arXiv subjects

M. Reza Rahimi Tabar

Publications and source records attributed to M. Reza Rahimi Tabar.

At least 19 recordsLinked to original sources

arXiv2023

Assessing the Suitability of the Langevin Equation for Analyzing Measured Data Through Downsampling

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms, ranging from continuous trajectories reminiscent of Brownian motion to noncontinuous trajectories featuring jump events. The Langevin equation serves as a powerful tool for generating stochasticity and capturing the complex behavior of measured data with continuous stochastic characteristics. However, the traditional modeling framework of the Langevin equation falls short when it comes to capturing the presence of abrupt changes, particularly jumps, in trajectories that exhibit non-continuity. Such non-continuous changes pose a significant challenge for general processes and have profound implications for risk management. Moreover, the discrete nature of observed physical phenomena, measured with a finite sample rate, adds another layer of complexity. In such cases, data points often appear as a series of discontinuous jumps, even when the underlying trajectory is continuous. In this study, we present an analytical framework that goes beyond the limitations of the Langevin equation. Our approach effectively distinguishes between diffusive or Brownian-type trajectories and trajectories with jumps. By employing downsampling techniques, where we artificially lower the sample rate, we derive a set of measures and criteria to analyze the data and differentiate between diffusive and non-diffusive behaviors. To further demonstrate its versatility and practical applicability, we have applied our proposed method to real-world data in various scientific fields, turbulence, optical tweezers for trapped particles, neuroscience, renewable energy, and market price analysis.

cond-mat.stat-mech↗

arXiv2023

Data-Driven Reconstruction of Stochastic Dynamical Equations based on Statistical Moments

Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid. If such processes are Markov, then their probability distribution is governed by the Kramers-Moyal (KM) equation, a partial differential equation that involves an infinite number of coefficients, which depend on the state variable. The KM coefficients must be evaluated based on measured time series for a data-driven reconstruction of the governing equations for the stochastic dynamics. We present an accurate method of computing the KM coefficients, which relies on computing the coefficients' conditional moments based on the statistical moments of the time series. The method's advantages over state-of-the-art approaches are demonstrated by investigating prototypical stochastic processes with well-known properties.

cond-mat.stat-mech↗

arXiv2023

Discontinuous Jump Behavior of the Energy Conversion in Wind Energy Systems

The power conversion process of a wind turbine can be characterized by a stochastic differential equation (SDE) of the power output conditioned to certain fixed wind speeds. An analogous approach can also be applied to the mechanical loads on a wind turbine, such as generator torque. The constructed SDE consists of the deterministic and stochastic terms, the latter corresponding to the highly fluctuating behavior of the wind turbine. Here we show how advanced stochastic analysis of the noise contribution can be used to show different operating modes of the conversion process of a wind turbine. The parameters of the SDE, known as Kramers-Moyal (KM) coefficients, are estimated directly from the measurement data. Clear evidence is found that both, continuous diffusion noise and discontinuous jump noise are present. The difference in the noise contributions indicates different operational regions. In particular, we observe that the jump character or discontinuity in power production has a significant contribution in the regions where the control system switches strategies. We find that there is a high increase in jump amplitude near the transition to the rated region, and the switching strategies cannot result in a smooth transition. The proposed analysis provides new insights to the control strategies of the wind turbine.

eess.SY↗

arXiv2019

Analysis and data-driven reconstruction of bivariate jump-diffusion processes

We introduce the bivariate jump-diffusion process, comprising two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, non-parametric estimation procedure of higher-order (up to 8) Kramers-Moyal coefficients that allows one to reconstruct relevant aspects of the underlying jump-diffusion processes and to recover the underlying parameters. The procedure is validated with numerically integrated data using synthetic bivariate time series from continuous and discontinuous processes. We further evaluate the possibility of estimating the parameters of the jump-diffusion model via data-driven analyses of the higher-order Kramers-Moyal coefficients, and the limitations arising from the scarcity of points in the data or disproportionate parameters in the system.

nlin.AO↗

arXiv2019

Exact enumeration approach to first-passage time distribution of non-Markov random walks

We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of a fractional Brownian motion with a Hurst exponent $H\in(1/2,1)$ that describes numerous non-Markov stochastic phenomena in physics, biology and geology, and for which the limit $H=1/2$ represents a Markov process.

cond-mat.stat-mech↗

arXiv2018

The Excursion set approach: Stratonovich approximation and Cholesky decomposition

The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first crossing distribution of a suitably chosen barrier by random walks having correlated steps: The shape of the barrier is determined by the physics of nonlinear collapse, and the correlations between steps by the nature of the initial density fluctuation field. We describe analytic and numerical methods for calculating such first up-crossing distributions. While the exact solution can be written formally as an infinite series, we show how to approximate it efficiently using the Stratonovich approximation. We demonstrate its accuracy using Monte-Carlo realizations of the walks, which we generate using a novel Cholesky-decomposition based algorithm, which is significantly faster than the algorithm that is currently in the literature.

astro-ph.CO↗

arXiv2016

Suppressing the non-Gaussian statistics of Renewable Power from Wind and Solar

The power from wind and solar exhibits a nonlinear flickering variability, which typically occurs at time scales of a few seconds. We show that high-frequency monitoring of such renewable powers enables us to detect a transition, controlled by the field size, where the output power qualitatively changes its behaviour from a flickering type to a diffusive stochastic behaviour. We find that the intermittency and strong non-Gaussian behavior in cumulative power of the total field, even for a country-wide installation still survives for both renewable sources. To overcome the short time intermittency, we introduce a time-delayed feedback method for power output of wind farm and solar field that can change further the underlying stochastic process and suppress their strong non- gaussian fluctuations.

physics.soc-ph↗

arXiv2016

Short term fluctuations of wind and solar power systems

Wind and solar power are known to be highly influenced by weather events and may ramp up or down abruptly. Such events in the power production influence not only the availability of energy, but also the stability of the entire power grid. By analysing significant amounts of data from several regions around the world with resolutions of seconds to minutes, we provide strong evidence that renewable wind and solar sources exhibit multiple types of variability and nonlinearity in the time scale of {\it seconds} and characterise their stochastic properties. In contrast to previous findings, we show that only the jumpy characteristic of renewable sources decreases when increasing the spatial size over which the renewable energies are harvested. Otherwise, the strong non-Gaussian, intermittent behaviour in the cumulative power of the total field survives even for a country-wide distribution of the systems. The strong fluctuating behaviour of renewable wind and solar sources can be well characterised by Kolmogorov-like power spectra and $q-$exponential probability density functions. Using the estimated potential shape of power time series, we quantify the jumpy or diffusive dynamic of the power. Finally we propose a time delayed feedback technique as a control algorithm to suppress the observed short term non-Gaussian statistics in spatially strong correlated and intermittent renewable sources.

physics.data-an↗

arXiv2015

Fully Developed Turbulence in the view of Horizontal Visibility Graphs

We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network features which is in agreement with recent empirical studies.

physics.flu-dyn↗

arXiv2013

Surface roughness analysis of the hydrophilic SiO_2/TiO_2 nano bi-layers by Level crossing approach

The effect of etching time on the statistical properties of the hydrophilic surface of SiO_2/TiO_2/Glass nano bi-layer has been studied using Atomic Force Microscopy (AFM) and stochastic approach based on the level crossing analysis. We have created a rough surface of the hydrophilic SiO_2/TiO_2 nano bi-layer system by using 26% Potassium Hydroxide (KOH) solution. Measuring the average apparent contact angle assessed the degree of hydrophilicity and the optimum condition was determined at 10 min etching time. Level crossing analysis based on AF images provided deeper insight into the microscopic details of the surface topography. For different etching time, it has been shown that the average frequency of visiting a height with positive slope behaves Gaussian for heights near the mean value and obeys power law for the heights far away from the mean value. Finally, by applying the generalized total number of crossings with positive slope, it was found that the both high heights and deep valleys of the surface are extremely effective in hydrophilic degree of the SiO_2/TiO_2/Glass nano bi-layer investigated system.

cond-mat.mtrl-sci↗

arXiv2013

Dynamic renormalization group analysis of propagation of elastic waves in two-dimensional heterogeneous media

We study localization of elastic waves in two-dimensional heterogeneous solids with randomly distributed Lamé coefficients, as well as those with long-range correlations with a power-law correlation function. The Matin-Siggia-Rose method is used, and the one-loop renormalization group (RG) equations for the the coupling constants are derived in the limit of long wavelengths. The various phases of the coupling constants space, which depend on the value $ρ$, the exponent that characterizes the power-law correlation function, are determined and described. Qualitatively different behaviors emerge for $ρ<1$ and $ρ>1$. The Gaussian fixed point (FP) is stable (unstable) for $ρ<1$ ($ρ>1$). For $ρ<1$ there is a region of the coupling constants space in which the RG flows are toward the Gaussian FP, implying that the disorder is irrelevant and the waves are delocalized. In the rest of the disorder space the elastic waves are localized. We compare the results with those obtained previously for acoustic wave propagation in the same type of heterogeneous media, and describe the similarities and differences between the two phenomena.

cond-mat.dis-nn↗

arXiv2013

Numerical simulation of the localization of elastic waves in two- and three-dimensional heterogeneous media

Localization of elastic waves in two-dimensional (2D) and three-dimensional (3D) media with random distributions of the Lamé coefficients (the shear and bulk moduli) is studied, using extensive numerical simulations. We compute the frequency-dependence of the minimum positive Lyapunov exponent $γ$ (the inverse of the localization length) using the transfer-matrix method, the density of states utilizing the force-oscillator method, and the energy-level statistics of the media. The results indicate that all the states may be localized in the 2D media, up to the disorder width and the smallest frequencies considered, although the numerical results also hint at the possibility that there might a small range of the allowed frequencies over which a mobility edge might exist. In the 3D media, however, most of the states are extended, with only a small part of the spectrum in the upper band tail that contains localized states, even if the Lamé coefficients are randomly distributed. Thus, the 3D heterogeneous media still possess a mobility edge. If both Lamé coefficients vary spatially in the 3D medium, the localization length $Λ$ follows a power law near the mobility edge, $Λ\sim(Ω-Ω_c)^{-ν}$, where $Ω_c$ is the critical frequency. The numerical simulation yields, $ν\simeq 1.89\pm 0.17$, significantly larger than the numerical estimate, $ν\simeq 1.57\pm 0.01$, and $ν=3/2$, which was recently derived by a semiclassical theory for the 3D Anderson model of electron localization...

cond-mat.dis-nn↗

arXiv2011

The level crossing and inverse statistic analysis of German stock market index (DAX) and daily oil price time series

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, $ν_α^+$, where $T_α =1/ν_α^+ $ is the average waiting time for observing the level $α$ again. We estimate the probability $P(K, α)$, which provides us the probability of observing $K$ times of the level $α$ with positive slope, in time scale $T_α$. For analyzed time series we found that maximum $K$ is about 6. We show that by using the level crossing analysis one can estimate how the DAX and oil time series will develop. We carry out same analysis for the increments of DAX and oil price log-returns,(which is known as inverse statistics) and provide the distribution of waiting times to observe some level for the increments.

q-fin.ST↗

arXiv2011

Long range correlation in cosmic microwave background radiation

We investigate the statistical anisotropy and Gaussianity of temperature fluctuations of Cosmic Microwave Background radiation (CMB) data from {\it Wilkinson Microwave Anisotropy Probe} survey, using the multifractal detrended fluctuation analysis, rescaled range and scaled windowed variance methods. The multifractal detrended fluctuation analysis shows that CMB fluctuations has a long range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of temperature fluctuation of CMB is mainly due to the long-range correlations and the map is consistent with a Gaussian distribution.

astro-ph↗

arXiv2011

Markov Properties of Electrical Discharge Current Fluctuations in Plasma

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal's coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyal's coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyal's coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.

cond-mat.stat-mech↗

arXiv2009

Fractal Analysis of Discharge Current Fluctuations

We use the multifractal detrended fluctuation analysis (MF-DFA) to study the electrical discharge current fluctuations in plasma and show that it has multifractal properties and behaves as a weak anti-correlated process. Comparison of the MF-DFA results for the original series with those for the shuffled and surrogate series shows that correlation of the fluctuations is responsible for multifractal nature of the electrical discharge current.

cond-mat.stat-mech↗

arXiv2009

Conductance of disordered graphene superlattice

We study the conductance of disordered graphene superlattices with short-range structural correlations. The system consists of electron- and hole-doped graphenes of various thicknesses, which fluctuate randomly around their mean value. The effect of the randomness on the probability of transmission through the system of various sizes is studied. We show that in a disordered superlattice the quasiparticle that approaches the barrier interface almost perpendicularly transmits through the system. The conductivity of the finite-size system is computed and shown that the conductance vanishes when the sample size becomes very large, whereas for some specific structures the conductance tends to a nonzero value in the thermodynamics limit.

cond-mat.mes-hall↗

arXiv2009

Turbulent-Like Behavior of Seismic Time Series

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 both manifest significant changes. For a moderate or large-size earthquake the typical time at which the PDF undergoes the transition from a Gaussian to a non-Gaussian is about 5-10 hours. Thus, the transition represents a new precursor for detecting such earthquakes.

physics.geo-ph↗