Fractal-based Approach Research Articles

Enhancement of medical MRI images based on fractal operators

This paper presents texture enhancement algorithms for medical images. MRI brain scans often contain large, low-contrast grey areas that hold important information for doctors. Improving the texture helps highlight these areas for more detailed analysis. The study found that fractal operators are especially effective for processing medical images. The mathematical basis of these operators is explained through the Grünwald-Letnikov fractional derivatives. The process of creating fractal differential masks and applying them to enhance images is described. The fractal-based approach improves image qualities such as contrast, correlation, energy, and homogeneity. It was concluded that this method is well-suited for MRI image enhancement, both visually and based on metrics, making it a practical solution for real-world applications.

Two 3D Fractal-Based Approaches for Topographical Characterization: Richardson Patchwork versus Sdr.

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.

Heat transport analysis of nanoliquid in a microchannel with aggregation kinematics: a modified Buongiorno model approach

ABSTRACT Convective heat transmission of Ti O 2 − EG nanoliquid under slip and convective regime in a microchannel is examined using a modified Buongiorno model. The fractal-based approach is employed to describe the aggregation of nanoparticles. The impact of molecular dynamics, particularly on dynamic viscosity and thermal conductivity due to the aggregation of nano-sized particles, is simulated with the help of two significant models: namely, the Krieger-Dougherty model and the Maxwell-Bruggeman model, respectively. The aspect of the interfacial layer enables us to get a realistic nanoliquid model. The solutions for the designed nondimensional mathematical model are obtained numerically. The variation in flow and thermal distribution for pertinent parameters are visualized graphically. The study reveals that the thermophysical characteristics sturdily depend on nanoparticle concentration and cluster formation. It is emphasized that the viscous dissipation and radiative heat transfer contribute towards magnifying the irreversibilities in a microchannel. The findings are useful in bioconvection and various heat transfer applications.

A GENERALIZED FRACTAL-BASED APPROACH FOR STRESS-DEPENDENT PERMEABILITY OF POROUS ROCKS

The pore geometry of porous rocks is fundamental for accurate description of stress dependence of effective permeability, which is an important parameter of mass transfer in porous rocks. An important physical assumption that porous rocks contain numerous elliptical or spherical pores has been shown to be successfully applied to many aspects of hydromechanical coupling properties of porous rocks. To investigate the detailed description of pore structures on the degree of effect on the coupled hydromechanical process, in this work, a generalized stress-dependent model for permeability of porous rocks has been proposed based on fractal geometry theory and mechanics of porous rock. The proposed model is expressed as a nonlinear function of pore structure parameters, such as aspect ratio ([Formula: see text]), the fractal dimensions ([Formula: see text] and [Formula: see text]) for tortuosity, the initial fractal dimension ([Formula: see text]), and initial porosity ([Formula: see text]) as well as matrix elastic constants ([Formula: see text] and [Formula: see text]) of porous rocks without any empirical parameter. The validity of the proposed models is verified by the good agreements between available experimental data and theoretical predictions of stress-dependent permeabilities of porous rocks. Detailed discussions of the essential effects of pore structures parameters and material elastic constants of porous rocks on the dimensionless stress-dependent permeabilities are performed. It is found that the stress parameters ([Formula: see text] and [Formula: see text]) have remarkable effects on the dimensionless stress-dependent permeabilities compared with other parameters ([Formula: see text] and [Formula: see text]). The proposed model may contribute to a better quantitative understanding of the coupled hydromechanical properties of porous rocks.

Fractal-based approach on analyzing the trends of climate dynamics

The terminology “climate change” refers to changes that occur over longer periods of time in the climate and weather patterns of the world. This paper investigates the climate changing patterns by providing a relationship between carbon dioxide emissions and natural parameters such as temperature and precipitation anomaly. The irregularity of the temperature anomaly and precipitation anomaly is analyzed using the fractal dimension via the Hurst exponent. The range of fractal dimensions for the parameters is estimated between 1.01 and 1.60. From the obtained values of fractal dimension, the parameters are classified and their short-term forecast is presented from 2023 to 2032 using the autoregressive integrated moving average model.

Fractal Geometry in High-Frequency Trading: Modeling Market Microstructure and Price Dynamics

This theoretical article delves into the intricate world of high-frequency trading (HFT) without empirical testing of real-world data, focusing on the incorporation of fractal geometry principles to enhance our understanding of market microstructure and price dynamics. In the introduction, we outline the significance of this research in the context of modern financial markets and lay out the objectives of our theoretical analysis. The article then takes an in-depth dive into fractal geometry fundamentals, illuminating its core concepts and its relevance within financial markets. Subsequently, the article explores the landscape of high-frequency trading, offering an overview of this dynamic domain and how fractal geometry can be incorporated into trading models. The section on modeling market microstructure presents theoretical approaches to understanding order flow dynamics, including novel derivations and equations. It then transitions into fractal-based approaches for analyzing the complexities of market microstructure, providing both an original perspective and numbered equations. Moreover, this article investigates the theoretical modeling of price dynamics, underscoring the pivotal role of fractal geometry in enriching these models. The discussion revolves around the fundamental autoregressive models and multifractal models, and it elucidates how fractal geometry principles, such as the Hurst exponent, come into play. We explore the self- similarity of price dynamics, fractal dimensions, and how these aspects can be integrated into high-frequency trading strategies. Overall, this article offers a comprehensive theoretical exploration of fractal geometry's implications in the realm of high-frequency trading, providing valuable insights for both researchers and practitioners seeking to fathom the complexities of market microstructure and price dynamics. The incorporation of fractal principles into financial models fosters a deeper understanding of self-similarity and complexity within financial markets, even in the absence of empirical data.

Fractal-Based Approaches to Pore Structure Investigation and Water Saturation Prediction from NMR Measurements: A Case Study of the Gas-Bearing Tight Sandstone Reservoir in Nanpu Sag

Pore space of tight sandstone samples exhibits fractal characteristics. Nuclear magnetic resonance is an effective method for pore size characterization. This paper focuses on fractal characteristics of pore size from nuclear magnetic resonance (NMR) of tight sandstone samples. The relationship between the fractal dimension from NMR with pore structure and water saturation is parameterized by analyzing experimental data. Based on it, a pore structure characterization and classification method for water-saturated tight sandstone and a water saturation prediction method in a gas-bearing sandstone reservoir have been proposed. To verify the models, the fractal dimension from NMR of 19 tight sandstone samples selected from the gas-bearing tight sandstone reservoir of Shahejie Formation in Nanpu Sag and that of 16 of them under different water saturation states are analyzed. The application result of new methods in the gas-bearing tight sandstone reservoir of Shahejie Formation in Nanpu Sag shows consistency with experimental data. This paper has facilitated the development of the NMR application by providing a non-electrical logging idea in reservoir quality evaluation and water saturation prediction. It provides a valuable scientific resource for reservoir engineering and petrophysics of unconventional reservoir types, such as tight sandstone, low porosity, and low permeability sandstone, shale, and carbonate rock reservoirs.

A Fractal-Based Approach to Lightning Protection of Historical Buildings and Monuments: The Parthenon Case Study

A fractal-based approach to the lightning protection of historical buildings and monuments against direct lightning flashes is introduced. The proposed methodology is based on a stochastic lightning attachment model that considers physical criteria on downward and upward leaders’ inception and propagation. The model foresees multiple competing upward leaders incepting from vulnerable points of the monument under protection and considers the branching and tortuous behavior of the lightning attachment phenomenon. Applying the proposed methodology to the Parthenon has shown that the risk of direct lightning flashes per year that cause physical damage to the monument is not acceptable without an external lightning protection system (LPS); two different LPSs are evaluated in terms of lightning interception efficiency. Lightning risk assessment results are discussed and compared with those obtained by implementing the procedures of the International Electrotechnical Commission (IEC) 62305.

PO-1327 Fractal-based radiomic approach to tailor the chemotherapy treatment in rectal cancer

PO-1327 Fractal-based radiomic approach to tailor the chemotherapy treatment in rectal cancer

A fractal-based approach for cracking characterization and whole process prediction exploration of PP fiber reinforced ECC containing sustainable ingredients

This study focuses on an eco-friendly engineered cementitious composite (SSPP-ECC) using high-content fly ash (FA) as a cementitious cleaner production alternative, waste superfine sand as silica sand replacement and economical polypropylene (PP) fiber as expensive polyvinyl alcohol (PVA) fiber replacement. The lack of quantitative sustainability assessment and prediction of high ductility SSPP-ECC has impeded the engineering application of SSPP-ECC. This study presents a fractal-based cracking whole process preliminary analysis for SSPP-ECC structural life cycle assessment in order to promote a wider application of SSPP-ECC as large-deformation structural materials, as well as develop the application of fractal geometry in ECC by novel evaluation modes. A new and SSPP-ECC with up to 60% cement replacement by fly ash was designed, followed by a four-point flexural test accompanying with surface crack monitoring. The typical deformation hardening SSPP-ECC has been proved to have engineering potential in improving the structural safety due to good deformation following and crack controlling capacities. It is recommended to combine the fractal dimension and average crack width to reflect the overall fracture energy in the four-point flexural failure process of SSPP-ECC, which would have reliable and effective evaluation effects. Based on the correlation analysis results, the quantitative assessment and prediction models of cracking whole process could be established for eco-friendly SSPP-ECC structural life cycle assessment, which can be benefit to the structural life cycle assessment of SSPP-ECC engineering application based on non-destructive parameters of load and deflection. The eco-friendly SSPP-ECC, as a potential cleaner production, not only is a technically reasonable strategy, but also would lead to significant sustainability benefits with a growing level of environmental awareness.

Experimental study of hydraulic properties in grain packs: Effects of particle shape and size distribution

Uniform and multi-dispersed grain packs have been frequently used to conceptually study flow in porous media. Numerical simulations were previously used to address the effect of particle shape on characteristics, such as pore space fractal dimension, moisture characteristic curve (MCC) and saturated hydraulic conductivity (SHC) of grain packs. However, experimental observations are still required since fractal-based approaches have been extensively proposed to model various properties in porous media. In this study, 16 angular sand and 16 spherical glass bead samples with different particle size distributions (PSDs) from well- to poorly-sorted were packed. The MCC was measured using the combination of sandbox and pressure plates methods. The pore space fractal dimension (DMCC), calculated from the measured MCC, ranged from 0.80 to 2.86 in sand and from ‐0.18 to 2.81 in glass bead packs, which indicated that DMCC may be negative in homogeneous media (e.g., glass bead packs) consistent with several studies in the literature. Results showed greater DMCC for the sand packs than the glass bead packs with the same geometric mean diameter values and PSDs. This clearly demonstrated the effect of particle shape on DMCC in the studied packs. The critical path analysis (CPA) approach was used to estimate the SHC measured using the constant-head method. We found that the CPA estimated the SHC accurately, within a factor of four of the measurements on average. Although the CPA is theoretically known to be accurate in media with broad pore size distributions, we experimentally found that it estimated the SHC in various types of grain packs reasonably well.

FRACTAL-BASED MODELS STUDY OF THE RELATIVE HYDRAULIC CONDUCTIVITY AND SWCC OF BENTONITE BY SYNCHROTRON RADIATION SAXS AND X-RAY COMPUTED TOMOGRAPHY

Fractal-based approaches have become popular for describing the hydraulic functions. The SWCC and relative hydraulic conductivity were calculated and compared based on fractal models by the fractal dimension ([Formula: see text] determined by small angle X-ray scattering (SAXS) and X-ray computed tomography (CT). Pore structure parameters including pore size, [Formula: see text], tortuosity and tortuosity fractal dimension, porosity, characteristic length were investigated. The SWCC and relative hydraulic conductivity were predicted, compared and verified. The results indicated that the [Formula: see text] of GMZ01 calculated by SAXS and CT were 2.60 and 2.72, respectively, and the difference was small. The [Formula: see text] of GMZ01 calculated by CT was 2.62. [Formula: see text] calculated by SAXS and CT has a large difference. Nitrogen adsorption revealed the effectiveness of SAXS in predicting porosity in the nanoscale self-similar interval. A SWCC fractal model considering the tortuosity fractal dimension was improved. The tortuosity of GMZ01, CaGMZ, GMZ07 and SY are calculated as 1.53, 1.47, 1.60 and 1.29, respectively. When the tortuosity was considered, the hydraulic conductivity became lower. For GMZ01, the SWCC predicted by the fractal dimension measured by SAXS was closer to the experimental data than the SWCC predicted by the fractal dimension measured by CT. The fractal model was difficult to describe SWCC under low matric suction, while the predicted SWCC had a good correlation with the experimental value in high matric suction. The relative hydraulic conductivity calculated by Xu and Yu model was larger than that calculated by Xu model.

Fractality in water distribution networks: application to criticality analysis and optimal rehabilitation

ABSTRACT Fractals have been identified as a common feature in many natural and artificial networks that exhibit self-similarity of the topological patterns, i.e. different parts of the system have similar structures to each other as well as to the whole system. This study investigates the fractality in water distribution networks (WDNs) and the application of the fractal property in WDNs analysis. Specifically, we explore the existence of fractal topological patterns in eight real-world WDNs of different complexities by using the box-covering algorithm. The results demonstrate all of the studied WDNs are fractal. Moreover, the application of the fractal property is demonstrated via critical pipe identification and optimal rehabilitation of benchmark real-world WDNs. All results show that the fractal-based approach can achieve better or equally good solutions compared with conventional methods in a much more efficient way, e.g. via automation of some processes or significant reduction in the search space/components to consider.

A fractal-based approach to evaluate the effect of microstructure on the permeability of two-dimensional porous media

The complex and heterogeneous microstructure of underground porous media usually results from geological processes such as deposition, compaction, cementation and fluid-mineral interactions. Variations in these microstructural characteristics largely determine the differences in the transport properties of porous media. The fractal geometry theory has been successfully applied to characterize the microstructure and transport properties of underground reservoirs. In this study, two-dimensional porous media with differently heterogeneous structures are reconstructed by utilizing the quartet structure generation set method. Fractal dimension and lacunarity are implemented to quantify the complex microstructure and analyze the relationships among these parameters. Under specific porosity, the fractal dimension increases with the reduction of lacunarity according to a power law relationship. Meanwhile, permeability has a perfect power law relationship with porosity under the same heterogeneity. The stronger heterogeneity increases the degree of pore aggregation, resulting in increased pore radius for fluid flow. For porous media with the same porosity, permeability has a significant positive power law relationship with lacunarity and a negative relationship with fractal dimension. The results demonstrate that fractal parameters are helpful to fully understand the influence of complex microstructure and chemical reactions on the macroscopic physical properties of porous media.

Shielding Failure of High-Voltage Substations: A Fractal-Based Approach for Negative and Positive Lightning

A fractal-based approach is presented for the direct-stroke shielding analysis of high-voltage substations. The proposed method considers the effect of lightning polarity and the stochastic nature of the lightning attachment phenomenon. An application to a typical 69 kV substation reveals that shielding failures may occur even if the shielding design is realized with IEEE Std 998-2012 methods. This can be explained by the fact that the shielding design methods adopted by IEEE Std 998 do not consider the effects of lightning polarity and object height on striking distance. In addition, IEEE Std 998 methods adopt a deterministic approach on shielding failure analysis neglecting the branched and tortuous behavior of lightning discharges. Fractal-based simulation results show a considerable dispersion of striking distance and a significantly higher shielding failure probability for downward positive lightning than negative lightning. This work forms a discussion framework on shielding failure analysis following a stochastic approach; this approach may explain unexpected shielding failures, such as those reported in IEEE surveys, and can be used for the direct-stroke shielding design of mission-critical high-voltage substations.

EDITORIAL: AN INTRODUCTION TO FRACTALS IN CONSTRUCTION MATERIALS

In recent years, the application of fractal theory in construction materials has drawn tremendous attention worldwide. This special issue section containing seven papers publishes the recent advances in the investigation and application of fractal-based approaches implemented in construction materials. The topics covered in this introduction mainly include: (1) the fractal characterization of construction materials from nano- to micro-scales; (2) combining fractals methods with other theoretical, numerical and/or experimental methods to evaluate or predict the macroscopic behavior of construction materials; (3) the relationship of fractal dimension with the macro-properties (i.e. mechanical property, shrinkage behavior, permeability, frost resistance, abrasion resistance, etc.) of construction materials.

A fractal-based approach for reconstructing pore structures of GGBFS-blended cement pastes

The durability and mechanical behavior of cementitious materials can be substantially affected by changes in pore structure that occur during the hydration process. An accurate analysis of pore structure thus plays an important role in the interpretation and prediction of the performance of cementitious materials. This study investigated an analytical fractal reconstruction procedure for cementitious materials and demonstrated its application by reconstructing pore structure using fractal theory from a geometric perspective. For this purpose, microstructural characteristics of ground granulated blast-furnace slag-based cement pastes were evaluated using the results of mercury intrusion porosimetry measurements. Fractal characteristics in the mesopores and larger capillary pores were quantified using the pore surface fractal type, whereas those in the middle capillary pores were quantified using the solid mass fractal type. As a result of reconstructing pore structure, variations in the cumulative pore volumes appeared similar to those of the measured pore structure. Moreover, the differential pore size distributions of all pore regions were quantified as the fractal dimensions. These results indicated that the investigated methodology can be practically applied for the analysis of changes in pore structure caused by hydration in cementitious materials.

Experimental Analytical Study on Fractal Behaviors of the Density Current

Density current is caused by the difference in density with the ambient fluid, believed to hold fractal features. A comprehensive laboratorial study on fractal properties of density current is conducted. Variations of the bed slope, fluid concentration, discharge and channel narrowing are studied along with the fractal analysis of the density current. Experiments were performed in 28 different modes in a flume with 8 m length, 35 cm width and 60 cm depth and 1–3% longitudinal slope. All the experiments are recorded by the high-resolution cameras, and the pictures of the density current evolution are transformed into several snapshots. MATLAB codes are also developed for image processing and calculating the fractal indices of the images. Results indicated that as the flume bed slope increases, the fractal dimension of the density current decreases. Conversely, discharge and concentration of the density current depict a negative correlation with the fractal dimension. Moreover, when the vertex angle has a minimum value of 155° in non-narrowed channel, the angle escalated to 176.34° and 180° for local and protracted narrowing, respectively, a sign of transmuting from mono- to multi-fractality. Unlike discharge boosts, α range decreases 11.4% and α angle grows 7.8%, a sign of mono-fractality. However, when bed slope increases, α range increases 6.4% and the density current turns multi-fractal. Besides, current concentration shows a significant fractal-based correlation with the Reynolds numbers, R2 = 0.9. Finally, the correlation between the Richardson number and entrainment ratio enhances significantly from R2 = 0.81 to R2 = 0.92 when a fractal-based approach is applied.

Hybrid Stochastic Fractal-Based Approach to Modeling the Switching Kinetics of Ferroelectrics in the Injection Mode

The paper is devoted to the development and implementation of a hybrid stochastic fractal-based approach for modeling electron-induced kinetics of polarization switching in ferroelectrics as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes the initial value problem for the fractional order differential equation. Computational schemes for solving fractional differential problem are constructed using the Adams–Bashforth–Moulton type predictor-corrector methods. The stochastic algorithm based on the Monte Carlo method is proposed to simulate the domain nucleation process during restructuring the domain structure in ferroelectrics. The polarization switching current of ferroelectrics in the electron injection mode is evaluated to demonstrate the computational experiment results with a comparison of the experimental data.

Assessment of Fractal/Wrinkling Theories for Describing Turbulent Reacting Fine Structures under MILD Combustion Regimes

ABSTRACT This paper presents an assessment study of a modification introduced to a recently developed extended version of Eddy Dissipation Concept (EDC) chemistry/flow interaction approach for modeling Moderate or Intense Low-oxygen Dilution (MILD) combustion conditions. Compared to traditional combustion regimes, MILD combustion systems produce higher thermal efficiency and lower pollutant emissions. However, numerical simulation of turbulent flames under MILD combustion conditions poses challenges mainly due to strong coupling between turbulent flow and chemical kinetics over a wide range of turbulent flow conditions. Hence, combustion modeling is key for describing the interaction between chemistry and turbulent flow in MILD reacting flow regimes. This study examines the performance of a hybrid combustion approach (called hereafter wrinkling-EDC) which models the reacting scales of turbulent flows based on a fractal-based flame surface density and turbulent intermittency approaches in, respectively, premixed and diffusion flame regimes. Simulations are performed for two MILD combustion conditions of a Jet-in-Hot-Coflow burner, namely HM1 and HM3 flames, using wrinkling-EDC as well as the extended EDC. In addition, the results of the standard EDC model are provided for reference. The predictions of all three models are compared with their counterparts’ experimental measurements of temperature and species concentrations. For both HM1 and HM3 flames, the results indicate that, compared to the standard and extended EDC approaches, the wrinkling-EDC model produces better predictions of the mixing field (close to the centerline of the burner) and temperature field. However, the predictions of all models become more comparable downstream of the burner. In addition, while all models produce comparable predictions of major species, intermediate and slow-forming species are best predicted downstream of the burner by the standard EDC model.