Fractal Parameters Research Articles

The SARS-CoV-2 Virus Detection with the Help of Artificial Intelligence (AI) and Monitoring the Disease Using Fractal Analysis

This paper introduces an AI model designed for the diagnosis and monitoring of the SARS-CoV-2 virus. The present artificial intelligence (AI) model founded on the machine learning concept was created for the identification/recognition, keeping under observation, and prediction of a patient’s clinical evaluation infected with the CoV-2 virus. The deep learning (DL)-initiated process (an AI subset) is punctually prepared to identify patterns and provide automated information to healthcare professionals. The AI algorithm is based on the fractal analysis of CT chest images, which is a practical guide to detecting the virus and establishing the degree of lung infection. CT pulmonary images, delivered by a free public source, were utilized for developing correct AI algorithms with the aim of COVID-19 virus observation/recognition, having access to coherent medical data, or not. The box-counting procedure was used with a predilection to determine the fractal parameters, the value of the fractal dimension, and the value of lacunarity. In the case of a confirmation, the analysed image is used as input data for a program responsible for measuring the degree of health impairment/damage using fractal analysis. The support of image scans with computer tomography assistance is solely the commencement part of a correctly established diagnostic. A profiled software framework has been used to perceive all the details collected. With the trained AI model, a maximum accuracy of 98.1% was obtained. This advanced procedure presents an important potential in the progress of an intricate medical solution to pulmonary disease evaluation.

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.

Кореляційно-фазовий інтелектуальний аналіз комплексного ступеню когерентності лазерних автофлуоресцентних зображень плазми крові та діагностика онкологічних змін органів людини

The theoretical foundations of correlation-phase analysis of laser images of human blood plasma are presented. The values and ranges of change of statistical (moments of the 1st - 4th orders), correlation (Gram-Charlier decomposition coefficients of autocorrelation functions) and fractal (slopes and variance of extremes of logarithmic dependences of power spectra) parameters of the coordinate distributions of CSP are investigated. The objective criteria for diagnosing oncological changes in the blood plasma of a cancer patient are determined.

Інтелектуальна система оцінювання ступеня локальної деполяризації полів лазерної автофлуоресценції двопроменезаломлюючих мереж протеїнових кристалів

The theoretical foundations of the description of scattered coherent radiation fields using a new correlation parameter - the degree of local depolarization (DLD) - are presented. The data of measuring the coordinate distributions of the DLD of laser images of healthy and pathologically altered rat skin are presented. The values and ranges of change of statistical (moments of the 1st - 4th orders), correlation (correlation area) and fractal (slopes and variance of extremes of logarithmic dependences of power spectra) parameters of the coordinate distributions of the DLD are investigated. The objective criteria for diagnosing oncological changes in the structure of the rat skin are determined.

ANALYSIS OF CHANGES IN FRACTAL, STATISTICAL AND KINETIC PARAMETERS DURING THE HETEROANNIHILATION OF PARTICLES ON THE SIMULATED STRUCTURALLY INHOMOGENEOUS SURFACES

To investigate the mechanisms of interaction of particles on structurally inhomogeneous surfaces, the influence of surface morphology, distribution of interacting particles and their mobility on the mechanisms of ongoing processes, various modeling approaches are widely used. The paper presents the results of comparison of kinetic, statistical and fractal parameters changing in the process of heteroannihilation of particles distributed chaotically and multifractally on a simulated structurally inhomogeneous surface. To simulate the complex behavior of particles in time and space during heteroannihilation with changes in their mobility across the surface and various interaction probabilities, a class IV probabilistic cellular automaton method was applied. Based on the simulation results, it is shown that the interaction probability, initial distribution, and mobility of interacting particles influence the formation of kinetic modes at different iterations of the heteroannihilation process. It was found that a decrease in the mobility of interacting particles leads to a longer preservation of spatial heterogeneity in the system. An increase in the mobility of interacting particles and the probability of their interaction increases the rate of change in the fractal dimensionality and the rate coefficients of heteroannihilation kinetics. Decrease of fractal dimensionality during heteroannihilation is accompanied by decrease of asymmetry and increase of excess characterizing shape and degree of symmetry of distribution of interacting particles. At the same time, large values of asymmetry and excess indicate a significant deviation from the normal distribution of interacting particles on the surface.

Stage division of urban growth based on logistic model of fractal dimension curves

The time series of fractal dimension values of urban form always take on sigmoid curves. The basic model of these curves is logistic function. From the logistic model of fractal dimension curves, we can derive the speed formula and acceleration formula of urban growth. Using the inflexions of the fractal parameter curves, we can identify the different phases of city development. The main results are as follows. (1) Based on the curve of fractal dimension of urban form, urban growth can be divided into four stages: initial slow growth, accelerated fast growth, decelerated fast growth, and terminal slow growth. The three dividing points are 0.2113Dmax, 0.5Dmax, and 0.7887Dmax, where Dmax is the capacity of fractal dimension. When the fractal dimension reaches half of its capacity value, 0.5Dmax, the urban growth speed reaches its peak. (2) Based on the curve of fractal dimension odds, urban growth can also be divided into four stages: initial slow filling, accelerated fast filling, decelerated fast filling, terminal slow filling. The three dividing points are 0.2113Zmax, 0.5Zmax, and 0.7887Zmax, where Zmax=/(2-Dmax) denotes the capacity of fractal dimension odds (Dmax < 2). Empirical analyses show that the first scheme based fractal dimension is suitable for the young cities and the second scheme based on fractal dimension odds can be applied to mature cities. A conclusion can be drawn that logistic function is one of significant model for the stage division of urban growth based on fractal parameters of cities. The results of this study provide a new way of understanding the features and mechanism of urban phase transition.

Diamond like-carbon coatings for electric vehicle transmission efficiency

A barrier to the adoption of battery electric vehicles is consumer range anxiety. This paper investigates the driving range conceded as a result of the parasitic frictional losses incurred at the gear mesh in a two-stage battery electric vehicle transmission. Amelioration of the parasitic losses through changes to surface roughness and application of thin wear resistant coatings such as DLC are considered. The tribo-dynamics model of the gear frictional losses includes topographical structure of the respective surfaces characterised through surface specific fractal parameters. Analysis shows that the use of the investigated amorphous hydrogenated undoped DLC coating could potentially save 1.1 km of vehicle range during extra urban driving and 0.9 km under urban driving over a full battery discharge cycle.

Preparation and characterization of Y-shaped fractal frequency selective fabric

In order to explore the electromagnetic transmission performance of frequency selective fabrics (FSFs) with fractal units, six samples of Y-shaped fractal parameters with different sizes were prepared by computer embroidery technology, and tested using anechoic chamber test method. The effects of unit type, polarization mode, incident angle and unit size parameters on the transmission performance of different samples were respectively analyzed in depth. The results show that for the aperture type and patch type FSFs, the incident angle has a certain influence. When the incident angle of the two groups of samples is 0°, the resonance peak is the largest. When the incident angle increases to 45°, there are two resonance peaks of different amplitudes in the range of 4 GHz ∼ 20 GHz. The size and spacing of the unit pattern have both visible effects on the transmission coefficient, but the former has a greater impact on the transmission coefficient. There is a certain tension and contraction between the base fabrics during the preparation of the flexible FSFs, which are controlled to make the sample size more accurate. In addition, in order to reduce the calculation time and improve the design efficiency, two kinds of patch type and aperture type with the same size were simulated and optimized using HFSS algorithm. Comparison of measured and simulated results verify the effectiveness of simulation design.

A fully analytical nonlinear dynamic model of spindle-holder-tool system considering contact characteristics of joint interfaces

The productivity, surface finish, and dimensional accuracy during machining are directly related to the vibration characteristics of tool tip. Moreover, the dynamics of tool tip is not only determined by the flexibility of tool, collet, holder and spindle, but also depends on the contact characteristics of joint interfaces. This paper proposes a fully analytical model of the spindle-holder-tool system considering the nonlinear contact characteristics of joint interfaces. The dynamics of spindle, holder, collet and tool are modeled applying Timoshenko beam theory considering the combined shear and rotational effects, in which the tapered sections of spindle, holder and collet are modeled using multi-stepped beam to account for the taper effect. Under highly dynamic cutting load, the variation in the spacing of joint interfaces will induce the changes in the contact characteristics due to the corresponding vibrations. Therefore, the contact behaviors of spindle/holder, collet/holder, collet/nut, and tool/collet interfaces are analytically modeled using the distributed nonlinear spring-damping layers. The fractal theory and the slicing method are applied to derive the vibration displacement-dependent stiffness matrix of nonlinear springs in joint interfaces considering the surface morphology, geometry, material properties, and locking force of joint interfaces. Furthermore, the five degree of freedom (DOF) nonlinear stiffness model of the spindle-bearing joint dependent on vibration displacement is also considered. The effectiveness of the established analytical dynamic model is verified through vibration testing and modal hammering experiments. The changes in the vibration characteristics by considering the connection ways of joint interfaces, the fractal parameters of joint interfaces and the rotation speed are also investigated. The developed model can provide some theoretical principles for the optimization at design stage without prototypes.

Numerical assessment of multiple vaccinations to mitigate the transmission of COVID-19 via a new epidemiological modeling approach

Vaccines play a crucial role in mitigating the transmission of COVID-19. The primary objective of COVID-19 vaccination campaigns is to induce immunity in individuals, thereby reducing the risk of infection, severe illness, and subsequent transmission within communities. The present study mainly focuses on examining the impact of multiple vaccinations on the transmission dynamics of COVID-19 using a new epidemic modeling approach. The vaccinated individuals are divided into three subclasses according to their vaccination status. The primary, secondary and booster shots of COVID-19 vaccines are considered in the construction of the model. Initially, the model is constructed using classical integer order differential equations and basic necessary properties are carried out. Furthermore, utilizing a fractional and fractal–fractional epidemiological approach with an exponential kernel, the model is extended with these operators in order to provide insights into the potential benefits of this vaccination strategy in controlling the spread of the disease. The uniqueness and existence criteria of the fractional and fractal–fractional models are presented and an efficient numerical solution is investigated using the modified Adams–Bashforth method. The impact of both fractional (memory index) and fractal parameters is demonstrated graphically for R0<1 and R0>1 showing the converges of solution trajectories to the disease-free and endemic steady states respectively. Moreover, we examine the impact of various vaccination rates (first and second dose, and booster short) on the reduction and mitigation of the disease incidence.

Morphological Control of thin Dielectric Films Obtained by RF Magnetron Sputtering and Thermal Evaporation in Vacuum

Thin dielectric Al2O3 and SrO films obtained by thermal evaporation in vacuum, as well as Si3N4 and SiO2 films obtained by RF magnetron sputtering, were studied by atomic force microscopy. The metric and fractal parameters of dielectric layers are estimated using the Gwyddion graphical program for analyzing data from scanning probe microscopy. It has been established that the maximum values of the fractal dimension are characteristic of aluminum oxide films with a thickness of 0.5 μm, while the smallest root-mean-square roughness is characteristic of strontium oxide films. The prospects for using the analyzed dielectric films as insulating layer of sensitive elements of strain gauge pressure sensors with a conductive elastic element are demonstrated.

A brief note on entire fracture surface topography parameters for 18Ni300 maraging steel produced by LB-PBF after LCF

The concept of entire fracture surface investigation is helpful in explaining fatigue phenomena. In this paper, this method has been applied for 18Ni300 maraging steel using a 3D measurement system. Before post-mortem analysis, the specimens produced by laser beam powder bed fusion (LB-PBF) were tested under low-cycle fatigue (LCF) for eight strain amplitudes in the interval 0.3% to 1.0%. The attention was placed on the relationship between the fatigue features, represented by the strain level and the fatigue life as well as the fracture surface topography evaluated in the form of areal, volume and fractal dimension parameters. It was found that fatigue life predictions calculated using the core material volume Vmc, obtained with the entire fracture surface method were within a scatter band with factors of ±1.5. The present results can be useful for the analysis of damaged structural elements exposed to LCF, especially for materials produced by additive manufacturing (AM). The outcomes of this brief note are important for the development of other fractographic methods and validation of fatigue life evaluation procedures.

Fractal Parameters as Independent Biomarkers in the Early Diagnosis of Pediatric Onset Inflammatory Bowel Disease

Inflammatory bowel disease (IBD), which encompasses two different phenotypes—Crohn’s disease (CD) and ulcerative colitis (UC)—consists of chronic, relapsing disorders of the gastrointestinal tract. In 20–30% of cases, the disease begins in the pediatric age. There have been just a few studies that used fractals for IBD investigation, but none of them analyzed intestinal cell chromatin. The main aim of this study was to assess whether it is possible to differentiate between the two phenotypes in pediatric patients, or either of the phenotypes versus control, using the fractal dimension and lacunarity of intestinal cell chromatin. We analyzed nuclei from at least seven different intestinal segments from each group. In the majority of colon segments, both the fractal dimension (FD) and the lacunarity significantly differed between the UC group and CD group, and the UC group and control group. In addition, the ileocecal valve and rectum were the only segments in which CD could be differentiated from the controls based on the FD. The potential of the fractal analysis of intestinal cell nuclei to serve as an observer-independent histological tool for ulcerative colitis diagnosis was identified for the first time in this study. Our results pave the way for the development of computer-aided diagnosis systems that will assist the physicians in their clinical practice.

Freezing Characteristics of a Water Droplet on a Multiscale Superhydrophobic Surface.

Superhydrophobic surfaces have the potential to retard ice formation owing to their super water-repellant nature arising from high static contact angle and low contact angle hysteresis. Most of the previous studies have focused on patterned surfaces with mono-scaled prismatic structures. In contrast, the freezing behavior on multiscaled rough superhydrophobic surfaces that are of practical significance is relatively little studied. This article presents, for the first time, the freezing dynamics of a water droplet interacting with multiscale fractal superhydrophobic surfaces which validates well with experimental measurements. It is shown that the dual effects of increased contact angle and poor interfacial conduction due to trapped air cavities within the roughness features of the superhydrophobic surface lead to increasing freezing time with increasing surface hydrophobicity, determined as a function of the fractal surface parameters. A comparison of the freezing dynamics of sessile droplets of identical contact angle on a smooth versus a rough superhydrophobic surface shows that interfacial asperity thermal resistance contributes to over 14% increase in the freeze time. It is further shown that by tailoring the multiscale characteristics, the freeze time may be increased by up to 7-fold compared to freezing on a smooth surface. The application of the numerical model to studying ice formation on several practical superhydrophobic surfaces of a range of metallic materials and fabrication methods is also discussed, which offers guidelines for the design of anti-icing surfaces in practice.

A mixed-lubricated friction model of water lubricated bearing based on fractal theory

To the water lubricated bearing, its mixed-lubricated friction model is generally established based on the traditional statistical model, whose accuracy is not high due to the inaccurate characterization of surface topography. Therefore, this paper employs the fractal theory that has scale-independent characteristics and high precision to characterize the surface topography of the bearing and journal, and then establishes the fractal contact model of asperity, combining the average Reynolds equation of the film, proposes a mixed-lubricated friction model based on fractal theory. The scanning experiments of surface topography are carried out to obtain the fractal parameters and measurements of the friction coefficient are performed to verify the effectiveness of the proposed mixed-lubricated model. Subsequently, the proposed mixed-lubricated friction model is employed to analyze the effects of the number of groove, the position of groove and the fractal parameters on the lubrication and friction characteristics of the water lubricated bearing. Results indicate when the grooves are in the non-main load-carrying regions, the friction characteristics of the bearing slightly changes, and the lower surface roughness is beneficial to improve the lubrication and friction properties of the bearing.

Predicting irreducible water saturation of unconventional reservoirs by using NMR T2 spectra: Methods of morphological division and fractal models

AbstractIrreducible water saturation restricts an efficient petroleum drainage in unconventional reservoirs. T2 cutoff value identification by using NMR T2 spectrum is the key to clarifying irreducible water saturation. In this paper, saturation and centrifugal T2 spectra of sandstone and coal samples were carried out to calculate T2 cutoff value, with methods of single fractal dimension, multi‐fractal dimension, and spectrum morphological discrimination; In addition, the applicability of these three methods in characterizing T2 cutoff was discussed. The parameters related to T2 cutoff can be divided into two types: (1) The first type is morphological parameters including main peak position ™ and smaller pore volume percentage (SPVP); with an increase of T2 cutoff, TM increases linearly and SPVP decreases exponentially, and the correlation between SPVP and T2 cutoff is stronger than that of TM; (2) Second type is fractal parameters of D2 (larger pore), D−10‐ D10 and D−10/D10; with the increase of T2 cutoff, all single and multi‐fractal dimensions increase linearly, and correlation between D2 and T2 cutoff is stronger than that of multi‐fractal dimension. When calculating the T2cutoff of samples with developed macro‐pores, spectrum morphological methods should be preferentially used, while the fractal dimension discrimination methods need to be used for T2cutoff of samples with developed micro‐pores.

Modified residual power series approach for the computational results of Newell-Whitehead-Segel model with fractal derivatives

In the current work, we provide the modified residual power series approach to obtain the fractal solution of the Newell-Whitehead-Segel (NWS) model with fractal derivatives. The proposed strategy relies on the two-scale fractal scheme and residual power series scheme (RPSS) that systematically produces the fractal solution in a convergent power series without the need for any constraint parameters. Three numerical applications are provided to display the validity, authenticity, and robustness of the suggested scheme. The connectivity between the fractal solution and the exact solution has been demonstrated by plotted and numerical findings. The 2D and 3D graphical visuals demonstrate the physical behavior of the NWS fractal model at various fractional orders. It is worth noticing that the behavior of the solution demonstrates that changing the fractal parameter reflects the nature of the solution and yields the exact solution very rapidly.

Dynamics of granular debris flows against slit dams based on the CFD–DEM method: effect of grain size distribution and ambient environments

AbstractEarth surface flows in nature, like debris flows and rock avalanches, have threatened people’s safety and infrastructure during past decades. Though grain size distribution (GSD) has been acknowledged as a crucial characteristic in granular material behaviour, its coupled effects associated with environments on engineering structures such as the slit dam remain unclear. To bridge the gap, this paper reveals the coupled effect of the GSD and ambient environments (i.e. slope angles and saturation conditions) on avalanche/debris flows’ impact on the slit dam using a Computational Fluid Dynamics/Discrete Element Method (CFD–DEM) model. To describe strain-dependent rheological characteristics of debris fluids, the Herschel–Bulkley–Papanastasiou model is implemented in the finite volume method framework. A power grain size distribution law is considered to quantify GSDs, in which a fractal parameter takes charge of GSD types. After model verification with experimental/theoretical results, the impact force against slit dams, granular dynamics and final deposit patterns under a series of ambient circumstances are presented. Taking advantage of the CFD–DEM method, the impact force and kinetic energy induced by fluid and solid phases are discriminated. The contribution of solid and fluid phases to both impact force and dynamics appears to be dependent on GSDs. Accordingly, compared with saturated avalanche flows (i.e. debris flows), slit dams result in higher retaining efficiency when confronted with dry avalanche flows. Regarding a narrow diameter range used in analyses, the grain diameter ratio is then enlarged up to eight to reveal the potential size effect. As for the coupled role of GSDs and slope angles, in contrast to slope angles, the influence of GSD on avalanche flow interaction with slit dams is much smaller. Additionally, provided a narrow diameter range, the effect of GSDs on impact force can be partially attributed to the change in average grain diameter. After presenting the significance of ambience and GSDs to avalanche/debris flows, a series of parametric studies around the effect of fluid grid size, particle shape and the initial porosity of granular samples are discussed, aiming to advance the understanding of their influence in the interactions between debris flows and the slit dam.

Analytical solutions of fractal and anomalous diffusion models for pressure and rate transient analysis

In this study, we examine the modeling of the naturally fractured reservoirs based on the fractal, Metzler, and Raghavan anomalous diffusion models which are different from Darcy flux law. The governing equations of these models are presented for a vertical well producing at either a constant rate (CR) or constant bottomhole pressure (CBHP) production in an infinite-acting reservoir. New analytical and early- and late-time asymptotic approximate solutions were derived for the finite-wellbore problem for the Raghavan anomalous model. The approximate solutions identify the fractal and anomalous diffusion parameters that influence behaviors of the early- and late-time pressure and rate transient data. The method of Laplace transformation is used to find the solutions in dimensionless forms which are then inverted to the real-time domain using a numerical inversion algorithm. In addition, we compare the solutions for the fractal, Metzler anomalous, and Raghavan anomalous models and delineate the similarities and differences among these solutions. We show the effect of fractal parameters on diffusion models, the relationship between the fractal model, and Raghavan and Metzler anomalous models, in terms of dimensionless pressure and dimensionless pressure derivative responses in the reservoir. We show that the “dimensionless” pressure defined by Raghavan is not a dimensionless quantity unless the Euclidean dimension d=2 (or for a fractal structure with the mass fractal dimension df=2). To the best of our knowledge, in the literature, there exists no study providing a detailed review and comparing the applicability of each diffusion model on real field well-test data as well as providing new analytical solutions and early- and late-time asymptotic approximate solutions for the anomalous diffusion for both the CR and CBHP cases for the finite-wellbore problem. Hence, this study fills this gap. In addition, we apply the three diffusion models to an interference well test data from the Kizildere geothermal reservoir in Turkey by using the ensemble smoother with multiple data assimilation (ES-MDA) method. The results show that the fractal model in terms of the goodness of fit (root-mean-square error – RMSE) best matches the field test data.

Determination of dielectric performance and surface heteromorphology in single-walled carbon nanotube/vinylester polymer composites by fractal approaches

This study aims to establish a relationship between the dielectric characteristics and fractal parameters of single walled carbon nanotube reinforced vinylester based nanocomposites manufactured by sheet molding compound process. The complex dielectric permittivity was analyzed and interpreted using electric modulus formalism. The topography of both unfilled and single-walled carbon nanotube reinforced nanocomposites has been investigated using scanning electron microscopy (SEM) to provide correlation between experimental dielectric data and fractal theory. The self-similar microstructure was observed in micro photos for both materials. The superficial particle and cluster coverage ratio were calculated with the application of the scaling theory. Additionally, critical exponent and the fractal dimensions that determine the environment-area relationship have been determined by Slit Island Method (SIM) which is used to process 2-dimensional digital microscopic images. Fractal dimensions estimated with SIM were compared with the fractal dimensions computed obtained by box counting method for reliable results. It has been revealed that the surface of the composite consists of amorphous clusters with different sizes independent of each other and the structure is self-affine. In addition, the superficial area and cluster size have been shown to have a significant effect on the fractal dimension. As a result, the relationship between the dielectric permittivity of the material, determined by the electrical module formalism, and the morphological surface formation defined by the fractal analysis method and the SIM method, were determined and the results were compared with similar studies in the literature in this article.