[Show abstract][Hide abstract] ABSTRACT: 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.
Full-text · Article · Aug 2015 · Journal of Statistical Mechanics Theory and Experiment
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We study the metal–insulator transition in one-dimensional Anderson binary alloy with long-range disordered hopping integrals and on-site energies using the transfer matrix method. In this model, the on-site energies and hopping integrals are distributed randomly with long-range correlations characterized by power spectrum of the type , with different exponents and , respectively. We determine the critical value of long-range correlation exponent of hopping integral in the presence of only off-diagonal disorder in which the transition from localized to extended states occurs in thermodynamic limit. When both of the on-site energies and hopping integrals are disordered, there are two parameters and that control the metal–insulator transition in the system. We draw the phase diagram which separates the localized regime from extended one and it shows the critical values of for a given value of .
No preview · Article · Jan 2015 · Post Communist Economies
[Show abstract][Hide abstract] ABSTRACT: With increasing the contribution of renewable energies in power production, the task of reducing dynamic instability in power grids must also be addressed from the generation side, because the power delivered from such sources is spatiotemporally stochastic in nature. Here we characterize the stochastic properties of the wind and solar energy sources by studying their spectrum and multifractal exponents. The computed power spectrum from high frequency time series of solar irradiance and wind power reveals a power-law behaviour with an exponent ∼ 5/3 (Kolmogorov exponent) for the frequency domain 0.001 Hz f
No preview · Article · Oct 2014 · The European Physical Journal Special Topics
[Show abstract][Hide abstract] ABSTRACT: Although fluctuations in the waiting time series have been studied for a long time, some important issues
such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained
unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations
with Hurst exponents belonging to the interval 1/2 < H < 1. We also study positive-negative level asymmetry
of the waiting time distribution. We find that the logarithmic difference of waiting times series has a short-range
correlation, and then we study its stochastic nature using the Markovian method and determine the corresponding
Kramers-Moyal coefficients. As an example, we analyze the velocity fluctuations in high Reynolds number
turbulence and determine the level dependence ofMarkov time scales, as well as the drift and diffusion coefficients.
We show that the waiting time distributions exhibit power law tails, and we were able to model the distribution
with a continuous time random walk.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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 be 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 the Lamé coefficients vary spatially in the 3D medium, the localization length Λ follows a power law near the mobility edge, Λ∼(Ω−Ωc)−ν, where Ωc is the critical frequency. The numerical estimate, ν≃1.89±0.17, is significantly larger than the numerical estimate, ν≃1.57±0.01, and ν=3/2 (which was recently derived by a semiclassical theory for the 3D Anderson model of electron localization). If the shear modulus is constant but the bulk modulus varies spatially, the plane waves with transverse polarization propagate without any scattering—leading to a band of completely extended states, even in the 2D media. At the mobility edge of such media the localization length follows the same type of power law as Λ but with an exponent νT≃1/2 for both 2D and 3D media.
[Show abstract][Hide abstract] ABSTRACT: Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the "waiting times" series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2<H<1. We also study positive-negative level asymmetry of the waiting time distribution. We find that the logarithmic difference of waiting times series has a short-range correlation, and then we study its stochastic nature using the Markovian method and determine the corresponding Kramers-Moyal coefficients. As an example, we analyze the velocity fluctuations in high Reynolds number turbulence and determine the level dependence of Markov time scales, as well as the drift and diffusion coefficients. We show that the waiting time distributions exhibit power law tails, and we were able to model the distribution with a continuous time random walk.
Full-text · Article · Jun 2013 · Physical Review E
[Show abstract][Hide abstract] ABSTRACT: The effect of etching time on the statistical properties of hydrophilic surfaces of SiO2/TiO2/glass nano bilayers has been studied using atomic force microscopy (AFM) and a stochastic approach based on a level crossing analysis. We have created rough surfaces of the hydrophilic SiO2/TiO2 nano bilayer system by using 26% potassium hydroxide (KOH) solution. Measuring the average apparent contact angle allowed us to assess the degree of hydrophilicity, and the optimum condition was determined to be 10 min etching time. A level crossing analysis based on AFM images provided deeper insight into the microscopic details of the surface topography. With different etching times, it has been shown that the average frequency of visiting a height with positive slope behaves in a Gaussian manner for heights near the mean value and obeys a power law for 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 have a great effect on the hydrophilic degree of the SiO2/TiO2/glass nano bilayer investigated system.
No preview · Article · May 2013 · Physica A: Statistical Mechanics and its Applications
[Show abstract][Hide abstract] ABSTRACT: Large-scale ab initio molecular-dynamics simulations have been carried out to
compute, at human-body temperature, the vibrational modes and lifetimes of pure and hydrated
dipalmitoylphosphatidylcholine (DPPC) lipids. The projected atomic vibrations calculated from
the spectral energy density are used to compute the vibrational modes and the lifetimes. All the
normal modes of the pure and hydrated DPPC and their frequencies are identified. The computed
lifetimes incorporate the full anharmonicity of the atomic interactions. The vibrational modes of
the water molecules close to the head group of DPPC are active (possess large projected spectrum
amplitudes) in the frequency range 0.5–55 THz, with a peak at 2.80THz in the energy spectrum.
The computed lifetimes for the high-frequency modes agree well with the recent data measured at
room temperature where high-order phonon scattering is not negligible. The computed lifetimes
of the low-frequency modes can be tested using the current experimental capabilities. Moreover,
the approach may be applied to other lipids and biomolecules, in order to predict their vibrational
dispersion relations, and to study the dynamics of vibrational energy transfer.
[Show abstract][Hide abstract] ABSTRACT: Using the cross-correlation of the wavelet transformation, we propose a general method of studying the scale dependence of the direction of coupling for coupled time series. The method is first demonstrated by applying it to coupled van der Pol forced oscillators and coupled nonlinear stochastic equations. We then apply the method to the analysis of the log-return time series of the stock values of the IBM and General Electric (GE) companies. Our analysis indicates that, on average, IBM stocks react earlier to possible common sector price movements than those of GE.
Full-text · Article · Feb 2013 · Journal of Statistical Mechanics Theory and Experiment
[Show abstract][Hide abstract] ABSTRACT: Glossary
Definition of the Subject
Stochastic Time Series Analysis
Applications: Processes in Time
Applications: Processes in Scale
[Show abstract][Hide abstract] ABSTRACT: Analysis of flow in fluidized beds, a common chemical reactor, is of much current interest due to its fundamental as well as industrial importance. Experimental data for the successive increments of the pressure fluctuations time series in a fluidized bed are analyzed by computing a multiscale probability density function (PDF) of the increments. The results demonstrate the evolution of the shape of the PDF from the short to long time scales. The deformation of the PDF across time scales may be modeled by the log-normal cascade model. The results are also in contrast to the previously proposed PDFs for the pressure fluctuations that include a Gaussian distribution and a PDF with a power-law tail. To understand better the properties of the pressure fluctuations, we also construct the shuffled and surrogate time series for the data and analyze them with the same method. It turns out that long-range correlations play an important role in the structure of the time series that represent the pressure fluctuation.
Preview · Article · Jul 2012 · Journal of Statistical Mechanics Theory and Experiment
[Show abstract][Hide abstract] ABSTRACT: We study the electronic properties of superlattice with rough interfaces in two and three dimensions using the transfer-matrix method and direct diagonalization of the Anderson Hamiltonian. The system consists of layers with an average constant width, but with stochastic roughness added to the interfaces between the layers. The numerical results indicate that, in the thermodynamic limit, the two-dimensional superlattice is an insulator in the presence of even small roughness. In three-dimensional systems, however, the superlattice exhibits a metal-insulator transition with a well-defined mobility edge located at an energy Ec that we compute numerically. For three-dimensional superlattice, the localization length follows a power law near the mobility edge ξ(E)∼(Ec−E)−ν, where the exponent is ν≃1.6. We also show that the existence of the extended states in three-dimensional superlattices gives rise to a finite conductivity in the limit M/L→∞, where L is the length and M the width of the bar.
[Show abstract][Hide abstract] ABSTRACT: We report the complete assignment of the vibrational spectrum of dipalmitoylphosphatidylcholine (DPPC), which belongs to the most ubiquitous membrane phospholipid family, phosphatidylcholine. We find that water hydrating the lipid headgroups enables efficient energy transfer across membrane leaflets on sub-picosecond time scales. The emergence of spatially extended vibrational modes upon hydration, underlies this phenomenon. Our findings illustrate the importance of collective molecular behavior of biomembranes and reveal that hydrated lipid membranes can act as efficient media for the transfer of vibrational energy.
Full-text · Article · May 2012 · The Journal of Physical Chemistry B
[Show abstract][Hide abstract] ABSTRACT: The single and multiple scattering regimes of electromagnetic waves in a disordered system with fluctuating permittivity are studied by numerical simulations of Maxwell's equations. For an array of emitters and receivers in front of a medium with randomly varying dielectric constant, we calculate the backscattering matrix from the signal responses at all receiver points j to electromagnetic pulses generated at each emitter point i. We show that the statistical properties of the backscattering matrix are in agreement with the recent experimental results for ultrasonic waves (Aubry A. and Derode A., Phys. Rev. Lett., 102 (2009) 084301) and light (Popoff S. M. et al., Phys. Rev. Lett., 104 (2010) 100601). In the multiple scattering regime the singular value distribution of the backscattering matrix obeys the quarter-circle law.
[Show abstract][Hide abstract] ABSTRACT: We investigate the structure and electronic properties of phosphatidylcholine (PC) under different degrees of hydration at the single-molecule and monolayer type level by linear scaling ab initio calculations. Upon hydration, the phospholipid undergoes drastic long-range conformational rearrangements which lead to a sickle-like ground-state shape. The structural unit of the tilted gel-phase PC appears to be a water-bridged PC dimer. We find that hydration dramatically alters the surface potential, dipole and quadrupole moments of the lipids and consequently guides the interactions of the lipids with other molecules and the communication between cells.
No preview · Article · Mar 2012 · The Journal of Chemical Physics
[Show abstract][Hide abstract] ABSTRACT: 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.