org/abs/physics/0510043v1