Multifractal Scaling Research Articles

Multifractal Analysis for Evaluating the Representation of Clouds in Global Kilometer‐Scale Models

AbstractClouds are one of the largest sources of uncertainty in climate predictions. Global km‐scale models need to simulate clouds and precipitation accurately to predict future climates. To isolate issues in their representation of clouds, models need to be thoroughly evaluated with observations. Here, we introduce multifractal analysis as a method for evaluating km‐scale simulations. We apply it to outgoing longwave radiation fields to investigate structural differences between observed and simulated anvil clouds. We compute fractal parameters which compactly characterize the scaling behavior of clouds and can be compared across simulations and observations. We use this method to evaluate the nextGEMS ICON simulations via comparison with observations from the geostationary satellite GOES‐16. We find that multifractal scaling exponents in the ICON model are significantly lower than in observations. We conclude that too much variability is contained in the small scales leading to less organized convection and smaller, isolated anvils.

Multifractal Analysis of the Impact of Fuel Cell Introduction in the Korean Electricity Market

This study employs multifractal detrended fluctuation analysis to investigate the impact of fuel cell introduction in the Korean electricity market via the lens of multifractal scaling behavior. Using multifractal analysis, the research delineates discrepancies between peak and off-peak hours, accounting for the daily cyclicity of the electricity market, and proposes a crossover point detection method based on the Chow test. Furthermore, the impacts of fuel cell introduction are evidenced through various methods that encompass multifractal spectra and market efficiency. The findings initially indicate a higher degree of multifractality during off-peak hours relative to peak hours. In particular, the crossover points emerged solely during off-peak hours, unveiling short- and long-term dynamics predicated on a near-annual cycle. Additionally, the average Hurst exponent for the short-term was 0.542, while the average for the long-term was 0.098, representing a notable discrepancy. The introduction of fuel cells attenuated the heterogeneity in the scaling behavior, which is potentially attributable to the decreased volatility in both the supply and demand spectra. Remarkably, after the introduction of fuel cells, there was a discernible decrease in the influence of long-range correlation within multifractality, and the market exhibited an increased propensity toward random-walk behavior. This phenomenon was also detected in the market deficiency measure, from an average of 0.536, prior to the introduction, to an average of 0.267, following the introduction, signifying an improvement in market efficiency. This implies that the introduction of fuel cells into the market engendered increased supply stability and a consistent increase in demand, mitigating volatility on both the supply and demand sides, thus increasing market efficiency.

Structured multifractal scaling of the principal cryptocurrencies: Examination using a self‐explainable machine learning

AbstractThis paper introduces a novel statistical testing technique known as segmented detrended multifractal fluctuation analysis (SMF‐DFA) to analyze the structured scaling properties of financial returns and predict the long‐term memory of financial markets. The proposed methodology is applied to assess the efficiency of major cryptocurrencies, expanding upon conventional approaches by incorporating different fluctuation regimes identified through a change‐point detection test. A single‐factor model is employed to characterize the endogenous factors influencing scaling behavior, leading to the development of a self‐explanatory machine learning approach for price forecasting. The proposed method is evaluated using daily data from three major cryptocurrencies spanning from April 2017 to December 2022. The analysis aims to determine whether the digital market has experienced significant changes in recent years and assess whether this has resulted in structured multifractal behavior. The study identifies common periods of local scaling among the three prices, with a noticeable decrease in multifractality observed after 2018. Furthermore, complementary tests on shuffled and surrogate data are conducted to explore the distribution, linear correlation, and nonlinear structure, shedding light on the explanation of structured multifractality to some extent. Additionally, prediction experiments based on neural networks fed with multi‐fractionally differentiated data demonstrate the utility of this new self‐explanatory algorithm for decision‐makers and investors seeking more accurate and interpretable forecasts.

Multifractal characterization of fried foods pore microstructure

This study aimed to unravel the multifractal properties of internal microstructure in relation to textural evolution of meat-analog (MA) based coated fried foods. Wheat and rice flour-based batters were used to coat MA model that was deep fried at 180 °C for 2, 4 and 6 min in canola oil. Internal pore microstructures were investigated by X-ray microtomography based multifractal analysis (MFA) and texture were assessed by mechanical texture analyzer. Results showed that batter coatings greatly influenced the formation of internal microstructure during frying as well as post-frying mass redistribution and textural evolution. The frying time impacted the evolution of micropores, and porosity showed a positive correlation with the fat content of MA-based fried products. Porous, low-moisture and high-fat containing coated fried MA-based product demonstrated higher textural stability. Internal microstructure (pore distribution) of fried MAs were heterogenous and possessed multifractal scaling behavior, as depicted by MFA outcomes (Singularity & Rényi spectra). Strong correlation observed between moisture-fat, texture, porosity and selected multifractal parameters (Δα, Δfα, R-L, D1, D2, ΔD).

Is there a time-varying nexus between stock market liquidity and informational efficiency? – A cross-regional evidence

PurposeThis study aims to measure the degree of volatility comovement between stock market liquidity and informational efficiency across Asia, Europe, North-South America, Africa, and the Pacific Ocean over three decades. In particular, the authors analyze the extent of the time-varying nexus between different aspects of stock market liquidity and multifractal scaling properties of the stock return series across various regions and diversified market conditions. This study further investigates several factors altering the degree of dynamic conditional correlations (DCCs) between the efficiency and liquidity of the domestic stock markets.Design/methodology/approachThe study measures five aspects of stock market liquidity – tightness, depth, breadth, immediacy, and adjusted immediacy. The authors evaluate the multifractal scaling properties of the stock return series to measure the level of stock market efficiency across the regions and diversified market conditions. The study uses the dynamic conditional correlation-multivariate generalized autoregressive conditional heteroscedasticity framework to quantify the degree of volatility comovement between liquidity and efficiency over the period.FindingsThe study finds the presence of stronger volatility comovement between inefficiency and illiquidity due to the price impact characteristics of the stock markets irrespective of different regions and diversified market conditions. The extent of time-variation increased following the shock periods, indicating the significant role of the financial crisis in increasing the volatility comovement between inefficiency and illiquidity. The highest degree of time-varying correlation is observed in the developed stock markets of Northwestern and Northern Europe compared to the regional and emerging counterparts. On the other hand, weak DCCs are observed in the emerging stock markets of Europe.Originality/valueThe output of the present study assists investors in identifying diversification opportunities across the regions. Additionally, the study has significant implications for market regulators, aiding in predicting future troughs and peaks. The prediction, in turn, helps formulate capital market development plans during dynamic economic situations.

Anisotropic size effect of 3D printed LC3-based engineered cementitious composites (LC3-ECC)

One of the critical factors affecting the development of 3D concrete printing (3DCP) is the challenging issue of in-situ reinforcement. Engineered Cementitious Composites (ECC) are printable self-reinforced materials, and their application in 3DCP technology can facilitate de-steelisation. However, traditional ECC materials pose certain concerns for sustainable environmental development. The integration of Limestone Calcined Clay Cement (LC3) suitable for 3DCP into ECC (LC3-ECC) presents an ideal solution to the aforementioned challenges. Moreover, conducting comprehensive research into its size effects is an essential step from experimentation to engineering application. A thorough exploration of the size effects of 3D printed LC3-ECC in compression, shear, and flexural fracture aspects is conducted to derive size effect laws. The relationship between the anisotropic mechanical properties and size effects has been established. The mold-cast LC3-ECC precisely follows the Bažant size effect law (SEL). The fiber orientation effect enhances bridging efficiency, leading to the fact that the mechanical properties of certain printed LC3-ECC are hardly affected by the size effect. The mechanical performance of some printed LC3-ECC depends on interlayer strength, making its primary reason for size effect not in the Fracture Process Zone (FPZ) energy release, hence closer to the Multifractal Scaling Law (MFSL). LC3-ECC exhibits weak anisotropy in mechanical properties, showing satisfactory stability. However, under flexural fracture behavior, the anisotropic size effect is higher, necessitating careful consideration in structural design.

Multifractal Scaling of Singularity Spectra ofDigital Mueller-matrix Images of BiologicalTissues: Fundamental and Applied Aspects

Multifractal Scaling of Singularity Spectra ofDigital Mueller-matrix Images of BiologicalTissues: Fundamental and Applied Aspects

Monofractality in the Solar Wind at Electron Scales: Insights from Kinetic Alfvén Waves Turbulence.

The breakdown of scale invariance in turbulent flows, known as multifractal scaling, is considered a cornerstone of turbulence. In solar wind turbulence, a monofractal behavior can be observed at electron scales, in contrast to larger scales where multifractality always prevails. Why scale invariance appears at electron scales is a challenging theoretical puzzle with important implications for understanding solar wind heating and acceleration. We investigate this long-standing problem using direct numerical simulations of three-dimensional electron reduced magnetohydrodynamics. Both weak and strong kinetic Alfvén waves turbulence regimes are studied in the balanced case. After recovering the expected theoretical predictions for the magnetic spectra, a higher-order multiscale statistical analysis is performed. This study reveals a striking difference between the two regimes, with the emergence of monofractality only in weak turbulence, whereas strong turbulence is multifractal. This result, combined with recent studies, shows the relevance of collisionless weak KAW turbulence to describe the solar wind at electron scales.

Multifractal Scaling characteristics of lineament networks of a fractured sandstone aquifer system

Multifractal Scaling characteristics of lineament networks of a fractured sandstone aquifer system

Multifractal structure of cholinergic innervation in the tunica albuginea of rat testis. Comparison with different models simulating nerve networks

The complexity of the distribution of cholinergic innervation of the albuginea suggests that its structural pattern may exhibit multiple scaling rules rather than a single global scale. Therefore, the study of nerve fibers could be approached through multifractal analysis. The cholinergic fiber plexuses of the rat testicular albuginea, visualized by a histochemical technique for the detection of acetylcholine sterases, will be analyzed for the possible detection of their multifractal structure, calculating several types of multifractal spectra, namely multifractal spectrum f(α) versus α, and the generalized dimension DQ versus Q. In the present study, the results will be compared with the multifractal spectra of plexus models consisting of the elaboration of interconnected line lattices generated, either employing a binary matrix or using a tessellation matrix, and according to various realizations of randomly distributed points in a two-dimensional space. The results of this study suggest that the cholinergic nerve plexuses of the testicular albuginea of the rat show a multifractal behavior, and the multifractality of the real data is greater than that of the simulated networks. However, Voronoi tessellations models show a more remarkable similarity of the multifractal scale with the real data in comparison with those generated by a binary matrix.

Spatiotemporal Variation and Long-Range Correlation of Groundwater Levels in Odessa, Ukraine

Increasing groundwater levels (GWLs) may become one of the most serious issues for the city of Odessa, Ukraine. This study investigated the spatial distribution characteristics and multifractal scaling behaviour of the groundwater-level/-depth fluctuations for a Quaternary aquifer in the city of Odessa using a geostatistical approach and multifractal detrended fluctuation analysis (MF-DFA). These two methods were applied to monthly GWL fluctuation time series from 1970 to 2020 to monitor 72 hydrogeological wells situated in different parts of the city of Odessa. The spatial distribution of the GWLs revealed an overall trend of decline and recovery from 1970 to 2020 in the study area, except for most of the southern region, where a persistent recovery of the groundwater depth was observed. The MF-DFA results suggest that the dynamics of the GWL fluctuations have multifractal characteristics in the Odessa area. In addition, both long-range correlations and fat-tail probability distribution contribute to the multifractality. However, long-range correlations among the fluctuations made a major contribution to the observed multifractality of the GWL fluctuation time series. The generalised Hurst exponents show a wide range of change (0.20 < h(q) < 2.85), indicating the sensitivity of the GWL fluctuations to changes in small-scale factors and large-scale factors. Regarding the long-range correlations of the GWL depths, the Hurst exponents (q = 2) demonstrated the positive persistence of groundwater-depth recovery in the southern region and the persistence of groundwater-depth variation in the other regions of the study area. The dynamic changes in the GWL depths in the Odessa area may be influenced by both natural and anthropogenic factors.

Multifractal analysis of meat-analog based coated fried foods texture profile

Texture profile of meat-analog (MA) based fried food products is a complex structure, and rarely studied subject. MA-based fried products mechanical-texture-profile were considered as “fractal geometry” to characterize their textural properties by employing complex statistical approach namely multifractal analysis (MFA). Wheat and rice flour-based batter systems were used to coat the MA, and were fried (at 180 °C) for 2, 4, and 6 min in canola oil. Instrumental puncture test was employed to get mechanical-texture-profile of MA-based fried products and obtained profile was evaluated by MFA. Results revealed that batter-formulation and frying time (FT) impacts the evolution of textural attributes (hardness, brittleness, crispiness), moisture-fat profile and microstructural properties of MA-based coated fried product. The MFA outcomes (Singularity spectra & Rényi spectra) depicts that breakage structure (force distribution) of studied MA-based fried products are non-homogeneous and possesses multifractal scaling behavior. Higher heterogeneity of force distribution is observed in lower concentration of force at outer-crust region compared to inner-core region of coated MA. Heterogeneity of force distribution are positively correlated with FT. Batter-formulation showed substantial impact on texture-profile of MA-based coated fried products and consequently influenced the obtained multifractal parameters. Principal component analysis (PCA) reveals varying extent of correlation between moisture-fat, textural attribute, microporosity and selected multifractal parameters (Δα, Δfα, R-L, ΔD) of fried MA. Industrial relevanceComplex structural pattern of batter coated fried meat-analog (MA)s mechanical texture profile have been successfully and statistically characterized by employing multifractal analysis. This study unraveled the interdependencies among batter-formulation, frying process, mass-profile, microstructure, textural attributes and multifractal parameters. Findings of this study could be used to customize textural attributes of the low fat-containing fried foods. Overall, this work will serve as a ground for designing the production process of emerging MA-based batter-coated fried product.

Geometric Properties of Water-ice Clouds as Observed from Jezero Crater in the First 600 sols with the NavCam Instrument On Board the Mars2020 Rover, Perseverance

In the first 600 sols of the Mars2020 mission, LS 5.6o – 316.8o, 46 cloud movies and 145 cloud surveys were collected to observe clouds at Jezero Crater, the landing site of the Perseverance Rover. Cloud movies were processed using the Mean-Frame Subtraction (MFS) method for revealing cloud structures, which were subsequently analyzed using digital-image processing. Two-dimensional Fast Fourier Transforms (2D-FFT) were used to compute cloud structure sizes ranging from 2.90 to 15.25 km for clouds between 30 and 50 km altitude, based on coincident Mars Climate Sounder vertical profiles of atmospheric water-ice. Same-value thresholding was used to detect the cloud structures in MFS-processed and projected cloud movies. The resolution dependence that was needed to resolve these structures over various thresholds was examined to find multifractal scaling of Mars clouds for resolutions between 0.1 and 1.6 km. We characterize the multiscaling observed in the images and its implications for the design of cloud-tracking cameras from the surface as well as for cloud-resolving models.

Are clean energy markets efficient? A multifractal scaling and herding behavior analysis of clean and renewable energy markets before and during the COVID19 pandemic

The literature lacks thorough and adequate evidence of the efficiency and herding behavior of clean and renewable energy markets. Therefore, the key objective of this paper is to explore the multifractality and efficiency of six clean energy markets by applying a robust method of Multifractal detrended fluctuation analysis (MFDFA) on daily data over a lengthy period. In addition, to examine the inner dynamics of clean energy markets around the global pandemic (COVID19), the data are further divided into two sub-periods of before and during COVID19. Our sampled clean energy markets exhibit multifractal behavior with a significant impact on the efficiency and intensified presence of multifractality during the COVID19 period. Overall, TXCT and BSEGRNX were the most efficient clean energy markets, but the ranking of TXCT deteriorated significantly in the sub-periods. The presence of multifractality and herding behavior symmetry intensified during the crisis period, which gives a potential for advancing portfolio management techniques. Moreover, our study provides practical implications and new insights for various market participants for better management and understanding of risks.

Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland

Revealing spatio-temporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (μ-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q«0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seems to be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion.

Asymmetric efficiency in petroleum markets before and during COVID-19

Petroleum markets encountered exceptional challenges during the outbreak period. In this backdrop, the price dynamics in petroleum markets were also significantly influenced by fearsome environment and unprecedented risk experienced during the pandemic. In this direction, the study attempts to investigate the efficiency dynamics of the petroleum markets before and during the COVID-19 pandemic. The study utilizes high frequency data of four major petroleum markets namely, crude oil, Brent oil, diesel and natural gas. In order to unveil asymmetric multifractal scaling behavior of petroleum markets we employ a widely recognized approach known as asymmetric multifractal detrended fluctuation analysis (A-MF-DFA). The results confirm the presence of prevailing market inefficiencies in petroleum markets. In fact, the findings suggest that asymmetric multifractality is more pronounced during the downward trends. Also, the findings stress that market efficiency dynamics in the petroleum sector are dependent upon investment horizon, market conditions and investor behavior. More importantly, the sub-period analysis of COVID-19 era uncovers deteriorating market efficiencies in petroleum markets. Furthermore, the natural gas market emerges as the most efficient market before and during the COVID-19 time period.

Spontaneous Stochasticity in the Presence of Intermittency.

Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain nondeterministic in the limit where the random input, namely, the thermal noise, vanishes. Here, we investigate the fate of spontaneous stochasticity in the presence of spatial intermittency, with multifractal scaling of the lognormal type, as usually encountered in turbulence studies. In principle, multifractality enhances the underlying roughness, and should also favor the spontaneous stochasticity. This letter exhibits a case with a less intuitive interplay between spontaneous stochasticity and spatial intermittency. We specifically address Lagrangian transport in unidimensional multifractal random flows, obtained by decorating rough Markovian monofractal Gaussian fields with frozen-in-time Gaussian multiplicative chaos. Combining systematic MonteCarlo simulations and formal stochastic calculations, we evidence a transition between spontaneously stochastic and deterministic behaviors when increasing the level of intermittency. While its key ingredient in the Gaussian setting, roughness here surprisingly conspires against the spontaneous stochasticity of trajectories.

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra.

Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time, while during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectra alone. By integrating this index with multifractal spectra, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

Analysis of fractal properties of horizontal component of Earth’s magnetic field of different geomagnetic conditions using MFDFA

Depending on the orientation of the interplanetary magnetic field, solar disturbances induce perturbations in the geomagnetic field as observed by magnetometers on the ground. This study examines the signatures of fractal property of the geomagnetic field’s horizontal component (H time series), as measured by the ground-based magnetometer at Bangui [BNG] (4.33°N, 18.57°E). The Multifractal detrended fluctuation analysis (MF-DFA) method is employed in the study, as it can explore higher-dimensional fractal and multifractal characteristics hidden in the time series. By incorporating MF-DFA, we investigated the changes in the fractal properties of H time series under various geomagnetic conditions, and quantified using Hurst exponent (H) and generalized Hurst exponent h(q). A clear difference in the behaviour of H component during quiet, moderate and intense storm periods is revealed through the analysis of the scaling exponents for different levels of geomagnetic activity. The generalized Hurst exponent h(q) values are found to be higher during the quiet periods, compared to moderate and severe storms periods. It is also observed that both the storm periods and geomagnetically quiet periods are characterized by fractional Brownian motion. The strong q-dependence of h(q) and multifractal scaling exponent τq indicates strong multifractal characteristics of the geomagnetic field data. Thus, the present study reveals that the degree of multifractality is more for the time series of quiet period compared to the one belongs to storm period. Also our results show that the scaling properties of the H time series possess a long-range correlation, showing a long-term persistence of the previous state.

Clean Energy Action Index Efficiency: An Analysis in Global Uncertainty Contexts

Climate change, the scarcity of fossil fuels, advances in clean energy, and volatility of crude oil prices have led to the recognition of clean energy as a viable alternative to dirty energy. This paper investigates the multifractal scaling behavior and efficiency of green finance markets, as well as traditional markets such as gold, crude oil, and natural gas between 1 January 2018, and 9 March 2023. To test the serial dependency (autocorrelation) and the efficient market hypothesis, in its weak form, we employed the Lo and Mackinlay test and the DFA method. The empirical findings showed that returns data series exhibit signs of (in)efficiency. Additionally, there is a negative autocorrelation among the crude oil market, the Clean Energy Fuels Index, the Global Clean Energy Index, the gold market, and the natural gas market. Arbitration strategies can be used to obtain abnormal returns, but caution should be exercised as prices may increase above their actual market value and reduce the profitability of trading. This work contributes to the body of knowledge on sustainable finance by teaching investors how to use predictive strategies on the future values of their investments.