Power-law Correlations Research Articles

Long-range correlation analysis of high frequency prefrontal electroencephalogram oscillations for dynamic emotion recognition

Numerous previous studies have proved the enormous potential of high frequency EEG in emotion recognition, however, the current existing EEG analytic methods are not so effective when dealing with high frequency oscillations. Therefore, a novel refined-detrended fluctuation analysis method multi-order detrended fluctuation analysis (MODFA) was proposed. The best fitting order is selected according to the inflection point in the dependence degree curve of high frequency EEG and multi-order polynomial. MODFA measures the power-law long-range correlation of high frequency nonlinear signals. Prefrontal EEG signals were recorded during six emotion-inducing tasks (neutral, fear, sad, happy, anger, and disgust). To confirm the susceptibility and efficiency of MODFA indices, including hurst-exponent MODFA-h1 and intercept MODFA-a1, on emotion recognition, we compared MODFA with original detrended fluctuation analysis, as well as the conventionally used fuzzy entropy (FE) and power spectral density (PSD) on high frequency EEG oscillations (62.50–93.75 Hz). The results showed that MODFA achieved the best performance in binary emotion classification (positive and negative, accuracy = 96.81%), ternary classification (neutral, positive, and negative, accuracy = 76.39%), and six-classification (accuracy = 42.17%). Moreover, along with inducing time, the cumulative effects of the four negative emotions (fear, sad, anger, and disgust) were observed by MODFA-a1, FE, and PSD, which demonstrated that the accumulation of negative emotions are associated with the prefrontal lobe and could be measured via high frequency gamma rhythms. These findings indicated the nonlinear dynamics of high frequency brain activity during emotion induction, and the prefrontal EEG-based emotion recognition might have great application prospect in real-life practice.

High Grashof number turbulent natural convection on an infinite vertical wall

The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

Tempered fractional Brownian motion on finite intervals

Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic correlation time the power-law correlations between the increments of fractional Brownian motion. Here, we investigate such tempered fractional Brownian motion confined to a finite interval by reflecting walls. Specifically, we explore how the tempering of the long-time correlations affects the strong accumulation and depletion of particles near reflecting boundaries recently discovered for untempered fractional Brownian motion. We find that exponential tempering introduces a characteristic size for the accumulation and depletion zones but does not affect the functional form of the probability density close to the wall. In contrast, power-law tempering leads to more complex behavior that differs between the superdiffusive and subdiffusive cases.

Expanding and self-organizing 2D universe models emerging from frozen trivalent spin networks

We revisit the topic of self-organized criticality (SOC) in simple statistical graph models, with the purpose of capturing essential processes leading to the emergence of macroscopic spacetime from the microscopic dynamics in loop quantum gravity. We performed a large set of simulations based on extensions of the frozen trivalent spin network (TSN) model explored previously by Ansari and Smolin. Their model mimicked the sandpile dynamics by the application of random vertex propagation rules in the TSN, leading to an SOC behavior in the distribution of the avalanche sizes, as well as a slowly expanding, two-dimensional dual (triangulated) space. Here we show that a growth scheme for the stochastic, slow external driving force, differing from the classical sandpile model, also resulted in power-law distributed avalanche sizes. Our simulations also produced expanding dual spaces, with two basic classes of evolution: one with power-law correlations in ‘space’ and ‘time’, and the other with ‘loitering’ and exponential phases. Our work expands the range of models in which critical states in the TSN may lead to expansion effects in the dual space, without fine-tuning.

Cross-correlated fractal components of H-wave amplitude fluctuations in medial gastrocnemius and soleus muscles

The time series of the H-wave amplitude in soleus muscle (SOL) shows fractal (long-range) correlation, which is attributed to input from supraspinal centers. However, whether such long-range power-law correlated input also contributes to the synergistic muscles remains unclear. The purpose of this study was therefore to examine the correlation in the fractal components of H-wave amplitude fluctuations between the synergistic muscles used for plantar flexion, i.e., the medial head of the gastrocnemius muscle (MG) and SOL. In eight young male participants, consecutive H-reflexes were recorded almost simultaneously from the MG and SOL at a stimulation frequency of 0.5 Hz for 30 min. We performed detrending moving-average cross-correlation analysis (DMCA) for each of the H- and M-wave amplitude time series between MG and SOL to assess the existence of a common noise input contributing to these long-range correlations. The cross-correlation coefficient ρDMCA (−1 to 1) was calculated to quantify the strength of the correlation between two different time series. The results indicated a significant long-range power-law correlation between H-wave amplitudes in MG and SOL (ρDMCA: 0.50 (0.22) and 0.22 (0.17), mean (standard deviation) for the original and randomly shuffled surrogate data, respectively, P < 0.05). This was not the case for M-wave amplitudes (ρDMCA: 0.29 (0.23) and 0.20 (0.15), P > 0.05). We conclude that there is a common noise input governing these synergistic muscles, possibly due to supraspinal origin, causing long-range power-law correlations in monosynaptic reflexes.

Impact of momentum resolution on factorial moments due to power–law correlations between particles

The effect of momentum resolution on factorial moments due to the power–law correlation function is studied. The study is motivated by searching for the critical point of the strongly interacting matter in heavy-ion collisions using the intermittency method. We observe that factorial moments are significantly affected by the finite momentum resolution. The effect is superficially significant compared to intuitive expectations. The results depend on the power of the correlation function and the number of uncorrelated particles.

The extended generalized radial flow model and effective conductivity for truncated power law variograms

Pumping tests are established for characterizing spatial average properties of aquifers. At the same time, they are promising tools to identify heterogeneity characteristics such as log-conductivity variance and correlation scales. We present the extended Generalized Radial Flow Model (eGRF) which combines the characterization of well flow in fractal geometry with an upscaled conductivity for pumping tests in heterogeneous media. We show that the eGRF is a generalization of previously solutions, such as that of Barker, Butler and Neuman. We derive effective conductivities for uniform and well flow conditions in heterogeneous log-normal media with a truncated power law correlation structure through the upscaling procedure Coarse Graining. The radial-dependent effective conductivity for well flow reflects the gradual change of heterogeneity impact on average pumping test drawdowns. We then combine upscaled conductivities with the eGRF model to determine the effective pumping test solution. We provide a proof of concept by comparing theoretical upscaling results with Monte Carlo well flow simulations in heterogeneous fractal fields. The eGRF and upscaling results are implemented and made freely available as python code for transport simulation as well as pumping test analysis.

High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid.

We have performed density-matrix renormalization group studies of a square lattice t-J model with small hole doping, δ≪1, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, J_{2}=J_{1}/2, such that the undoped (δ=0) "parent" state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, K_{SC}≈1, consistent with a strongly diverging SC susceptibility, χ∼T^{-(2-K_{SC})} as the temperature T→0. The spin-spin correlations-as in the undoped state-fall exponentially suggesting that the SC "pairing" correlations evolve smoothly from the insulating parent state.

Robust d-Wave Superconductivity in the Square-Lattice t-J Model.

Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.

Scaling of factorial moments in cumulative variables

A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion collisions are analyzed in transverse-momentum, pT, space.In this regard, we have studied the dependence of the second scaled factorial moment F2 of particle multiplicity distribution on the number of subdivisions of transverse momentum-interval used in the analysis. The study is performed using a simple model with a power-law two-particle correlation function in pT. We observe that F2 values depend on the size and position of the pT interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, F2 calculated in subdivisions of the cumulative pT becomes independent of the cumulative-pT interval. The scaling behaviour of F2 for the cumulative variable is observed. Moreover, F2 follows a power law with the number of subdivisions of the cumulative-pT interval with the intermittency index close to the correlation function's exponent.

Experimental Study on the Relationship Between Capillary Pressure and Resistivity Index in Tight Sandstone Rocks

To further understand the relationship between the capillary pressure and resistivity index of tight reservoir sandstones, we measured these parameters using the semiporous plate method in four tight clayey sandstones from the Junggar Basin, China. To provide a benchmark for analyzing our results, we applied the same experimental procedures to four clay-free, tight Fontainebleau sandstones from the Paris Basin, France. We observed approximate power law relationships between the resistivity index and water saturation for Fontainebleau sandstones and Junggar Basin sandstones, in agreement with the Archie’s equation and Waxman-Smits equation, respectively. The capillary pressure and resistivity index data were differently related in the two types of sandstones. We observed a power law correlation for the Fontainebleau sandstones, whereas the Junggar sandstones showed a linear relationship. These differences in behavior appear to be primarily linked to the presence of clays in the Junggar sandstones but not in the Fontainebleau sandstone, and the difference in pore structure between the two types of sandstones.

The Flow Pattern Transition and Water Holdup of Gas–Liquid Flow in the Horizontal and Vertical Sections of a Continuous Transportation Pipe

A series of experiments were conducted to investigate the flow pattern transitions and water holdup during oil–water–gas three-phase flow considering both a horizontal section and a vertical section of a transportation pipe simultaneously. The flowing media were white mineral oil, distilled water, and air. Dimensionless numbers controlling the multiphase flow were deduced to understand the scaling law of the flow process. The oil–water–gas three-phase flow was simplified as the two-phase flow of a gas and liquid mixture. Based on the experimental data, flow pattern maps were constructed in terms of the Reynolds number and the ratio of the superficial velocity of the gas to that of the liquid mixture for different Froude numbers. The original contributions of this work are that the relationship between the transient water holdup and the changes of the flow patterns in a transportation pipe with horizontal and vertical sections is established, providing a basis for judging the flow patterns in pipes in engineering practice. A dimensionless power-law correlation for the water holdup in the vertical section is presented based on the experimental data. The correlation can provide theoretical support for the design of oil and gas transport pipelines in industrial applications.

Re-touch rebound patterns and contact time for a droplet impacting a superhydrophobic cylinder

BackgroundDroplet impact on a superhydrophobic cylinder differs from that on a flat surface. After bouncing, once re-touch takes place, the contact time τc would increase, which is unfavorable for some applications. The increased τc may strongly depend on the Weber number and radius ratio, R*, of cylinder to droplet. MethodsThe impact is investigated via lattice Boltzmann method simulations. The particular emphasis is placed on re-touch rebound patterns and τc. Significant findingsRebound patterns and τc both strongly depend on a combined parameter, α=We/R*, characterizing the asymmetry of droplet spreading and retraction. As α increases, upward rebound and stretched breakup take place sequentially for the first bouncing, whereas rebound patterns change as intact re-touch rebound and separate re-touch rebound for the second bouncing. Increasing α enhances the asymmetry, which promotes the first rebound, thereby reducing τc regardless of rebound patterns. The enhanced asymmetry also accelerates rebound and thus reduces τc in the separate re-touch rebound regime, whereas it hinders rebound, leading to a significantly increased τc. The power-law correlations of τc vs α are developed for the first and second bouncing. Besides, a method is proposed to suppress or prevent the re-touch, which is proven to effectively reduce τc.

Numerical study on complex conductivity characteristics of hydrate-bearing porous media

The complex conductivity method is frequently used in hydro-/petro-/environmental geophysics, and considered to be a promising tool for characterizing and quantifying the properties of subsurface rocks, sediments and soils. We report a study on the complex conductivity characteristics of porous media containing gas hydrates through numerical modelling. The effects of the hydrate saturation, pore-water salinity and micro-distribution mode were studied, and hydrate-saturation evaluation correlations based on complex conductivity parameters were developed. A pore-scale numerical approach for developing the finite-element based models for hydrate-bearing porous media is proposed and a two-dimensional (2D) model is built to compute the complex conductivity responses of porous media under various conditions. We demonstrate that the simple 2D model can capture the dominant characteristics of the complex conductivity of hydrate-bearing porous media within the frequency range related to the induced polarization. The in-phase conductivity, quadrature conductivity and effective dielectric constant can be correlated with the saturation based on a power law in the log-log space, by which the hydrate-saturation evaluation models can be derived. A constant saturation exponent of the power-law correlation between the hydrate saturation and quadrature conductivity can be obtained when the pore-water conductivity exceeds 1.0 S/m. This is highly desirable in the hydrate-saturation models due to the variations of the pore-water conductivity in the processes of hydrate formation and dissociation. Within the framework of the complex conductivity analysis, the micro-distribution modes of hydrates in porous media can be categorized into two types. These are the fluid-suspending mode and grain-attaching mode. The in-phase conductivity exhibits significant variations under the same saturation and salinity but different micro-distribution modes, which can be attributed to the change in the tortuosity of the electrical conduction paths in the void space of porous media.

An Empirical Correlation for the Penetration of a Cryogenic Liquid Jet into a Gaseous Crossflow

Empirical correlations have been widely used to map the penetration and trajectory of an injected liquid jet into a gaseous crossflow. Such correlations for the case of cryogenic liquid injection into a gaseous crossflow of the same species are limited. In this study, medium-resolution images of the injection of cryogenic liquid nitrogen into a gaseous nitrogen crossflow with momentum blowing ratios of 1-4 and Weber numbers of 1500-4500 are captured and image analysis is used to identify the jet boundary. Using these data, an empirical correlation for the penetration of liquid nitrogen into a gaseous crossflow as a function of momentum blowing ratio and downstream distance from the point of injection is developed. Minimizing the root mean square error of the correlation parameters over the full range of experimental conditions investigated leads to a power-law correlation with a mean error of 16%.

Nonequilibrium Floquet Steady States of Time-Periodic Driven Luttinger Liquids

Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the driving frequency approximately match twice the dispersion energy, which correspond to resonant states. In experimental systems of Lieb-Liniger bosons we predict a change from power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.

Fractional Brownian motion of worms in worm algorithms for frustrated Ising magnets.

We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. Viewing each step of the worm construction as a position increment (step) of a random walker, we demonstrate that the persistence exponent θ and the dynamical exponent z of this random walk depend only on the universal power-law exponents of the underlying critical phase and not on the details of the worm algorithm or the microscopic Hamiltonian. Further, we argue that the detailed balance condition obeyed by such worm algorithms and the power-law correlations of the underlying equilibrium system together give rise to two related properties of this random walk: First, the steps of the walk are expected to be power-law correlated in time. Second, the position distribution of the walker relative to its starting point is given by the equilibrium position distribution of a particle in an attractive logarithmic central potential of strength η_{m}, where η_{m} is the universal power-law exponent of the equilibrium defect-antidefect correlation function of the underlying spin system. We derive a scaling relation, z=(2-η_{m})/(1-θ), that allows us to express the dynamical exponent z(η_{m}) of this process in terms of its persistence exponent θ(η_{m}). Our measurements of z(η_{m}) and θ(η_{m}) are consistent with this relation over a range of values of the universal equilibrium exponent η_{m} and yield subdiffusive (z>2) values of z in the entire range. Thus, we demonstrate that the worms represent a discrete-time realization of a fractional Brownian motion characterized by these properties.

Simulation of Rayleigh-Benárd convection at up to [formula omitted] by generalized elliptic-relaxation hybrid RANS-LES model

We performed simulations of Rayleigh-Benárd convection (RBC) for very high Ra number, 109,1012,1013,1014 and 1016, thus beyond the reach of classical LES, by using an elliptic-relaxation hybrid RANS-LES (ER-HRL) model paired with a compound wall treatment that allows much coarser mesh resolution in the near wall region. The standard switching criterion used in the hybrid RANS-LES modeling based on wall distance is modified and linked to the local turbulence properties in order to sustain the modeled turbulence production in the RBC configuration. The proposed hybrid model successfully predicts the main integral and mean flow features at Ra=109 for which experimental and LES data exists. The Nusselt number obtained is closely following the power law correlation based on 0.307 exponent up to Ra=1013. For higher Ra number, the Nusselt number displays a Ra-scaling behaviour that is consistent with the so-called ultimate regime, where Nu≈Ra1/2. Furthermore, unlike LES, the ER-HRL model provides generally good results even when using a very coarse mesh at high Ra number. The instantaneous three-dimensional fields reveal interesting features of the Rayleigh-Benárd convection at very high Ra number such as a strong correlation between instantaneous pressure and temperature fields, a major similarity of the flow structures in the near-wall region to those present in the impinging jet, existence of the superstructures and their tendency to cluster and localise with increasing Ra number. The simulations are performed with an in–house unstructured finite-volume code T-Flows, using second-order-accuracy discretisation schemes for space and time.

Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches

Resting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. A distinctive attribute of systems at criticality is the presence of long-range correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow-band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, brain activity is a broadband phenomenon, and a significant piece of information useful to precisely discriminate between normal (critical) and pathological behavior (non-critical), may be encoded in the broadband spatio-temporal cortical dynamics. Here we propose to characterize the temporal correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that the avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms.

Bilayer Coulomb phase of two-dimensional dimer models: Absence of power-law columnar order.

Using renormalization group (RG) analyses and Monte Carlo (MC) simulations, we study the fully packed dimer model on the bilayer square lattice with fugacity equal to z (1) for interlayer (intralayer) dimers, and intralayer interaction V between neighboring parallel dimers on any elementary plaquette in either layer. For a range of not-too-large z>0 and repulsive interactions 0<V<V_{s} (with V_{s}≈2.1), we demonstrate the existence of a bilayer Coulomb phase with purely dipolar two-point functions, i.e., without the power-law columnar order that characterizes the usual Coulomb phase of square and honeycomb lattice dimer models. The transition line z_{c}(V) separating this bilayer Coulomb phase from a large-z disordered phase is argued to be in the inverted Kosterlitz-Thouless universality class. Additionally, we argue for the possibility of a tricritical point at which the bilayer Coulomb phase, the large-z disordered phase and the large-V staggered phase meet in the large-z, large-V part of the phase diagram. In contrast, for the attractive case with V_{cb}<V≤0 (V_{cb}≈-1.2), we argue that any z>0 destroys the power-law correlations of the z=0 decoupled layers, and leads immediately to a short-range correlated state, albeit with a slow crossover for small |V|. For V_{c}<V<V_{cb} (V_{c}≈-1.55), we predict that any small nonzero z immediately gives rise to long-range bilayer columnar order although the z=0 decoupled layers remain power-law correlated in this regime; this implies a nonmonotonic z dependence of the columnar order parameter for fixed V in this regime. Further, our RG arguments predict that this bilayer columnar ordered state is separated from the large-z disordered state by a line of Ashkin-Teller transitions z_{AT}(V). Finally, for V<V_{c}, the z=0 decoupled layers are already characterized by long-range columnar order, and a small nonzero z leads immediately to a locking of the order parameters of the two layers, giving rise to the same bilayer columnar ordered state for small nonzero z.