Scaling Region Research Articles

Breaking the scaling relations of effective CO2 electrochemical reduction in diatomic catalysts by adjusting the flow direction of intermediate structures.

The electrocatalytic carbon dioxide reduction reaction (CO2RR) is a promising approach to achieving a sustainable carbon cycle. Recently, diatomic catalysts (DACs) have demonstrated advantages in the CO2RR due to their complex and flexible active sites. However, our understanding of how DACs break the scaling relationship remains insufficient. Here, we investigate the CO2RR of 465 kinds of graphene-based DACs (M1M2-N6@Gra) formed from 30 metal atoms through high-throughput density functional theory (DFT) calculations. We find that the intermediates *COOH, *CO, and *CHO have multiple adsorption states, with 11 structural flow directions from *CO to *CHO. Four of these structural flow directions have catalysts that can break the linear scale relationship. Based on the adsorption energy relationship between *COOH, *CHO and *CO, we propose the concepts of linear scaling, moderate breaking, and severe deviation regions, leading to the establishment of new descriptors that identify 14 catalysts with potential superior performance. Among them, ZnRu-N6@Gra and CrNi-N6@Gra can reduce CO2 to CH4 at a low limiting potential. We also discovered that DACs have independent bidirectional electron transfer channels during the adsorption and activation of CO2, which can significantly improve the flexibility and efficiency of regulating the electronic structure. Furthermore, through machine learning (ML) analysis, we identify electronegativity, atomic number, and d electron count as key determinants of catalyst stability. This work provides new insights into the understanding of the DAC catalytic mechanism, as well as the design and screening of catalysts.

A scaling region identification method for the divider dimension of urban thermal environments

Abstract A scaling region identification method for divider dimensions using the coefficient of determination is proposed to improve the estimation accuracy of the divider dimension in the study of urban thermal environment differentiation characteristics. The effectiveness of this method was verified by analyzing the urban surface thermal field differentiation characteristics by applying the estimated divider dimensions of Nanjing’s thermal environment surfaces and transect lines. The research results show that the urban thermal environment has fractal characteristics only within a certain temperature threshold range. When the constraint of scaling regions is considered, the calculated divider dimension of the surface thermal field surface increases, reflecting the more complex fractal structure of the thermal field. For each temperature grade, the “trough” position of the thermal field divider dimension surface estimated by the line-divider method is near the determination level of the high-temperature region based on robust statistics, allowing the spatial extent of the urban heat island (UHI) to be determined based on the “trough” feature of the thermal field divider dimension surface.

Intermittent Shot Noise Generating 1/f Fluctuations

When the rate of shot noise is controlled by on–off states we speak of intermittent shot noise. The on–off states lead to alternately occurring clusters of events and intermissions, respectively. We derive the power spectrum of the intermittent shot noise by applying the Wiener-Khinchin theorem. Besides reduced shot noise, we obtain excess noise, which depends on the parameters of the on–off states. We calculate the excess noise for power-law distributed on-states; within the scaling region, the excess noise is excellently approximated by [Formula: see text]. The behavior of the slope b and of the amplitude C in dependence of the on–off times is investigated. For large scaling regions, we find a preference for a pure 1/f shape. Finally, we regard the variance of events occurring within a time interval. In the presence of 1/f fluctuations, the variance of counts attains extreme values which are accompanied by an extreme property of slope b.

Investigating the phase behaviour of binary suspensions of cellulose nanocrystals and montmorillonite with nonlinear rheology, SAXS and polarized optical microscopy

Using microscopy imaging techniques, X-ray scattering, and nonlinear rheological measurements, we have examined microstructural changes, and phase behavior of cellulose nanocrystals (CNC)/montmorillonite (MMT) composite colloidal systems. Fourier-transform (FT) rheology-stress decomposition methods, Lissajous-Bowditch plots, and other techniques are used to both qualitatively and quantitatively determine the various phases that the suspensions exhibit. In the MAOS (medium amplitude oscillatory shear) region, multiple scaling regions, as well as quadratic scaling regions are obtained. The dependence of the normalized third relative intensity (I3/1) values on angular frequency (ω) also provided new insights into how nonlinear parameters depend on the various CNC/MMT phases. These findings allow us to differentiate various phases exhibited by the composite system, including the isotropic, biphasic, and chiral nematic liquid crystalline (LC) phases. The CNC/MMT nanocomposite system exhibits a variety of liquid crystalline phases, which may contribute to improved mechanical properties for the system, including increased mixture strength, stiffness, and toughness because of the particle alignment in the LC phase. Additionally, the field of optics and photonics may find use for this nanocomposite system in the fabrication of sensors, polarizers, and optical films; energy storage applications where the aligned structures facilitate ion transport; and the formulation of paints and coatings where the strain stiffening and shear thinning behavior of the CNC/MMT composite system are critical.

Multifractal detrended fluctuation analysis of rainfall time series in the Guadeloupe archipelago

Due to the vulnerability of the Caribbean islands to the climate change issue, it is important to investigate the behavior of rainfall. In addition, the soil of the French West Indies Islands has been contaminated by an organochlorine insecticide (Chlordecone) whose decontamination is mainly done by drainage water. Thus, it is crucial to investigate the fluctuations of rainfall in these complex environments. In this study, 19 daily rainfall series recorded in different stations of Guadeloupe archipelago from 2005 to 2014 were analyzed with the multifractal detrended fluctuation analysis (MF-DFA) method. The aim of this work is to characterize the long-range correlations and multifractal properties of the time series and to find geographical patterns over the three most important islands: Basse-Terre, Grande-Terre and Marie-Galante. This is the first study that addresses the analysis of multifractal properties of rainfall series in the Caribbean islands. This region is typically characterized by the almost constant influence of the trade winds and a high exposure to changes in the general atmospheric circulation. 12 stations exhibit two different power-law scaling regions in rainfall series, with distinct long-range correlations and multifractal properties for large and small scales. On the contrary, the rest of stations only show a single region of scales for relatively small scales. Hurst exponents reveal persistent long-range correlations which agree with other studies in nearby tropical locations. In the most eastern analyzed areas, larger scales exhibit higher persistence than smaller scales, which suggests a relationship between persistence and the highest exposure to the trade winds. Stronger conclusions can be drawn from multifractal spectra, which indicate that most rainfall series have a multifractal nature with higher complexity and degree of multifractality at the smallest scales. Furthermore, a clear dependence of multifractal nature on the latitude is revealed. All these results showed that MF-DFA is a robust tool to assess the nonlinear properties of environmental time series in a complex area.

Trend analysis in the presence of short- and long-range correlations with application to regional warming.

Many real-world time series exhibit both significant short- and long-range temporal correlations. Such correlations enhance the errors of linear trend analysis. In this paper, we provide a general framework for trend analysis under the consideration of such correlations. We propose a parsimonious model containing both a single short-range autoregressive parameter and long-range fractional parameter. We derive analytical closed-form results for the error bars of the least-squares estimate of the trend for such time series, highlighting the different effects of short- and of long-range correlations. We employ an ensemble method for the automated extraction of scaling regions to estimate the fractional parameter of the data model together with its error bar, and the Grünwald-Letnikov derivative for the identification of the autoregressive parameter. We apply this framework to the study of warming trends on gridded temperature data in central Europe. We make use of the redundancy of the trend signal in adjacent grid points using methods of spatial averaging and the first principal component of empirical orthogonal function analysis. We find good agreement between the results of these two methods. We find a statistically significant decadal warming trend in central Europe over the past 70 years, which shows a particularly dramatic increase over the past 20 years.

DFA as a window into postural dynamics supporting task performance: does choice of step size matter?

Introduction: Detrended Fluctuation Analysis (DFA) has been used to investigate self-similarity in center of pressure (CoP) time series. For fractional gaussian noise (fGn) signals, the analysis returns a scaling exponent, DFA-α, whose value characterizes the temporal correlations as persistent, random, or anti-persistent. In the study of postural control, DFA has revealed two time scaling regions, one at the short-term and one at the long-term scaling regions in the diffusion plots, suggesting different types of postural dynamics. Much attention has been given to the selection of minimum and maximum scales, but the choice of spacing (step size) between the window sizes at which the fluctuation function is evaluated may also affect the estimates of scaling exponents. The aim of this study is twofold. First, to determine whether DFA can reveal postural adjustments supporting performance of an upper limb task under variable demands. Second, to compare evenly-spaced DFA with two different step sizes, 0.5 and 1.0 in log2 units, applied to CoP time series. Methods: We analyzed time series of anterior-posterior (AP) and medial-lateral (ML) CoP displacement from healthy participants performing a sequential upper limb task under variable demand. Results: DFA diffusion plots revealed two scaling regions in the AP and ML CoP time series. The short-term scaling region generally showed hyper-diffusive dynamics and long-term scaling revealed mildly persistent dynamics in the ML direction and random-like dynamics in the AP direction. There was a systematic tendency for higher estimates of DFA-α and lower estimates for crossover points for the 0.5-unit step size vs. 1.0-unit size. Discussion: Results provide evidence that DFA-α captures task-related differences between postural adjustments in the AP and ML directions. Results also showed that DFA-α estimates and crossover points are sensitive to step size. A step size of 0.5 led to less variable DFA-α for the long-term scaling region, higher estimation for the short-term scaling region, lower estimate for crossover points, and revealed anomalous estimates at the very short range that had implications for choice of minimum window size. We, therefore, recommend the use of 0.5 step size in evenly spaced DFAs for CoP time series similar to ours.

Finite-volume effects in baryon number fluctuations around the QCD critical endpoint

We present results for the volume dependence of baryon number fluctuations in the vicinity of the (conjectured) critical endpoint of QCD. They are extracted from the nonperturbative quark propagator that is obtained as a solution to a set of truncated Dyson–Schwinger equations of (2+1)-flavor QCD in Landau gauge, which takes the backcoupling of quarks onto the Yang–Mills sector explicitly into account. This well-studied system predicts a critical endpoint at moderate temperatures and rather large chemical potential. We investigate this system at small and intermediate finite, three-dimensional, cubic volumes and study the resulting impact on baryon number fluctuations and ratios thereof up to fourth order in the region of the critical endpoint. Due to the limitations of our truncation, the results are quantitatively meaningful only outside the critical scaling region of the endpoint. We find that the fluctuations are visibly affected by the finite volume, particularly for antiperiodic boundary conditions, whereas their ratios are practically invariant.

Improved Superscaling in Quasielastic Electron Scattering with Relativistic Effective Mass

Superscaling in electron scattering from nuclei is re-examined, paying special attention to the definition of the averaged single-nucleon responses. The validity of the extrapolation of nucleon responses in the Fermi gas has been examined, which previously lacked a theoretical foundation. To address this issue, we introduce new averaged responses with a momentum distribution smeared around the Fermi surface, allowing for momenta above the Fermi momentum. This approach solves the problem of negativity in the extrapolation away from the scaling region and, at the same time, validates its use in the scaling analysis. This work has important implications for the interpretation of scaling data and contributes to the development of a more complete understanding of the scaling approach.

Box dimension of the border of Kingdom of Saudi Arabia

Fractal dimension unlike topological dimension is (usually) a non-integer number which measures complexity, roughness, or irregularity of an object with respect to the space in which the set lies. It is used to characterize highly irregular objects in nature containing statistical self-similarity such as mountains, snowflakes, clouds, coastlines, borders etc.In this article, box dimension (a version of fractal dimension) of the border of Kingdom of Saudi Arabia (KSA) is computed using a multicore parallel processing algorithm based on the classical box-counting method. A power law relation is obtained from numerical simulations which relates the length of the border with the scale size and provides a very close estimate of the actual length of the KSA border within the scaling regions and scaling effects on the length of KSA border are considered. The algorithm presented in the article is shown to be highly scalable and efficient and the speedup of the algorithm is computed using Amdahl's and Gustafson's laws. For simulations, a high performance parallel computer is employed using Python codes and QGIS software.

Geometric scaling in leading neutron events at HERA

This analysis provides new fits of the GBW model and the impact parameter-dependent saturation model (bSat or IP-Sat) to the leading neutron structure function HERA data in one pion exchange approximation. Both parametrizations of the dipole cross section provide good descriptions of the considered data. It is shown here for the first time that the experimental leading neutron production HERA data exhibits geometric scaling, which in this context means that the total $\gamma^* \pi^*$ cross section is a function of only one dimensionless variable $\tau = Q^2/Q_s^2(x)$. The geometric scaling region extends over a broad range of $Q^2$ and can be attributed to the presence of a saturation boundary which manifests at $Q^2\geq Q^2_s$. The scaling behaviour in leading neutron events is profoundly similar to what has been observed for the inclusive DIS events.

Using scaling-region distributions to select embedding parameters

Reconstructing state-space dynamics from scalar data using time-delay embedding requires choosing values for the delay τ and the dimension m. Both parameters are critical to the success of the procedure and neither is easy to formally validate. While embedding theorems do offer formal guidance for these choices, in practice one has to resort to heuristics, such as the average mutual information (AMI) method of Fraser & Swinney for τ or the false near neighbor (FNN) method of Kennel et al. for m. Best practice suggests an iterative approach: one of these heuristics is used to make a good first guess for the corresponding free parameter and then an “asymptotic invariant” approach is then used to firm up its value by, e.g., computing the correlation dimension or Lyapunov exponent for a range of values and looking for convergence. This process can be subjective, as these computations often involve finding, and fitting a line to, a scaling region in a plot: a process that is generally done by eye and is not immune to confirmation bias. Moreover, most of these heuristics do not provide confidence intervals, making it difficult to say what “convergence” is. Here, we propose an approach that automates the first step, removing the subjectivity, and formalizes the second, offering a statistical test for convergence. Our approach rests upon a recently developed method for automated scaling-region selection that includes confidence intervals on the results. We demonstrate this methodology by selecting values for the embedding dimension for several real and simulated dynamical systems. We compare these results to those produced by FNN and validate them against known results—e.g., of the correlation dimension—where these are available. We note that this method extends to any free parameter in the theory or practice of delay reconstruction.

Pomegranate Leaf Disease Detection Using Supervised and Unsupervised Algorithm Techniques

Pomegranate is a highly profitable fruit which produces abundantly in several Asian countries. However, due to a wide range of factors, the plants are infected with a wide range of illnesses that kill off the entire crop, leading to a catastrophically low product production. To address the issues in Phytopathology, this research suggests an image processing, supervised and unsupervised approach to wellness detection and categorization of pomegranate leaf. The diseases spread by insects and the environment affect the leaves. Some examples of these ailments include blight microbe, rot, and spot. The proposed system employs some images for training, and others for testing functions. First, a color image is preprocessed and employed k-means clustering to isolate the damaged region of the leaf. Locating the Region of Interest, scaling, color converting, and filtering are all part of the pre-processing process. Next, supervised learning models like ResNet and MobileNet are used to extract features and classify data. Classification criteria are utilized to locate the top-performing model. Metrics analysis reveals that MobileNet outperforms ResNet by 1.79%, providing an accuracy of 97.32%.

Inertial particles in superfluid turbulence: Coflow and counterflow

We use pseudospectral direct numerical simulations to solve the three-dimensional (3D) Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model of superfluid helium. We then explore the statistical properties of inertial particles, in both coflow and counterflow superfluid turbulence (ST) in the 3D HVBK system; particle motion is governed by a generalization of the Maxey–Riley–Gatignol equations. We first characterize the anisotropy of counterflow ST by showing that there exist large vortical columns. The light particles show confined motion as they are attracted toward these columns, and they form large clusters; by contrast, heavy particles are expelled from these vortical regions. We characterize the statistics of such inertial particles in 3D HVBK ST: (1) The mean angle Θ(τ) between particle positions, separated by the time lag τ, exhibits two different scaling regions in (a) dissipation and (b) inertial ranges, for different values of the parameters in our model; in particular, the value of Θ(τ), at large τ, depends on the magnitude of Uns. (2) The irreversibility of 3D HVBK turbulence is quantified by computing the statistics of energy increments for inertial particles. (3) The probability distribution function (PDF) of energy increments is of direct relevance to recent experimental studies of irreversibility in superfluid turbulence; we find, in agreement with these experiments, that, for counterflow ST, the skewness of this PDF is less pronounced than its counterparts for coflow ST or for classical fluid turbulence.

Exact results and the effect of monomer-monomer bond type for a grafted ideal chain.

We determine the equilibrium chain end probability density [Formula: see text] for a one-dimensional ideal chain of N monomers grafted to a planar surface. This distribution is also the distribution function of a three-dimensional chain where the tangential dimensions y, z are integrated out of the distribution. With a small modification of the analysis of Erukhimovich, Johner, and Joanny for free chains near a wall, we are able to obtain exact results for [Formula: see text] for any monomer number N though with the restriction that the monomer-monomer bonds lengths are exponentially distributed. In particular, we obtain exact values for [Formula: see text] and its derivative [Formula: see text] at the surface for any N and the full profile [Formula: see text] for selected values of N. To determine the effect of the bond distribution, we find [Formula: see text] numerically for Gaussian and uniformly distributed one-dimensional bonds and compare with the exact results for exponential bonds. We suggest several ways to quantify the effect of bond type based both on [Formula: see text] near the surface and in the scaling region [Formula: see text]. We then extract the large N limit of [Formula: see text] and show that it is similar to the chain end probability for continuous chains but shifted toward smaller x. We show the amount of shift is a measure of the magnitude of the correction to the continuous chain [Formula: see text]. We derive the value of the shift for exponential bonds and show that the value is different for other bond types. We argue the shift can be interpreted as an effective surface behind the actual surface.

Scaling Region of Weierstrass-Mandelbrot Function: Improvement Strategies for Fractal Ideality and Signal Simulation

Fractal dimension (D) is widely utilized in various fields to quantify the complexity of signals and other features. However, the fractal nature is limited to a certain scope of concerned scales, i.e., scaling region, even for a theoretically fractal profile generated through the Weierstrass-Mandelbrot (W-M) function. In this study, the scaling characteristics curves of profiles were calculated by using the roughness scaling extraction (RSE) algorithm, and an interception method was proposed to locate the two ends of the scaling region, which were named corner and drop phenomena, respectively. The results indicated that two factors, sampling length and flattening order, in the RSE algorithm could influence the scaling region length significantly. Based on the scaling region interception method and the above findings, the RSE algorithm was optimized to improve the accuracy of the D calculation, and the influence of sampling length was discussed by comparing the lower critical condition of the W-M function. To improve the ideality of fractal curves generated through the W-M function, the strategy of reducing the fundamental frequency was proposed to enlarge the scaling region. Moreover, the strategy of opposite operation was also proposed to improve the consistency of generated curves with actual signals, which could be conducive to practical simulations.

Classification of Household Room Air Conditioner User Groups by Running Time in the Hot Summer and Cold Winter Zone of China

Household room air conditioners (RACs) are widely used in residential buildings to maintain an indoor thermal climate in China’s hot summer and cold winter (HSCW) zone. The aggregate utilization of RACs in a region has a great impact on regional energy demand in both the heating and cooling seasons. Classifying household RAC users and identifying their RAC usage demands will contribute to better balanced regional energy management for building energy flexibility. In this study, a data-driven method was proposed to classify the household RAC user groups at the regional level, using running time as an indicator. The results showed that RAC users could be classified into four groups with different RAC usage demands. The Lower Class was determined by the absolute poverty line with the Gini coefficient. In addition, the Upper Class was distinguished through the determination of the scaling region in power-law distribution. At the same time, the similarities and differences between different classes in monthly and hourly periods and the flexibility potential were discussed. The rigid demand was observed in the monthly periods of June, July and August and during the hourly periods of 21:00–22:00 in both the bedroom and living-room.

Robust orbital diamagnetism in correlated Dirac fermions

We study orbital diamagnetism at zero temperature in (2 + 1)-dimensional Dirac fermions with a short-range interaction which exhibits a quantum phase transition to a charge density wave (CDW) phase. We introduce orbital magnetic fields into spinless Dirac fermions on the π-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact in the Dirac semimetal regime, while it is monotonically suppressed in the CDW regime. Around the quantum critical point of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. Besides, the scaling analysis implies that the robust orbital diamagnetism at weak magnetic fields in a Dirac semimetal regime would hold not only in our model but also in other interacting Dirac fermion systems as long as scaling regions are wide enough. The scaling behavior may also be regarded as a quantum, magnetic analogue of the critical Casimir effect which has been widely studied for classical phase transitions.

Dynamics of semiflexible generalized scale-free polymer networks

We study the relaxation dynamics of a new type of hyperbranched polymer networks, which are constructed using a degree distribution specific to scale-free networks. The topology of the constructed networks is controlled through three parameters: γ, which measures the density of links in the network, the minimum allowed degree Kmin and the maximum allowed degree Kmax. The static properties of the polymers are investigated through the mean square radius of gyration. We study the dynamics in the framework of the generalized Gaussian structures model by monitoring in detail the influence of networks’ construction parameters, namely γ, Kmin, and Kmax, and the stiffness parameter q on the relaxation quantities: averaged monomer displacement, storage modulus and loss modulus. In the intermediate (time or frequency) regions of the dynamical quantities we encounter a scaling behavior for γ=2.5 and usually a non-scaling behavior for other values of γ. Switching on the stiffness parameter q one is able to destroy, create or enlarge some scaling regions for other combinations of the parameters. Another way to widen a scaling region is to slightly increase Kmin.

Correlation sum scalings from mixed-mode oscillations in weakly coupled molecular lasers.

A model for two symmetrically coupled lasers is investigated, in which mixed-mode oscillations arise in the absence of coupling. For small enough coupling, we show that in the time series, certain dynamical transitions from different resonances in the chaotic regime may be explained by the overlap of suitable resonances. These are families of N : N + 1 resonances, which result in isolas as well as isolas consisting of intermediate-phase resonances N : N. It appears that the overlap of resonances can explain the onset of two different scaling regions in the dimension correlation sum, which display an explicit dependence on the optical coupling strength. For very small coupling ranges, there are larger scaling regions that look analogous to that for the uncoupled laser system. For larger coupling, but still well below the synchronization threshold, steeper and larger scaling regions arise, in particular, in the smaller partitions.