Values Of Scaling Exponents Research Articles

Experimental study of convective heat transfer with a multi-scale roughness

The heat transfer in a turbulent Rayleigh-Bénard convection with a multi-scale roughness at the bottom is studied experimentally. Two different regimes for the heat transfer are found. The first regime has scaling exponent γI=0.4 and corresponds to the reduced values of the Nusselt number. The second regime with enhanced values of the Nusselt number has a scaling exponent γII=0.32, which is noticeably larger than in the case of smooth boundaries. Significant variation in the Prandtl number (from 6.4 to 62) does not change the scaling exponent value of the second regime but increases the values of Nusselt number. The scaling exponent for the relation Re∼Raα is insensitive to the change of the heat transfer regime and is close to 1/2 for all values of Ra. The characteristic ratio of the velocity pulsations to the mean velocity does not depend on the Rayleigh number and is characterized by close values (about 0.8). The local temperature measurements support the mechanism of the transition from the reduced Nusselt number regime to the enhanced one, which is based on the formation of flows between obstacles.

Information theoretic measures for Lifshitz system

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in 3 + 1-dimensions. This geometry is the gravity dual to a class of 2 + 1-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent (z) present in the Lifshitz field theory.

Introduction of new attributes: Scaling Exponent and its double derivatives for better land seismic volume interpretation

For the first time, we propose to study the behavior of the correlation (scaling) exponent and its second order with prestack seismic data. For our research, we have chosen Dibrugarh prestack 3D seismic data from the Assam-Arakan Basin, India. We have improved the calculation process so that it is possible to read amplitude values directly from SEG-Y file and collect data from the entire chosen in- or cross-line. As a result, we can now study significant amount of data within less amount of time. After completing the analysis, we could identify the main stratigraphic layers, basement, and the zones of weak and prominent amplitudes from the survey. Strong amplitude zones correlate with low scaling exponent values. Weak amplitudes reflect as high scaling exponent zones. New attributes introduced give a scope to automatize the interpretation of 3D seismic data without learning.

THE TWO-SCALE FRACTAL DIMENSION: A UNIFYING PERSPECTIVE TO METABOLIC LAW

The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner’s 2/3 law and Kleiber’s 3/4 law are two facets of the same truth, manifested across different scale approximations.

Towards the origin of devotion and happiness: An acoustical and neuro-cognitive exploration of Indian spiritual music

Since the age of the Vedas, devotion has remained a key component of Indian music through centuries of changes and foreign influences. The brightest example of this is the Bhakti tradition, a pan-Indian movement (7th-15th Century CE), which integrated poetry and music in the transmission of spiritual and social goals. Devotees often report perception of emotions like devotion, happiness, awe while listening to spiritual music of their own religion and culture. This paper aims to study the acoustical and neuro-cognitive correlates of these emotions for two Indian spiritual music traditions – (a) Sikh Gurbani/ Shabad Kirtan, (b) Bangla Vaishnav Kirtan, both of which emerged from the Bhakti tradition. 5 Punjabi and 5 Bengali speaking participants listened to 3-minute long four songs from these two spiritual music traditions while EEG signals were recorded from each participant along with their emotion responses. Acoustical time series of these music clips and their corresponding EEG signals were analysed using nonlinear DFA technique. DFA Scaling Exponent values were calculated for multiple 30-second EEG segments across the total duration of each music clip to understand the perception and induction process of devotion and happiness in human brain, which is a novel step in the domain of music cognition and signal processing.

Polar Cap Patches Scaling Properties: Insights from Swarm Data

Among the effects of space weather, the degradation of air traffic communications and satellite-based navigation systems are the most notable. For this reason, it is of uttermost importance to understand the nature and origin of ionospheric irregularities that are at the base of the observed communication outages. Here we focus on polar cap patches (PCPs) that constitute a special class of ionospheric irregularities observed at very high latitudes in the F region. To this purpose we use the so-called PCP flag, a Swarm Level 2 product, that allows for identifying PCPs. We relate the presence of PCPs to the values of the first- and second-order scaling exponents and intermittency estimated from Swarm A electron density fluctuations and to the values of the Rate Of change of electron Density Index (RODI) for two different levels of geomagnetic activity, over a time span of approximately 3.5 years starting on 16 July 2014. Our findings show that values of RODI, first- and second-order scaling exponents and intermittency corresponding to measurements taken inside PCPs differ from those corresponding to measurements taken outside PCPs. Additionally, the values of the first- and second-order scaling exponents and of intermittency indicate that PCPs are in a turbulent state. Investigation of the coincidence of loss of lock (LoL) events with PCPs displayed that approximately 57.4% of LoLs in the Northern hemisphere and 45.7% in the Southern hemisphere occur in coincidence of PCPs when disturbed geomagnetic activity is considered. During quiet geomagnetic conditions these percentages decrease to 51.4% in the Northern hemisphere and to 20.1% in the Southern hemisphere.

The allocation of anatomical traits determines the trade-off between fine root resource acquisition-transport function.

Cortex radius (CR) and stele radius (SR) are important functional traits associated with the nutrient acquisition and transport functions of fine roots, respectively. However, for developmental and anatomical reasons, the resource acquisition-transport relationship of fine roots is expected to be different for different root orders. To address this issue, critical fine root anatomical traits were examined for the first three orders of roots of 59 subtropical woody plants. Designating the most distal fine roots as order one, SR scaled isometrically with respect to root radius (RR) (i.e., SR ∝ RR1.0) in the three root orders, whereas CR scaled allometrically with respect to RR (i.e., CR ∝ RR>1.0) with the numerical values of scaling exponents increasing significantly with increasing root orders thereby indicating a disproportional increase in CR with increasing root orders. There were also differences between normalized root tissue (CR/RR and SR/RR) and RR in different root orders. A negative isometric relationship (i.e., SR/RR ∝ RR-1.0) existed between SR/RR and RR in three order roots, whereas the allometric exponent between CR/RR and RR increased with root order (from 0.88 to 1.55). Collectively, the data indicate that root anatomical and functional traits change as a function of RR and that these changes need to be considered when modeling fine root resource acquisition-transport functions.

Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices

The synchronization of oscillator ensembles is pervasive throughout nonlinear science, from classical or quantum mechanics to biology, to human assemblies. Traditionally, the main focus has been the identification of threshold parameter values for the transition to synchronization as well as the nature of such transition. Here, we show that considering an oscillator lattice as a discrete growing interface provides unique insights into the dynamical process whereby the lattice reaches synchronization for long times. Working on a generalization of the Kuramoto model that allows for odd or non-odd couplings, we elucidate synchronization of oscillator lattices as an instance of generic scale invariance, whereby the system displays space-time criticality, largely irrespective of parameter values. The critical properties of the system (like scaling exponent values and the dynamic scaling Ansatz which is satisfied) fall into universality classes of kinetically rough interfaces with columnar disorder, namely, those of the Edwards-Wilkinson (equivalently, the Larkin model of an elastic interface in a random medium) or the Kardar-Parisi-Zhang (KPZ) equations, for Kuramoto (odd) coupling and generic (non-odd) couplings, respectively. From the point of view of kinetic roughening, the critical properties we find turn out to be quite innovative, especially concerning the statistics of the fluctuations as characterized by their probability distribution function (PDF) and covariance. While the latter happens to be that of the Larkin model irrespective of the symmetry of the coupling, in the generic non-odd coupling case the PDF turns out to be the Tracy-Widom distribution associated with the KPZ nonlinearity. This brings the synchronization of oscillator lattices into a remarkably large class of strongly-correlated, low-dimensional (classical and quantum) systems with strong universal fluctuations.

The origin of the density scaling exponent for polyatomic molecules and the estimation of its value from the liquid structure.

In this article, we unravel the problem of interpreting the density scaling exponent for the polyatomic molecules representing the real van der Waals liquids. Our studies show that the density scaling exponent is a weighted average of the exponents of the repulsive terms of all interatomic interactions that occur between molecules, where the potential energy of a given interaction represents its weight. It implies that potential energy is a key quantity required to calculate the density scaling exponent value for real molecules. Finally, we use the well-known method for potential energy estimation and show that the density scaling exponent could be successfully predicted from the liquid structure for fair representatives of the real systems.

Altered distribution of resting periods of daily locomotor activity in patients with delayed sleep phase disorder.

Delayed sleep phase disorder (DSPD) and mood disorders have a close relationship. However, the shared mechanisms by DSPD and mood disorders have not been well-elucidated. We previously found that micro-fluctuations in human behaviors are organized by robust statistical laws (behavioral organization), where the cumulative distributions of resting and active period durations take a power-law distribution form and a stretched exponential functional form, respectively. Further, we found that the scaling exponents of resting period distributions significantly decreased in major depressive disorder (MDD). In this study, we hypothesized that DSPD had similar characteristics of the altered behavioral organization to that of MDD. Locomotor activity data were acquired for more than 1 week from 17 patients with DSPD and 17 age- and gender-matched healthy participants using actigraphy. We analyzed the cumulative distributions of resting and active period durations in locomotor activity data and subsequently derived fitting parameters of those distributions. Similar to patients with MDD, we found that resting period distributions took a power-law form over the range of 2–100 min, with significantly lower values of scaling exponents γ in patients with DSPD compared with healthy participants. The shared alteration in γ suggests the existence of similar pathophysiology between DSPD and MDD.

Variable source depth beneath the Indian Ocean geoid low area: Insights from L1 and L2 norm-based scaling power spectrum inversion

Indian Ocean geoid low, situated at the south of the Indian peninsula, is an intriguing feature. Hitherto, several interpretations have been put forth to explain the genesis and causative depths of the anomaly. In this work, we investigate the scaling spectral inversion approach utilizing gravity data to estimate the causative depth and nature of the source from this region. In practice, crustal or sub-surface heterogeneities follow scaling or fractal characteristics, and comparative studies across various regions suggest that the scaling power spectrum method provides better insights into the sub-surface source distribution. An optimum fitting and comparison between the modeled and observed power spectrum have been attained by utilizing two norm penalties e.g. L1 and L2 norms for various combinations of depth and scaling exponents. Equally important, the L1 norm misfit function yields better results when compared to the L2 norm function. We propose that estimated source depths (̴80 km and 120 km, respectively) are perfect examples of a half-space model with a source following scaling or fractal characteristics (scaling exponent value of ̴1.78) along the upper mantle boundary. However, the scaling spectrum windowing analysis of the studied region reveals a variable depth to long wavelength sources as 1014 km, 431 km, and 94 km, which conform well with the recently published depth range. Further, the weight of low and high wavenumbers indicates that the causative source depths might be due to the above-stated depth range rather than a single model fit. The study has demonstrated a good case for wider use of L1 norm-based power spectrum inversion for source depth estimation from potential field data. We further suggest that the causative source for the Indian Ocean geoid low may extend deeper than upper mantle discontinuities.

Formation factors for a class of deterministic models of pre-fractal pore-fracture networks

The main aim of this paper is to reveal effects of fractal features on the formation factors associated with different transport processes in scale invariant pore-fracture networks. Accordingly, we explore a class of deterministic infinitely ramified networks associated with pre-fractal standard Sierpinski carpets (including Sierpinski cubes and inverse Menger sponges). The focus is placed on the effects of network ramification, connectivity, and loopiness on the transport streamline constriction and tortuosity of transmission paths. The differences between the formation factors associated with the diffusibility, electrical conductivity, and hydraulic permeability are elucidated. Explicit expressions for the constrictivity and formation factors of deterministic pre-fractal networks are derived. In this regard, we stress that the electrical formation factor obeys the Archie law only if the random walk in the pre-fractal pore-fracture network is recurrent. We also note that the Archie's exponent can be either equal to, or less than the power-law exponent characterizing the scaling behavior of diffusibility. The notion of the structural formation factor is introduced. The values of scaling exponents characterizing the formation factors associated with different transport properties of the model networks are found to be within the ranges of field observations.

Application of scaling geology in magnetic basement mapping around the Middle Benue Trough in Northcentral Nigeria

Using the scaling spectral method applied on high resolution aeromagnetic data, we mapped the magnetic basement and estimated the scaling exponents across various lithologies within the Middle Benue Trough of Northcentral Nigeria. We estimated a depth range of 1.8–6.3 km, with an average of 3.7 km to the basement beneath the Cretaceous sediments of the trough. Shallow basement depths of <3 km are mostly found on the trough's northern and southeastern margins. These are uplifted Precambrian Basement Complex regions made up of older granite, gneiss, and migmatite. Deeper basement depths of >4 km predominate in the southwestern, central, and northeastern portions of the study area, trending along the trough's axis. These deep zones are filled with Cretaceous sediments that must have accumulated after the Mesozoic development of the Benue Trough's subsided graben structure. Our study estimated scaling exponent ranging from 0 to 2. There were some correlations with the geology of the area, particularly around the crystalline basement complex in the northern portion. Within the central portion of the Middle Benue Trough, however, the source distributions are less correlated, uneven, and not always consistent with the geology of the area. This could be due to the region's dynamic and unstable tectonics, as numerous magmatic intrusions have been emplaced into the Cretaceous sediments at various depths, potentially influencing the scaling exponent values.

Direct use of large-footprint lidar waveforms to estimate aboveground biomass

Many studies have established the strong connections between aboveground biomass and lidar height metrics; however, these relationships are site-specific. Field data required to derive these relationships are not readily available in many cases. We developed a model to estimate plot-level aboveground biomass density (AGBD) directly from large-footprint lidar waveform measurements. An individual tree-based aboveground biomass (AGB)-height allometric relationship was scaled up to the plot level using lidar-waveform sensed tree height and crown size distribution characteristics. The AGBD was estimated based on a waveform/foliage profile-weighted height-based allometric equation. The AGBD-height scaling exponent was then built on the allometric relationships of tree height with stem diameter and crown volume with tree height. Global vegetation structure data analysis demonstrated that one general model (scaling exponent ~ 1.6–1.8) works reasonably well across all global forest biomes except boreal forests (scaling exponent ~ 0.9). We applied the model to estimate aboveground biomass in two distinct geographic regions: temperate deciduous/conifer forests in the northeastern USA and a montane conifer forest in Sierra National Forest in California. Local vegetation structural data analysis leads to a consistent height scaling exponent for these two distinct biomes, slightly different from the global data analysis results. This model produced optimal AGBD estimates using the local height scaling exponent value. Adequate AGBD estimates with the general height scaling exponent value were also provided by our model. Our analysis suggests one general allometric relationship between plot-level AGBD and large-footprint lidar waveforms. Integrating local structure allometric relationships improve the predictive accuracy of the model. Our model outperformed the lidar height metrics-based approach for AGBD estimates and overcame the biomass underestimation problem using height metrics for high biomass regions. This model could potentially serve as a general and robust model for monitoring forest carbon stocks using large-footprint lidar waveform measurements such as the Global Ecosystem Dynamics Investigation (GEDI) mission at the continental and global scales. The model could be a framework for integrating a demography-based terrestrial ecosystem model and GEDI global mission measurements to improve global carbon stock and flux estimates.

Density Scaling of Translational and Rotational Molecular Dynamics in a Simple Ellipsoidal Model near the Glass Transition.

In this paper, we show that a simple anisotropic model of supercooled liquid properly reflects some density scaling properties observed for experimental data, contrary to many previous results obtained from isotropic models. We employ a well-known Gay–Berne model earlier parametrized to achieve a supercooling and glass transition at zero pressure to find the point of glass transition and explore volumetric and dynamic properties in the supercooled liquid state at elevated pressure. We focus on dynamic scaling properties of the anisotropic model of supercooled liquid to gain a better insight into the grounds for the density scaling idea that bears hallmarks of universality, as follows from plenty of experimental data collected near the glass transition for different dynamic quantities. As a result, the most appropriate values of the scaling exponent γ are established as invariants for a given anisotropy aspect ratio to successfully scale both the translational and rotational relaxation times considered as single variable functions of densityγ/temperature. These scaling exponent values are determined based on the density scaling criterion and differ from those obtained in other ways, such as the virial–potential energy correlation and the equation of state derived from the effective short-range intermolecular potential, which is qualitatively in accordance with the results yielded from experimental data analyses. Our findings strongly suggest that there is a deep need to employ anisotropic models in the study of glass transition and supercooled liquids instead of the isotropic ones very commonly exploited in molecular dynamics simulations of supercooled liquids over the last decades.

Diagnosing utility grid disturbances in photovoltaic integrated DC microgrid using adaptive multiscale morphology with DFA analysis

In this study, a novel approach is proposed to distinguish both single and mixed power quality (PQ) disturbances in the network connected to the utility grid in a photovoltaic (PV) integrated DC microgrid. To analyze PQ disturbances in the proposed system, AC voltage signals are captured at the PCC of the utility grid. The captured voltage signals contain strong noise which impacts the system robustness. To resolve this problem, an adaptive multiscale improved combination morphological filter (AMICMF) technique is introduced in the proposed system. In this technique, an improved combination morphological filter (ICMF) is first proposed by using the basic four morphological operations. Then multiscale operation (MICMF) is done by different structural element (SE) lengths chosen by sparse weighted Kurtosis index (SKI w ). The obtained optimized signal is processed through the detrended fluctuation analysis (DFA) which gives the scaling exponent ( λ ) values based on window length. These scaling exponent values are used to classify the PQ disturbances in terms of scatter plots. The performance of the proposed study is calculated by classification accuracy (CA) and relative computational time (RCT) and the efficacy of the proposed technique is validated by comparing the CA and RCT with existing techniques. The entire study is tested on MATLAB/Simulink environment. The complete study is tested and validated using a high-speed multifunction National Instrument USB6008 device for the online monitoring of PQ disturbances on the MATLAB/Simulink environment. • A new adaptive multiscale morphological filter is used for PQ analysis of DC microgrid. • The adaptation of the filter is accomplished using a sparse weighted kurtosis index. • Detrended fluctuation analysis is used to process the optimized signal to yield scaling exponents. • These scaling exponent values are used to classify the PQ disturbances in terms of scatter plots.

Persistence of Rainfall Time Series: Kırşehir Case Study

This study examines the persistence and long-term correlation of monthly and seasonal rainfall time series of Kırşehir for the period of 1960-2019, with widely used Hurst exponent and Detrended Fluctuation Analysis (DFA) analyses. Both Hurst exponent and DFA analyses could be used to detect the long-term memory and correlation that can be assessed as a reference of predictability. To support the analyses results Augmented Dickey Fuller and Mann-Kendall tests also applied to time series. Within various rainfall series, evidence of persistence and long-term correlation was identified. According to H exponent values of simple R/S and corrected R/S methods, 10 out of 12 months and winter, spring (only simple R/S), summer (only corrected R/S) and autumn season and according to DFA scaling exponent values 4 out of 12 months and winter and autumn seasons exhibit long term correlation. On the other hand, when the H exponent and DFA scaling exponent values compared only four monthly and two seasonal rainfall series concluded to be consistent with both H exponent and DFA scaling exponent results.

Divergent scaling of fine-root nitrogen and phosphorus in different root diameters, orders and functional categories: A meta-analysis

Fine-root nitrogen (N) and phosphorus (P) concentrations play an important role in driving ecological processes such as nutrient cycling in terrestrial ecosystems. Previous studies have demonstrated that the N versus P scaling relationship for fine roots (<2 mm in diameter) on average follows a 0.82-power law across plant functional groups and ecosystems. However, little is known about the N versus P scaling relationships for different fine-root classification groups (classes of diameters, branch orders, and functional categories, e.g., absorptive and transport roots). We used a dataset comprising 1037 N-P paired observations for a total of 227 woody species to explore N versus P scaling relationships in different fine-root groups. The overall means of fine-root N and P concentrations and N:P ratios across all of the woody species were 12.27 mg g−1, 1.01 mg g−1, and 15.14, respectively. N and P concentrations, N:P ratios, and the numerical values of the N versus P scaling exponents differed significantly within and across the different fine-root classes. The numerical values of absorptive roots N versus P scaling exponents varied within plant functional groups (e.g., life-form, phylogenetic and mycorrhizal groups). The numerical values of absorptive roots scaling exponents declined from 0.89 in boreal regions to 0.61 tropical regions. These results indicate that fine roots (<2 mm in diameter) should be carefully classified into different groups/categories when N and P scaling relationships need to be determined to predict plant growth and vegetation productivity. Our results shed important light on attempts to modeling fine-root biogeochemical processes in terrestrial ecosystems.

Hydrodynamic Process in the Langmuir-Blodgett Film Method.

Preparing organic coatings in a very controlled manner through the spreading of organic molecules on the water surface is one of the emphases for research in Langmuir-Blodgett (LB) technology. For preparing a homogeneous film and improving the quality of the film, it is our concern to have a deeper understanding of the dynamic process involved in spreading. Here, we present an overview of the hydrodynamic process under the influence of assisting the spreading solvent, which mainly focuses on the mechanical mechanisms of related phenomena. A typical spreading experiment of two-component mixed droplets on water substrate for the purpose of preparing LB films was carried out in this research. We perform the spreading of a liquid of silicone oil and oleic acid mixture on the horizontal surface of another immiscible deep water substrate, where the volatile silicone oil is the assisting spreading solvent with low viscosity. We find that it needs to exceed a certain critical value (60% in our experiment) to achieve a uniform and centrosymmetric spreading process, which is a key factor for getting a homogeneous film. We observe that the evolution of a large droplet into liquid film and then into small droplets under the action of surface tension gradient in experiments. Gravity-viscous and surface tension-viscous dominate successively in the whole spreading process, with its spreading radius r(t) ∝ t1/4 and r(t) ∝ t3/4, respectively. However, we also obtain singular values of scaling exponents -0.033 and -0.180, which is attributed to nonuniform distribution of the Laplace pressure caused by different curvatures near the capillary wave.

Application of leaf size and leafing intensity scaling across subtropical trees.

Understanding the scaling between leaf size and leafing intensity (leaf number per stem size) is crucial for comprehending theories about the leaf costs and benefits in the leaf size–twig size spectrum. However, the scaling scope of leaf size versus leafing intensity changes along the twig leaf size variation in different leaf habit species remains elusive. Here, we hypothesize that the numerical value of scaling exponent for leaf mass versus leafing intensity in twig is governed by the minimum leaf mass versus maximum leaf mass (M min versus M max) and constrained to be ≤−1.0. We tested this hypothesis by analyzing the twigs of 123 species datasets compiled in the subtropical mountain forest. The standardized major axis regression (SMA) analyses showed the M min scaled as the 1.19 power of M max and the ‐α (−1.19) were not statistically different from the exponents of M min versus leafing intensity in whole data. Across leaf habit groups, the M max scaled negatively and isometrically with respect to leafing intensity. The pooled data's scaling exponents ranged from −1.14 to −0.96 for M min and M max versus the leafing intensity based on stem volume (LIV). In the case of M min and M max versus the leafing intensity based on stem mass (LIM), the scaling exponents ranged from −1.24 to −1.04. Our hypothesis successfully predicts that the scaling relationship between leaf mass and leafing intensity is constrained to be ≤−1.0. More importantly, the lower limit to scaling of leaf mass and leafing intensity may be closely correlated with M min versus M max. Besides, constrained by the maximum leaf mass expansion, the broad scope range between leaf size and number may be insensitive to leaf habit groups in subtropical mountain forest.