Intermittency Parameter Research Articles

Lattice Boltzmann Simulation for two-dimensional bacterial turbulence

The minimal numerical simulation of two-dimensional bacterial turbulence is investigated by using the Lattice Boltzmann method (LBM). The dynamic behavior of incompressible 2D meso-scale turbulence is described by Toner–Tu theory and the Swift–Hohenberg-type fourth-order term. The double scaling of energy spectrum is obtained. At larger scale, the scaling behaviors of energy spectrum E(k)∼k5∕3. The energy spectrum E(k)∼k−8∕3 at smaller scale, which is corresponding to experiment and simulation results. The collection behavior of self-organized pattern is described. By a coarse-graining approach, the energy cascades to large scale and the enstrophy cascades to small scale at l<3R. The intermittency exists in two scaling region of energy spectrum. The measured scaling exponents ζ(p) are determined by a lognormal formula. The measured intermittency parameter is μ=0.26 which denotes the more intermittency in small scale range of 2D meso-scale turbulence.

Vortex statistics in two-dimensional turbulence based on IB-LBM

In this paper, the two-dimensional (2D) turbulence perturbed by arrays of cylinders placed both horizontally and vertically is investigated by Immersed Boundary Lattice Boltzmann Method (IB-LBM). The energy spectrum reveals the coexistence of the inverse and direct cascades in 2D grid turbulence. By observing at the distribution of fluxes in space, the energy and enstrophy fluxes have explained the physical mechanism of the double cascades where the two Kolmogorov laws for structure functions are simultaneously observed. The results of vortex statistics by the conditional analysis, which are based on a new and accurate vortex identification criteria called Liutex, show that the algebraic number density [Formula: see text], where [Formula: see text] is vortex area. The time-evolving vortex number density distribution constructs a theoretical framework involving a three-part: [Formula: see text]; [Formula: see text]; [Formula: see text], which is satisfied with the prediction well. The relationship between the vortex circulation [Formula: see text] and vortex area [Formula: see text] is [Formula: see text] and the one between the kinetic energy of vortex [Formula: see text] and [Formula: see text] is [Formula: see text] in the range where [Formula: see text]. Moreover, it has been found that vortices contain about 30% of the total energy of the flow by studying the energy ratio of all vortices to the entire flow field. What is more, it is an interesting phenomenon is that there is only a range where [Formula: see text] in the energy spectrum for the coherent structure field which is obtained by using Liutex as the extraction of vortices. The probability density function (PDF) of the fluctuations of longitudinal velocity shows that an indication of small intermittency in the direct cascade and the absence of intermittency in the inverse cascade range. On the other hand, the scaling exponents [Formula: see text] of the structure function for the inverse cascade are consistent with Kr67 model, which shows the absence of intermittency. While the measured intermittency parameters are [Formula: see text] and [Formula: see text], which explains that there is a very weak intermittent correction in the direct cascade, and ESS has verified the existence of intermittency in our 2D turbulence.

Study of Solder Joint Intermittent Fault Diagnosis Based on Dynamic Analysis

For intermittent fault diagnosis, it is important to extract fault features. Since different package modes have different dynamic characteristics, an intermittent fault diagnosis method based on the dynamic analysis of solder joints is proposed. First, solder joint intermittent fault dynamic models of different packaging modes are constructed, and the dynamic response characteristics of intermittent faults are analyzed based on the dynamic model. The intermittent fault characteristics of different packaging solder joints are proven to be different using the intermittent fault dynamic theoretical model. By analyzing the intermittent fault parameters, the generalized strength of intermittent faults is constructed as the intermittent fault feature to diagnose intermittent faults for different package modes. Next, combining the above dynamic analysis conclusions with the characteristics of intermittent fault parameters, it is possible to determine the location of the intermittent faults. Finally, two solder joint intermittent fault experiments under vibration are carried out, and the intermittent fault features are calculated by analyzing the intermittent fault time-domain signals. The results show that the dynamic-based intermittent fault diagnosis method enables intermittent fault diagnosis of solder joints in different package modes.

Avalanche statistics and the intermittent-to-smooth transition in microplasticity

Plastic flow at small scales is generally observed to be intermittent, whereas the stress-strain behavior of bulk crystals is mostly smooth. Here we find that when the external deformation rate of small-scale crystals approaches the speed of the crystallographic slip velocity, an intermittent-to-smooth transition of plastic flow is observed. By defining a rate-dependent intermittency parameter, this phenomenon can be captured with a power law covering 5.5 orders of magnitude for Au and Nb micron-sized single crystals with experiments and via simulations for Nb crystals. Our results indicate that the transition to smooth flow is driven by a gradual truncation of the underlying truncated power law that describes the intermittently evolving system. This is caused by a competition of internal and external rates, which aligns with the well-known transitions from serrated to nonserrated flow in metallic glasses or materials with dynamic strain aging.

Model Predictive-Based Secondary Frequency Control Considering Heat Pump Water Heaters

The extensive development of renewable energies in power systems causes several problems due to intermittent output power generation. To tackle the challenge, demand response contribution to ancillary service is currently well recognized under the smart grid infrastructure. The application of the heat pump water heater (HPWH) as a controllable load in primary frequency control is well presented in the literature; however, the motivation of this paper is to use HPWHs for secondary frequency control. To this end, a model predictive control (MPC) method for a two-area power system incorporating HPWHs to contribute to secondary frequency control is proposed in this paper. A detailed model of HPWH is employed as a controllable load to control the power consumption during water heating. The MPC method predicts the future control signals using a quadratic programming-based optimization. It uses the system model, past inputs and outputs, as well as system control signals to predict the next signals. The effective performance of the proposed method for the two-area power system with HPWH is demonstrated for different scenarios of load changes, intermittent renewable power generation and parameter variations as the sensitivity analysis.

Cascade and intermittency of the sea surface temperature in the oceanic system

In this paper, we analyze the sea surface temperature obtained from the global drifter program. The experimental Fourier power spectrum shows a two-decade power-law behavior as Eθ(f) ∝ f−7/3 in the frequency domain. Dimensional argument suggests a two-dimensional-like Lagrangian forward cascade, in which the enstrophy dissipation ϵΩ is involved. Using the Hilbert–Huang transform and multi-level segment analysis, the measured high-order statistics and the corresponding singularity spectrum confirm the existence of the intermittency with a measured intermittency parameter μθ ≃ 0.10, which is much weaker than the prediction by the conventional structure-function method.

Oxygen Transfer Numerical Investigation Using Intermittent Aeration Technology Under Regular Waves

Based on a combination of Reynolds-Averaged Navier-Stokes equations, standard k-e equations, and VOF technique, a 2-D dissolved oxygen transport mathematical model was conducted to investigate oxygen-supply characteristics for regular waves with a given still water depth d and various hydrodynamic parameters (incident wave height H and wave period T equivalent to incident wave length L) and intermittent aeration parameters (air flow rate per unit width q, aeration period Ta, aeration depth da and air source area Aa). A series of experiments were conducted to validate the mathematical model, and they agreed well with each other. In addition, a series of dimensionless parameters were conducted to assess their relationships with oxygen transfer coefficient respectively. It was found that oxygen transfer coefficient increased slightly with the increase of $$ q/{g}^2{T}_a^3 $$ . With the increasing $$ {d}_a^2/{A}_a $$ , oxygen transfer coefficient increased obviously for the small $$ {d}_a^2/{A}_a $$ scenarios; however, it increased slightly for the high $$ {d}_a^2/{A}_a $$ scenarios. With increasing HL/d2, a linear increase tendency of oxygen transfer coefficient appeared approximately. Furthermore, a simple prediction formula for oxygen transport coefficient was conducted using the numerical data, the dimensional analysis, and the least squares method, and it was validated well with the related experimental data.

Energy dissipation statistics along the Lagrangian trajectories in three-dimensional turbulent flows

Energy dissipation rate is relevant in the turbulent phenomenology theory, such as the classical Kolmogorov 1941 and 1962 refined similarity hypothesis. However, it is extremely difficult to retrieve experimentally or numerically. In this paper, the full energy dissipation, its proxy and the pseudo-energy dissipation rate along the Lagrangian trajectories in the three-dimensional turbulent flows are examined by using a state-of-art high resolution direct numerical simulation database with a Reynolds number Re λ = 400. It is found that the energy dissipation proxy e P is more correlated with the full energy dissipation rate e. The corresponding correlation coefficient ρ between the velocity gradient and e shows a Gaussian distribution. Furthermore, the coarse-grained dissipation rate is considered. The cross correlation ρ is found to be increased with the increasing of the scale τ. Finally, the hierarchical structure is extracted for the full energy dissipation rate, its proxy and the pseudo one. The results show a power-law behavior in the inertial range 10 ≤τ/τ η ≤ 100. The experimental scaling exponent of the full energy dissipation rate is found to be h L =0.69, agrees very well with the one found for the Eulerian velocity. The experimental values for e P and e S are around h L = 0.78, implying a more intermittent Lagrangian turbulence. Therefore, the intermittency parameter provided by e P and e S will be biased.

Level crossings and excess times due to a superposition of uncorrelated exponential pulses.

A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a superposition of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency parameter. Expressions for excess time statistics, that is, the rate of level crossings above a given threshold and the average time spent above the threshold, are derived from the joint distribution of the process and its derivative. Limits of both high and low intermittency are investigated and compared to previously known results. In the case of a strongly intermittent process, the distribution of times spent above threshold is obtained analytically. This expression is verified numerically, and the distribution of times above threshold is explored for other intermittency regimes. The numerical simulations compare favorably to known results for the distribution of times above the mean threshold for an Ornstein-Uhlenbeck process. This contribution generalizes the excess time statistics for the stochastic model, which find applications in a wide diversity of natural and technological systems.

Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence

We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=frac{2}{3} . The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.

An Exploration of the Effects of Cycle Time and Force Variations on Muscle Fatigue during Submaximal Intermittent Isometric Exertions

This study investigated the effects of two intermittent task parameters on muscle fatigue, namely cycle time and force level variation. Of particular interest was whether a constant low-level underlying force would contribute to fatigue. Twelve students participated in four experimental conditions, each lasting 8 minutes. Participants repeatedly performed intermittent isometric exertions of biceps brachii at two cycle times (5 or 10 seconds), and two force levels, varying either between 0% and 50%max isometric force or between 10% and 40%max force. These parameters and a duty cycle of 0.5 ensured a mean force exertion of 25%max for all conditions. Muscle fatigue was inferred from local Ratings of Perceived Exertion (RPE), maximum force and EMG(RMS). Significant (p&lt;0.05) increases in RPE and EMG(RMS), and reductions in maximum force overtime indicate fatigue development during all conditions. Conditions with force levels varying between 10% and 40%max force showed significantly greater RPE and EMG(RMS) recordings, but only marginal reductions in maximum force (p=0.350), compared to conditions with force varying between 0% and 50%max force. Cycle time did not significantly influence fatigue development since no significant changes occurred for RPE, maximum force or EMG(RMS). These results show accelerated fatigue development under conditions with a constant underlying force, despite the lower maximum exertion level, and irrespective of cycle time. Work involving intermittent static force exertions should thus include periods of complete relaxation between exertions to prevent the early onset of muscle fatigue.Keywords: Muscle fatigue, submaximal isometric exertions, intermittent tasks, cycle time, constant underlying force.

Temporal multiscaling characteristics of particulate matter [formula omitted] and ground-level ozone [formula omitted] concentrations in Caribbean region

A good knowledge of the intermittency of atmospheric pollutants is crucial for air pollution management. We consider here particulate matter PM10 and ground-level ozone O3 time series in Guadeloupe archipelago which experiments a tropical and humid climate in the Caribbean zone. The aim of this paper is to study their scaling statistics in the framework of fully developed turbulence and Kolmogorov’s theory. Firstly, we estimate their Fourier power spectra and consider their scaling properties in the physical space. The power spectra computed follows a power law behavior for both considered pollutants. Thereafter we study the scaling behavior of PM10 and O3 time series. Contrary to numerous studies where the multifractal detrended fluctuation analysis is frequently applied, here, the classical structure function analysis is used to extract the scaling exponent or multifractal spectrum ζ(q); this function provides a full characterization of a process at all intensities and all scales. The obtained results show that PM10 and O3 possess intermittent and multifractal properties. The singularity spectrum MS(α) also confirms both pollutants multifractal features. The originality of this work comes from a statistical modeling performed on ζ(q) and MS(α) by a lognormal model to compute the intermittency parameter μ. By contrast with PM10 which mainly depends on puffs of Saharan dust (synoptic-scale), O3 is more intermittent due to variability of its local precursors. The results presented in this paper can help to better understand the mechanisms governing the dynamics of PM10 and O3 in Caribbean islands context.

Extremal-point density of scaling processes: From fractional Brownian motion to turbulence in one dimension

In recent years several local extrema-based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work, we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal-point-density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD is independent of the intermittency parameter μ, suggesting that the intermittency correction does not change the distribution of extremal points but changes the amplitude. By introducing a coarse-grained operator, the power-law behavior of these scaling processes is then revealed via the measured EPD for different scales. For fBm the scaling exponent ξ(H) is found to be ξ(H)=H, where H is Hurst number, while for MRW ξ(μ) shows a linear relation with the intermittency parameter μ. Such EPD approach is further applied to the turbulent velocity data obtained from a wind tunnel flow experiment with the Taylor scale λ-based Reynolds number Re_{λ}=720, and a turbulent boundary layer with the momentum thickness θ based Reynolds number Re_{θ}=810. A scaling exponent ξ≃0.37 is retrieved for the former case. For the latter one, the measured EPD shows clearly four regimes, which agrees well with the corresponding sublayer structures inside the turbulent boundary layer.

Intrinsic flow structure and multifractality in two-dimensional bacterial turbulence.

The active interaction between the bacteria and fluid generates turbulent structures even at zero Reynolds number. The velocity of such a flow obtained experimentally has been quantitatively investigated based on streamline segment analysis. There is a clear transition at about 16 times the organism body length separating two different scale regimes, which may be attributed to the different influence of the viscous effect. Surprisingly the scaling extracted from the streamline segment indicates the existence of scale similarity even at the zero Reynolds number limit. Moreover, the multifractal feature can be quantitatively described via a lognormal formula with the Hurst number H=0.76 and the intermittency parameter μ=0.20, which is coincidentally in agreement with the three-dimensional hydrodynamic turbulence result. The direction of cascade is measured via the filter-space technique. An inverse energy cascade is confirmed. For the enstrophy, a forward cascade is observed when r/R≤3, and an inverse one is observed when r/R>3, where r and R are the separation distance and the bacteria body size, respectively. Additionally, the lognormal statistics is verified for the coarse-grained energy dissipation and enstrophy, which supports the lognormal formula to fit the measured scaling exponent.

Width of turbulent SOL in circular plasmas: A theoretical model validated on experiments in Tore Supra tokamak

The relation between turbulent transport and scrape off layer width is investigated in circular plasmas toroidally limited on the inner wall. A broad set of experimental observations collected in the Tore Supra scrape off layer is detailed and compared to turbulent interchange models. Blob E × B drift velocities measured in experiments agree reasonably well with an analytical model derived for isolated blobs. Based on a time averaged particle flux balance, it is also shown that the SOL width depends on both the blob drift velocity and a blob intermittency parameter, which is so far not predicted by isolated blob models. A set of 2D isothermal turbulence simulations are used to derive a power law regression of the density width function of global control parameters. Quantitative agreement is found between this regression and experimental density widths measured in Tore Supra, over a large set of plasma conditions. The sensitivity to control parameters (major radius, safety factor and normalized Larmor radius) is roughly explained by the sensitivity of the blob velocity model. The predictions are also extended to power decay length in limited plasma configurations. For ITER start-up phases, the predicted power decay length fall in the range of extrapolations based on multi-machine regressions.

Evaluation of welded joints of vertical stiffener to web under fatigue load by hotspot stress method

The feasibility of intermittent fillet weld at the connection of vertical web stiffener and web plate in steel box girder bridge was studied considering vehicular fatigue loading. The study was conducted using FEM models taken from real three span steel box girder bridge with three box-girders connected by reinforced concrete deck. Web-to-stiffener connections at the middle of span and near the support of the bridge were studied in detail using refined 3D linear finite element analysis. Then, using structural hot spot stress approach, fatigue load induced stress was evaluated on the welded parts, and parametric study was conducted on a range of intermittent fillet weld parameters to evaluate the maximum fatigue load induced stress. The results of the parametric study are compared with maximum fatigue stress thresholds specified in design codes to verify the applicability of the proposed detail. Finally, some conclusion and recommendations are given on the applicability of intermittent fillet weld for web-to-stiffener connections of steel box girder bridges.

Statistical analysis of the ion flux to the JET outer wall

Statistical analysis of the ion flux to the JET outer-wall is conducted in outer-wall limiter mounted Langmuir probe (OLP) time-series across a wide range of plasma current and line-averaged density during Ohmically heated horizontal target L-mode plasmas. The mean, μ, and the standard deviation, σ, of the ion-saturation current measured by the OLP show systematic variation with plasma current and density. Both increase as either plasma current decreases and/or density increases. Upon renormalization, achieved by subtraction of μ and rescaling by σ, the probability distribution functions (PDFs) of each signal collapse approximately onto a single curve. The shape of the curve deviates from a distribution in the tail of the PDF and is better described by a log-normal distribution. The invariance in the shape of the PDF, which occurs over approximately four decades of the ordinate, is shown to be the result of a balance between the duration time of the average burst wave-form, and the waiting time between bursts, . This implies that the intermittency parameter, , can be considered constant at the JET outer wall during horizontal target Ohmic L-mode operation. This result may be important both for model validation and prediction.

Intermittency measurement in two-dimensional bacterial turbulence.

In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β-limitation. A dual-power-law behavior separated by the viscosity scale ℓ_{ν} was observed for the qth-order Hilbert moment L_{q}(k). This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R, e.g., the bacterial body length. The measured scaling exponents ζ(q) of both the small-scale (k>k_{ν}) and large-scale (k<k_{ν}) motions are convex, showing the multifractality. A log-normal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are μ_{S}=0.26 and μ_{L}=0.17, respectively, for the small- and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f(α) versus α. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation.

Compressible turbulent mixing: Effects of compressibility.

We studied by numerical simulations the effects of compressibility on passive scalar transport in stationary compressible turbulence. The turbulent Mach number varied from zero to unity. The difference in driven forcing was the magnitude ratio of compressive to solenoidal modes. In the inertial range, the scalar spectrum followed the k^{-5/3} scaling and suffered negligible influence from the compressibility. The growth of the Mach number showed (1) a first reduction and second enhancement in the transfer of scalar flux; (2) an increase in the skewness and flatness of the scalar derivative and a decrease in the mixed skewness and flatness of the velocity-scalar derivatives; (3) a first stronger and second weaker intermittency of scalar relative to that of velocity; and (4) an increase in the intermittency parameter which measures the intermittency of scalar in the dissipative range. Furthermore, the growth of the compressive mode of forcing indicated (1) a decrease in the intermittency parameter and (2) less efficiency in enhancing scalar mixing. The visualization of scalar dissipation showed that, in the solenoidal-forced flow, the field was filled with the small-scale, highly convoluted structures, while in the compressive-forced flow, the field was exhibited as the regions dominated by the large-scale motions of rarefaction and compression.

Multiscale Analysis of Intensive Longitudinal Biomedical Signals and Its Clinical Applications

Recent advances in wearable and/or biomedical sensing technologies have made it possible to record very long-term, continuous biomedical signals, referred to as biomedical intensive longitudinal data (ILD). To link ILD to clinical applications, such as personalized healthcare and disease prevention, the development of robust and reliable data analysis techniques is considered important. In this review, we introduce multiscale analysis methods for and the applications to two types of intensive longitudinal biomedical signals, heart rate variability (HRV) and spontaneous physical activity (SPA) time series. It has been shown that these ILD have robust characteristics unique to various multiscale complex systems, and some parameters characterizing the multiscale complexity are in fact altered in pathological states, showing potential usability as a new type of ambient diagnostic and/or prognostic tools. For example, parameters characterizing increased intermittency of HRV are found to be potentially useful in detecting abnormality in the state of the autonomic nervous system, in particular the sympathetic hyperactivity, and intermittency parameters of SPA might also be useful in evaluating symptoms of psychiatric patients with depressive as well as manic episodes, all in the daily settings. Therefore, multiscale analysis might be a useful tool to extract information on clinical events occurring at multiple time scales during daily life and the underlying physiological control mechanisms from biomedical ILD.