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Fuchs A, Herbert C, Rolland J, Wächter M, Bouchet F, Peinke J. Instantons and the Path to Intermittency in Turbulent Flows. Phys Rev Lett 2022; 129:034502. [PMID: 35905359 DOI: 10.1103/physrevlett.129.034502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Revised: 02/23/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular instantons with negative entropy pinpoint the trajectories responsible for the emergence of non-Gaussian statistics at small scales.
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Affiliation(s)
- A Fuchs
- Institute of Physics and ForWind, University of Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
| | - C Herbert
- Ens de Lyon, CNRS, Laboratoire de Physique, F-69364 Lyon, France
| | - J Rolland
- Université de Lille, CNRS, ONERA, Arts et Métiers Institute of Technology, Centrale Lille, UMR 9014 - LMFL - Laboratoire de Mécanique des fluides de Lille - Kampé de Fériet, F-59000 Lille, France
| | - M Wächter
- Institute of Physics and ForWind, University of Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
| | - F Bouchet
- Ens de Lyon, CNRS, Laboratoire de Physique, F-69364 Lyon, France
| | - J Peinke
- Institute of Physics and ForWind, University of Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
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2
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Schmietendorf K, Kamps O, Wolff M, Lind PG, Maass P, Peinke J. Bridging between load-flow and Kuramoto-like power grid models: A flexible approach to integrating electrical storage units. Chaos 2019; 29:103151. [PMID: 31675812 DOI: 10.1063/1.5099241] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Accepted: 08/16/2019] [Indexed: 06/10/2023]
Abstract
In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands toward short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow one to investigate storage-related issues from scratch. Our aim here is twofold: First, we remove this shortcoming by adopting a standard practice in electrical engineering and bring together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto-like framework with arbitrary grid components. Second, we use this concept and demonstrate the implementation of a storage unit in a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement, and point out their limitations by maximum capacity and finite-time response. With that, we provide a solid starting point for the integration of flexible storage units into Kuramoto-like grid models enabling to address current problems like smart storage control, optimal siting, and rough cost estimations.
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Affiliation(s)
- Katrin Schmietendorf
- ForWind and Institut für Physik, Universität Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
| | - O Kamps
- Center for Nonlinear Science, Universität Münster, Correnstraße 2, 48149 Münster, Germany
| | - M Wolff
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | - P G Lind
- Department of Computer Science, Oslo Metropolitan University, P.O. Box 4 St. Olavs plass, N-0130 Oslo, Norway
| | - P Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | - J Peinke
- ForWind and Institut für Physik, Universität Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
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3
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Abstract
A scalar Langevin-type process X(t) that is driven by Ornstein-Uhlenbeck noise η(t) is non-Markovian. However, the joint dynamics of X and η 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 chain Monte Carlo methods. Alternatively, an embedding strategy can be applied, where first the joint dynamics of X and its temporal derivative X[over ̇] is analyzed. Subsequently, the results can be used to determine the process parameters of X and η. In this paper, we propose a more direct approach that is purely based on the moments of the increments of X, which can be estimated for different time-increments τ from a given time series. From a stochastic Taylor expansion of X, analytic expressions for these moments can be derived, which can be used to estimate the process parameters by a regression strategy.
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Affiliation(s)
- B Lehle
- Institute of Physics, University of Oldenburg, D-26111 Oldenburg, Germany
| | - J Peinke
- Institute of Physics, University of Oldenburg, D-26111 Oldenburg, Germany
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4
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Lehle B, Peinke J. Analyzing a stochastic time series obeying a second-order differential equation. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:062113. [PMID: 26172667 DOI: 10.1103/physreve.91.062113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2014] [Indexed: 06/04/2023]
Abstract
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.
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Affiliation(s)
- B Lehle
- Institute of Physics, University of Oldenburg, D-2611 Oldenburg, Germany
| | - J Peinke
- Institute of Physics, University of Oldenburg, D-2611 Oldenburg, Germany
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5
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Abstract
Julia sets are self-similar separatrices of the coast-line type found in noninvertible 2-D maps. The same class of maps also generates hyperchaos (chaos with two mixing directions). Smale’s notion of a “nontrivial basic set” provides a connection. These sets arise when a chaotic (or hyperchaotic) attractor “explodes”. In the case of more than one escape route, this set becomes a “fuzzy boundary” (Mira). Its projection as the map becomes noninvertible (1-D ) is a “Julia set in 1 D ”. In the analogous hyperchaos case the 2-D limiting map contains a classical Julia set of the continuous type. An identically looking set can also be obtained within a non-exploded hyperchaotic attractor, however, as a “cloud”. Julia-like attractors therefore exist. The theory also predicts Mandelbrot sets for 4-D flows. Julia-like behavior is a new, numerically easy-to-test for property o f most nontrivial dynamical systems.
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Affiliation(s)
- O. E. Rössler
- Institute for Physical and Theoretical Chemistry, University o f Tübingen, West Germany
| | - C. Kahlert
- Institute for Physical and Theoretical Chemistry, University o f Tübingen, West Germany
| | - J. Parisi
- Physical Institute, University o f Tübingen, West Germany
| | - J. Peinke
- Physical Institute, University o f Tübingen, West Germany
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Parisi J, Peinke J, Röhricht B, Rau U, Klein M, Rössler OE. Notizen: Comparison Between a Generic Reaction- Diffusion Model and a Synergetic Semiconductor System. ACTA ACUST UNITED AC 2014. [DOI: 10.1515/zna-1987-0623] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
This paper gives a concrete physical interpretation of a simple dynamical model based on the universal Rashevsky- Turing theory of symmetry-breaking morphogenesis in terms of spatio-temporal nonlinear transport phenomena in a synergetic semiconductor system.
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Affiliation(s)
- J. Parisi
- Physikalisches Institut II, Universität Tübingen
| | - J. Peinke
- Physikalisches Institut II, Universität Tübingen
| | - B. Röhricht
- Physikalisches Institut II, Universität Tübingen
| | - U. Rau
- Physikalisches Institut II, Universität Tübingen
| | - M. Klein
- Institut für Physikalische und Theoretische Chemie. Universität Tübingen
| | - O. E. Rössler
- Institut für Physikalische und Theoretische Chemie. Universität Tübingen
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7
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Keylock CJ, Nishimura K, Peinke J. A classification scheme for turbulence based on the velocity-intermittency structure with an application to near-wall flow and with implications for bed load transport. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/2011jf002127] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Vasconcelos VV, Raischel F, Haase M, Peinke J, Wächter M, Lind PG, Kleinhans D. Principal axes for stochastic dynamics. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:031103. [PMID: 22060324 DOI: 10.1103/physreve.84.031103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2011] [Revised: 07/29/2011] [Indexed: 05/31/2023]
Abstract
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 the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
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Affiliation(s)
- V V Vasconcelos
- Physics Department, Faculty of Sciences, University of Lisbon, P-1649-003 Lisbon, Portugal
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9
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Stresing R, Kleinhans D, Friedrich R, Peinke J. Different methods to estimate the Einstein-Markov coherence length in turbulence. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 83:046319. [PMID: 21599307 DOI: 10.1103/physreve.83.046319] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2010] [Revised: 12/15/2010] [Indexed: 05/30/2023]
Abstract
We study the Markov property of experimental velocity data of different homogeneous isotropic turbulent flows. In particular, we examine the stochastic "cascade" process of nested velocity increments ξ(r):=u(x+r)-u(x) as a function of scale r for different nesting structures. It was found in previous work that, for a certain nesting structure, the stochastic process of ξ(r) has the Markov property for step sizes larger than the so-called Einstein-Markov coherence length l(EM), which is of the order of magnitude of the Taylor microscale λ [Phys. Lett. A 359, 335 (2006)]. We now show that, if a reasonable definition of the effective step size of the process is applied, this result holds independently of the nesting structure. Furthermore, we analyze the stochastic process of the velocity u as a function of the spatial position x. Although this process does not have the exact Markov property, a characteristic length scale l(u(x))≈l(EM) can be identified on the basis of a statistical test for the Markov property. Using a method based on the matrix of transition probabilities, we examine the significance of the non-Markovian character of the velocity u(x) for the statistical properties of turbulence.
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Affiliation(s)
- R Stresing
- Institute of Physics, University of Oldenburg, D-26111 Oldenburg, Germany
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10
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Manshour P, Ghasemi F, Matsumoto T, Gómez J, Sahimi M, Peinke J, Pacheco AF, Tabar MRR. Anomalous fluctuations of vertical velocity of Earth and their possible implications for earthquakes. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:036105. [PMID: 21230137 DOI: 10.1103/physreve.82.036105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2009] [Revised: 02/09/2010] [Indexed: 05/30/2023]
Abstract
High-quality measurements of seismic activities around the world provide a wealth of data and information that are relevant to understanding of when earthquakes may occur. If viewed as complex stochastic time series, such data may be analyzed by methods that provide deeper insights into their nature, hence leading to better understanding of the data and their possible implications for earthquakes. In this paper, we provide further evidence for our recent proposal [P. Mansour, Phys. Rev. Lett. 102, 014101 (2009)10.1103/PhysRevLett.102.014101] for the existence of a transition in the shape of the probability density function (PDF) of the successive detrended increments of the stochastic fluctuations of Earth's vertical velocity V_{z} , collected by broadband stations before moderate and large earthquakes. To demonstrate the transition, we carried out extensive analysis of the data for V_{z} for 12 earthquakes in several regions around the world, including the recent catasrophic one in Haiti. The analysis supports the hypothesis that before and near the time of an earthquake, the shape of the PDF undergoes significant and discernable changes, which can be characterized quantitatively. The typical time over which the PDF undergoes the transition is about 5-10 h prior to a moderate or large earthquake.
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Affiliation(s)
- Pouya Manshour
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran
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11
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Abstract
We apply a method based on the theory of Markov processes to fractal-generated turbulence and obtain joint probabilities of velocity increments at several scales. From experimental data we extract a Fokker-Planck equation which describes the interscale dynamics of the turbulence. In stark contrast to all documented boundary-free turbulent flows, the multiscale statistics of velocity increments, the coefficients of the Fokker-Planck equation, and dissipation-range intermittency are all independent of Rλ (the characteristic ratio of inertial to viscous forces in the fluid). These properties define a qualitatively new class of turbulence.
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Affiliation(s)
- R Stresing
- Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany
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12
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Lind PG, Haase M, Böttcher F, Peinke J, Kleinhans D, Friedrich R. Extracting strong measurement noise from stochastic time series: applications to empirical data. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 81:041125. [PMID: 20481695 DOI: 10.1103/physreve.81.041125] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2009] [Revised: 03/30/2010] [Indexed: 05/29/2023]
Abstract
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function, the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method, we apply the algorithm to synthetic as well as climatological measurement data, namely, the daily North Atlantic Oscillation index, shedding light on the discussion of the nature of its underlying physical processes.
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Affiliation(s)
- P G Lind
- Center for Theoretical and Computational Physics, University of Lisbon, Avenida Professor Gama Pinto 2, 1649-003 Lisbon, Portugal
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13
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Manshour P, Saberi S, Sahimi M, Peinke J, Pacheco AF, Rahimi Tabar MR. Turbulencelike behavior of seismic time series. Phys Rev Lett 2009; 102:014101. [PMID: 19257196 DOI: 10.1103/physrevlett.102.014101] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2008] [Indexed: 05/27/2023]
Abstract
We report on a stochastic analysis of Earth's vertical velocity time series 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 transition in their probability density function from Gaussian to non-Gaussian. The transition occurs 5-10 hours prior to a moderate or large earthquake, hence representing a new and reliable precursor for detecting such earthquakes.
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Affiliation(s)
- P Manshour
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran
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14
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Nawroth AP, Peinke J, Kleinhans D, Friedrich R. Improved estimation of Fokker-Planck equations through optimization. Phys Rev E Stat Nonlin Soft Matter Phys 2007; 76:056102. [PMID: 18233713 DOI: 10.1103/physreve.76.056102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2007] [Indexed: 05/25/2023]
Abstract
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 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 optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine.
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Affiliation(s)
- A P Nawroth
- Institut for Physics, Carl-von-Ossietzky University Oldenburg, D-26111 Oldenburg, Germany
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Ghasemi F, Sahimi M, Peinke J, Friedrich R, Jafari GR, Tabar MRR. Markov analysis and Kramers-Moyal expansion of nonstationary stochastic processes with application to the fluctuations in the oil price. Phys Rev E Stat Nonlin Soft Matter Phys 2007; 75:060102. [PMID: 17677203 DOI: 10.1103/physreve.75.060102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2007] [Revised: 05/09/2007] [Indexed: 05/16/2023]
Abstract
We describe a general method for analyzing a nonstationary stochastic process X(t) which, unlike many of the previous analysis methods, does not require X(t) to have any scaling feature. The method is used to study the fluctuations in the daily price of oil. It is shown that the returns time series, y(t)=ln[X(t+1)X(t)] , is a stationary and Markov process, characterized by a Markov time scale t_{M} . The coefficients of the Kramers-Moyal expansion for the probability density function P(y,tmid R:y_{0},t_{0}) are computed. P(y,tmid R:,y_{0},t_{0}) satisfies a Fokker-Planck equation, which is equivalent to a Langevin equation for y(t) that provides quantitative predictions for the oil price over times that are of the order of t_{M}. Also studied is the average frequency of positive-slope crossings, nu_{alpha};{+}=P(y_{i}>alpha,y_{i-1}<alpha) , for the returns, where T(alpha)=1nu_{alpha};{+} is the average waiting time for observing y(t)=alpha again.
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Affiliation(s)
- Fatemeh Ghasemi
- The Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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17
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Ghasemi F, Sahimi M, Peinke J, Tabar MRR. Analysis of non-stationary data for heart-rate fluctuations in terms of drift and diffusion coefficients. J Biol Phys 2006; 32:117-28. [PMID: 19669455 PMCID: PMC2646998 DOI: 10.1007/s10867-006-9006-z] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022] Open
Abstract
We describe a method for analyzing the stochasticity in 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 return 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 coefficients, as well as the amplitude of the return time series for healthy subjects are distinct from those with CHF. Thus, the method may potentially provide a diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, as it can distinguish small differences between the data for the two classes of subjects in terms of well-defined and physically-motivated quantities.
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Affiliation(s)
- F Ghasemi
- Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran
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18
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Tabar M, Ghasemi F, Peinke J, Friedrich R, Kaviani K, Taghavi F, Sadeghi S, Bizhani G, Sahimi M. New computational approaches to the analysis of interbeat intervals in human subjects. Comput Sci Eng 2006. [DOI: 10.1109/mcse.2006.29] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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19
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Siefert M, Peinke J. Different cascade speeds for longitudinal and transverse velocity increments of small-scale turbulence. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 70:015302. [PMID: 15324118 DOI: 10.1103/physreve.70.015302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2003] [Indexed: 05/24/2023]
Abstract
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 Kármán equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the differences in the scaling properties of these two structure functions.
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Affiliation(s)
- M Siefert
- Institut für Physik, Carl-von-Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany
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20
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Friedrich R, Renner C, Siefert M, Peinke J. Comment on "Indispensable finite time corrections for Fokker-Planck equations from time series data". Phys Rev Lett 2002; 89:149401-149402. [PMID: 12366083 DOI: 10.1103/physrevlett.89.149401] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2001] [Indexed: 05/23/2023]
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21
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Abstract
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) (max(R(lambda) approximately 1200). 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 Markov processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more comprehensive method, our results are very far from a possible universal state, even for R(lambda) above 1000.
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Affiliation(s)
- Ch Renner
- Fachbereich Physik, Carl-von-Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany
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22
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Friedrich R, Peinke J, Renner C. How to quantify deterministic and random influences on the statistics of the foreign exchange market. Phys Rev Lett 2000; 84:5224-5227. [PMID: 10990908 DOI: 10.1103/physrevlett.84.5224] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/1999] [Revised: 11/16/1999] [Indexed: 05/23/2023]
Abstract
It is shown that price changes of the U.S. dollar-German mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore, we show how Kramers-Moyal coefficients can be estimated from the empirical data. Finally, we present an explicit Fokker-Planck equation which models very precisely the empirical probability distributions, in particular, their non-Gaussian heavy tails.
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Affiliation(s)
- R Friedrich
- Institute fur Theoretische Physik, Universitat Stuttgart, D-70550 Stuttgart, Germany
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25
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Richter R, Kittel A, Heinz G, Flätgen G, Peinke J, Parisi J. Type-I intermittency in semiconductor breakdown: An experimental confirmation. Phys Rev B Condens Matter 1994; 49:8738-8746. [PMID: 10009653 DOI: 10.1103/physrevb.49.8738] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Heinz G, Richter R, Kittel A, Flätgen G, Peinke J, Parisi J. Experimental realization of mode locking during intrinsic quasiperiodicity in p-type germanium. Phys Rev B Condens Matter 1993; 48:12603-12608. [PMID: 10007628 DOI: 10.1103/physrevb.48.12603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Abstract
Abstract We observe the phenomenon of stochastic resonance in a semiconductor experiment. Originally, such an effect was predicted for bistable dynamical systems that are influenced by a periodic modulation as well as a random perturbation. In that case, a "resonance" peak can be observed in the power spectrum. The phenomenon investigated is the low-temperature impact ionization breakdown. There, bistability results from the competing states of low and high conductance.
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Affiliation(s)
- A. Kittel
- 1Physical Institute, University of Tübingen, Tübingen, Germany
| | - R. Richter
- 1Physical Institute, University of Tübingen, Tübingen, Germany
| | - M. Hirsch
- 1Physical Institute, University of Tübingen, Tübingen, Germany
| | - G. Flätgen
- 1Physical Institute, University of Tübingen, Tübingen, Germany
| | - J. Peinke
- 2C.R.T.B.T.-C.N.R.S., Grenoble, France
| | - J. Parisi
- 3Physical Institute, University of Bayreuth, Bayreuth, Germany
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Peinke J, Richter R, Parisi J. Spatial coherence of nonlinear dynamics in a semiconductor experiment. Phys Rev B Condens Matter 1993; 47:115-124. [PMID: 10004423 DOI: 10.1103/physrevb.47.115] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Richter R, Rau U, Kittel A, Heinz G, Peinke J, Parisi J, Huebener RP. On the Scaling of Type-1 Intermittency in a Semiconductor Experiment. ACTA ACUST UNITED AC 1991. [DOI: 10.1515/zna-1991-1202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract Spontaneous oscillations developing during low-temperature impact ionization breakdown in extrinsic germanium are looked at with respect to characteristic features of type-I intermittency
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Affiliation(s)
- R. Richter
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
| | - U. Rau
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
| | - A. Kittel
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
| | - G. Heinz
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
| | - J. Peinke
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
| | - J. Parisi
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
| | - R. P. Huebener
- 1Physical Institute, University of Tübingen, W-7400 Tübingen, Germany
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Rau U, Clauss W, Kittel A, Lehr M, Bayerbach M, Parisi J, Peinke J, Huebener RP. Classification of spontaneous oscillations at the onset of avalanche breakdown in p-type germanium. Phys Rev B Condens Matter 1991; 43:2255-2262. [PMID: 9997499 DOI: 10.1103/physrevb.43.2255] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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31
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Lehr M, Huebener RP, Rau U, Parisi J, Clauss W, Peinke J, Röhricht B. Nonequilibrium phase transition in the electronic transport of p-type germanium at low temperatures. Phys Rev B Condens Matter 1990; 42:9019-9024. [PMID: 9995115 DOI: 10.1103/physrevb.42.9019] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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32
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Peinke J, Parisi J, R�hricht B, Mayer KM, Rau U, Clau� W, Huebener RP, Jungwirt G, Prettl W. Classification of current instabilities during low-temperature breakdown in germanium. ACTA ACUST UNITED AC 1989. [DOI: 10.1007/bf01141278] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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33
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R�hricht B, Parisi J, Peinke J, Huebener RP. Spontaneous resistance oscillations inp-germanium at low temperatures and their spatial correlation. ACTA ACUST UNITED AC 1987. [DOI: 10.1007/bf01303901] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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34
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35
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Röhricht B, Wessely B, Peinke J, Mühlbach A, Parisi J, Huebener R. Chaos and Hyperchaos in the post-breakdown regime of p-germanium. ACTA ACUST UNITED AC 1985. [DOI: 10.1016/0378-4363(85)90356-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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36
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Abstract
p-Ge electrically driven into the post-breakdown regime at liquid-He temperatures produces voltage oscillations which can be attributed to the formation of a chaotic attractor. Under variation of an applied magnetic field, a change in this attractor takes place which apparently reflects an increase in attractor dimensionality. A sequence of phase plots is presented which is interpreted as a transition from ordinary chaos to hyperchaos.
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Affiliation(s)
- J. Peinke
- 1Physikalisches Institut II. Universität Tübingen
| | - B. Röhricht
- 1Physikalisches Institut II. Universität Tübingen
| | - A. Mühlbach
- 1Physikalisches Institut II. Universität Tübingen
| | - J. Parisi
- 1Physikalisches Institut II. Universität Tübingen
| | - Ch. Nöldeke
- 1Physikalisches Institut II. Universität Tübingen
| | | | - O. E. Rössler
- 2Institut für Physikalische und Theoretische Chemie. Universität Tübingen
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