Science topic
Fractals - Science topic
Patterns (real or mathematical) which look similar at different scales, for example the network of airways in the lung which shows similar branching patterns at progressively higher magnifications. Natural fractals are self-similar across a finite range of scales while mathematical fractals are the same across an infinite range. Many natural, including biological, structures are fractal (or fractal-like). Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time.
Publications related to Fractals (10,000)
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A simple and easy-to-implement discrete approximation is proposed for one-dimensional higher-order integral fractional Laplacian (IFL), and our method is applied to discrete the fractional biharmonic equation, multi-term fractional differential model and fractal KdV equation. Based on the generating function, a fractional analogue of the central di...
The atmosphere is a highly non-linear dynamic system, where equations can present some solutions known as strange attractors since they have non-integer dimensions, or in other words, fractional volumes. The fractality in meteorology and climatology is reflected in the self-similarity at different spatial and temporal scales. For instance, atmosphe...
In this paper, the design of an efficient fractional-order proportional-integral-derivative (FOPID) controller, tailored specifically for the regulation of micro direct current (DC) motors, is explored. A fresh approach is introduced using the gazelle optimization algorithm (GOA), a cutting-edge method set to manage the speed control of these small...
The simplest model to describe seismic activity assumes that earthquakes occur because of strain accumulation within the brittle crust to be released along weak frictional interfaces, i.e., faults, whose dynamic behaviour can be described by stability conditions, so that large seismic events would occur almost periodically if faults were perfectly...
This study represents the first application of multifractal analysis to characterize spatial microforms’ volumes resulting from face milling on flat surfaces, emphasizing its novelty. Photographs of samples of C35 steel and AA22024 aluminum alloy, subjected to various cutting conditions during milling, were utilized to apply the multifractal approa...
Research suggests that a fast, capacity-limited working memory (WM) system and a slow, incremental reinforcement learning (RL) system jointly contribute to instrumental learning. Thus, situations that strain WM resources alter instrumental learning: under WM loads, learning becomes slow and incremental, the reliance on computationally efficient lea...
The pore wall morphology of carbon fiber reinforced composite (CFRP) laminates is one of the key factors to determine their service performance. However, due to the direction angle of the material fibers, the original micro surface morphology of the pore wall is complex and difficult to characterize. In this paper, a method to reconstruct the micro...
Citation: Nikolopoulos, D.; Petraki, E., Rafique, M.; Alam. A.; Cantzos, D., Yannakopoulos, P. Fractal features in kHz electromagnetic observations preceding near-field earthquakes in Ilia, Greece. Geosciences 2022, 1, 0. https://doi.org/
The effusive–explosive energy emission process in a volcano is a dynamic and complex physical phenomenon. The importance of quantifying this complexity in terms of the physical and mathematical mechanisms that govern these emissions should be a requirement for deciding to apply a possible forecasting strategy with a sufficient degree of certainty....
In this study, surface roughness is analyzed within a supervised pattern recognition framework using machine learning methods to present a robust technique for the quantitative determination of surface roughness of rocks. To reach this goal, rock surfaces are classified based on statistical, fractal, geostatistical, directional, and spectral featur...
A comprehensive evaluation method is proposed to analyze dust pollution generated in the production process of mines. The method employs an optimized image-processing and deep learning framework to characterize the gray and fractal features in dust images. The research reveals both linear and logarithmic correlations between the gray features, frac...
Introduction Estimating the amount and intensity of precipitation and its spatial distribution in various return periods is necessary for flood estimation hydrological models. This information is obtained based on traditional methods through intensity-duration-frequency curves with many assumptions, such as the choice of suitable distribution for e...
This paper first determines the research method of rural tourism and the selection of research objects and carries out the corresponding pre-processing operation for the data. Secondly, the spatial distribution characteristics of key villages of rural tourism are analyzed by using the nearest neighbor index, standard deviation ellipse, geographic c...
La sucesión de Narayana (A000930 OEIS) [1] , conocida como la sucesión de las vacas de Narayana, es la versión hindú de los conejos de la sucesión de Fibonacci (OEIS A000045) [2] , esta secuencia lleva el nombre del notable matemático indio Narayana Pandita (1340-1400) publicado en el tratado de aritmética Ganita Kaumudi (La luz de la luna de las m...
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Forest is an important component of ecosystem. To estimate forest above-ground biomass (AGB) accurately, this paper proposed an individual tree AGB estimation method based on fractal geometry and individual tree volume. In this study, fractal parameters, such as fractal dimension and intercept were first calculated. And then, a fast tree volume est...
Citation: Ahmad, A.; Gong, J.; Al-Shbeil, I.; Rasheed A.; Ali, A.; Hussain, S. Analytic Functions Related to a Balloon-Shaped Domain. Fractal Fract. 2023, 7, 865. https:// Abstract: One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This articl...
This review article delves into the growing recognition of fractal structures in mesoscale phenomena. The article highlights the significance of realistic fractal-like aggregate models and efficient modeling codes for comparing data from diverse experimental findings and computational techniques. Specifically, the article discusses the current stat...
We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the structure of the resulting coupled integral equations encoded in terms of graphical diagrams. The resulting framewo...
The mechanical properties of water-rich coal and rock in a subzero environment are very different from those at room temperature, which causes many unexpected hazards for projects. In this study, coal and rock samples subjected to the coupled effects of water, temperature, and dynamic loads were taken as the research object, and the discussion was...
In this paper, the maximum Lyapunov exponent and chaotic phase space reconstruction method of the chaotic computing model are studied, the embedding dimension is obtained by using the saturated correlation dimension method, and the fractal scale of the chaotic model is determined by the DFA method. Based on the relevant policy documents, an index s...
Jiuzhai Valley, a World Natural Heritage Site, was significantly damaged by an earthquake in 2017. However, case studies on the restoration of World Natural Heritage sites are lacking. This study aimed to use the box-counting method to analyze fractal characteristics of the terrain in Shuzheng Valley. Research data were used to conduct artificial i...
This article addresses verbal representations of the mythic concept JÖTUNN (Engl. JOTUN) in Old Norse eddic texts. JÖTNAR as supernatural beings inherent to the Nordic mythic space are regarded as a class of open systems marked by a set of hypertrophied features. Etymological analysis of the concep's names followed by broader analogue speculations...
With the continuous expansion of the application range of gob–side entry retaining technology, the depth, height, and advancing speed of coal seams also increase, which brings great problems to the stability control of surrounding rock structures of gob–side entry retaining. As one of the main bearing structures of the surrounding rock, the stabili...
This study takes the landscape space of traditional Tibetan villages in western Sichuan as the research object, and three national-level traditional villages of different Tibetan clans in Gyatso, Amdo and Baima Tibet were selected as samples. Using the fractal theory, combined with counting-box dimension measurement and spatial analysis methods, it...
A signed product cordial labeling of graph with vertex set is a function ∶ () → {− , } such that each edge is assigned the label () (), the number of vertices with label − and the number of vertices with label differs by at most and the number of edges with label − and the number of edges with label differs by at most. A graph that admits signed pr...
To study the fractal characteristics of the pore structure and the main controlling factors of coal measure shale in the Wuxiang block in Qinshui Basin, gas adsorption (CO2 and N2), mercury intrusion porosimetry (MIP), total organic carbon (TOC) content, and X-ray diffraction (XRD) experiments were carried out. The fractal dimensions of the micropo...
Objectives: The aim of the present study was to compare the features of the structural complexity of the cerebral hemispheres in men and women using fractal analysis of outlined and skeletonized images, as well as quantitative analysis of digital skeletons of the cerebral hemispheres. Material and Methods: Magnetic resonance imaging brain scans of...
span lang="EN-US">Currently, the detection of pathology of lung cavities and their digitalization is one of the urgent problems of the healthcare industry in Kazakhstan. In this paper, the method of fractal analysis was considered to solve the task set. Diagnosis of lung pathology based on fractal analysis is an actively developing area of medical...
Modern man identifies Science as a set of disciplines based on observation, experience and calculation, which using formalized languages such as Geometry and Mathematics, try to provide an answer to the questions that human beings ask themselves. humans to understand the reasons for their existence and the nature of which they are part. In the mode...
span lang="EN-US">Steganography is a vital security approach that hides any secret content within ordinary data, such as multimedia. First, the cover image is converted into a wavelet environment using the integer wavelet transform (IWT), which protects the cover images from false mistakes. The grey wolf optimizer (GWO) is used to choose the pixel’...
We investigate the scaling law relating the size of the boundary of a solid tumor and the rate at which it is lysed by a cell population of non-infiltrating cytotoxic lymphocytes. We do it in the context of enzyme kinetics through geometrical, analytical and numerical arguments. Following the Koch island fractal model, a scale dependent function th...
Geometric heterogeneities in tight reservoir rocks saturated with a fluid mixture may exhibit different scale distribution characteristics. Conventional models of rock physics based on poroelasticity, which usually consider single‐scale pore structure and fluid patches, are inadequate for describing elastic wave responses. A major challenge is to e...
With the popularity and maturity of medical imaging technology, CT scans, and other medical technologies are increasingly utilized in clinical diagnosis and treatment. In the diagnosis and treatment of pneumonia or lung tumors, clinicians make extensive use of this technology and rely on CT images to assess the progression of disease or the effecti...
As a relatively new and mathematics-related discipline, fractal has had a certain influence on the development of many aspects of today's society. At the same time, the science of fractal geometry to explore and study the practical use of fractal properties and fractal geometry is called a fractal theory. What's more, the emergence of fractal theor...
The detection of particles with uncompensated charge and the determination of the features of their interaction during the formation of nanocrystals on substrates with a developed surface are an interesting area of research. The porous surface formed via the electrochemical etching of silicon acquired fractal properties as a result of the depositio...
Given a hypersurface S ⊂ R 2d , we study the bilinear averaging operator that averages a pair of functions over S, as well as more general bilinear multipliers of limited decay and various maximal analogs. Of particular interest are bilinear maximal operators associated to a fractal dilation set E ⊂ [1, 2]; in this case, the boundedness region of t...
The normal contact stiffness (NCS) on rough surfaces has a significant impact on the dynamic characteristics of helical gear. Aiming at the problem of inaccurate calculation of the NCS model under the traditional Hertz theory of smooth surfaces, a fractal prediction model of helical gear contact stiffness considering asperity lateral contact and in...
Due to the complexity of the microstructure of porous media, it is of great significance to explore the heat transport mechanism in porous media in many engineering applications. In this study, an expression for effective thermal conductivity (ETC) of porous media embedded with randomly distributed damaged tree-like bifurcation networks is derived...
In this study, local fuzzy fractional partial differential equations (LFFPDEs) are considered using a hybrid local fuzzy fractional approach. Fractal model behavior can be represented using fuzzy partial differential equations (PDEs) with local fractional derivatives. The current methods are hybrids of the local fuzzy fractional integral transform...
Citation: Saber, H.; Imsatfia, M.; Boulares, H.; Moumen, A.; Alraqad, T. On the Existence and Ulam Stability of BVP within Kernel Fractional Time. Fractal Fract. 2023, Abstract: This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ-Caputo fractional derivativ...
Recent mesoscopic characterisation of nutrient-transporting channels in E. coli has allowed the identification and measurement of individual channels in whole mature biofilms. However, their complexity under different physiological and environmental conditions remains unknown. Analysis of confocal micrographs of biofilms formed by cell shape mutant...
The journal retracts the article entitled “Fractional Model of Electron–Phonon Interaction” by Kulish et al [...]
p> This paper provides a visual based conceptual model and framework to help explain the behavior of electrical, electromagnetic and gravitational phenomenon. The model is conceptual only and the hypothetical particles and interactions presented are simply designed as a way to visualize and understand electromagnetic interactions. Further research...
Fractal patterns have been shown to change in resting- and task-state blood oxygen level-dependent signals in bipolar disorder patients. However, fractal characteristics of brain blood oxygen level-dependent signals when responding to external emotional stimuli in pediatric bipolar disorder remain unclear. Blood oxygen level-dependent signals of 20...
In order to investigate the difference in particle size distribution of soil along an urban–suburban–rural–desert (USRD) gradient in an arid zone, surface soil (0–20 cm) samples were gathered at the urban, suburban, rural, and desert gradients in Urumqi, a northwestern Chinese city. Laser diffraction technology was adopted for determining the parti...
The overall seismicity of Pakistan from 1820 to 2020 is analysed in terms of its multifractal behaviour. Seismic events of magnitude ML=3.0 and above are spatially clustered into four distinct groups, each one corresponding to a different region of high seismic activity. The Multifractal Detrended Fluctuation Analysis (MFDA) method applied on each...
The stability of the dump is related to the safe operation and economic benefit of the mine, and the mechanical properties of its constituent soils are important basic data to evaluate its stability, while the changes in the mechanical properties are influenced by its internal structure. Nuclear magnetic resonance and scanning electron microscope t...
Chaos and fractals are two branches of nonlinear science. However, few scholars have combined chaos and fractals for generating chaotic attractors with different topologies. The main goal of this paper is to combine fractals and chaos to generate separated multi-scroll attractors and nested multi-scroll attractors, as well as to compensate for the...
In recent years the combination of medical image watermarking and encryption is becoming popular due to a better trade-off between authenticity and security, since, each of these methods alone is insufficient to offer complete security. In the proposed work,
the watermark is embedded into the Fundus image using the Singular Value Decomposition (SVD...
An interesting feature of the brain is its ability to respond to disparate sensory signals from the environment in unique ways depending on the environmental context or current brain state. In dynamical systems, this is an example of multi-stability, the ability to switch between multiple stable states corresponding to specific patterns of brain ac...
![Development of stiffness with normal load using Hertz model [16] and...](publication/375925750/figure/fig5/AS:11431281207054317@1701053475466/Development-of-stiffness-with-normal-load-using-Hertz-model-16-and-Pohrt-and-Popov_Q320.jpg)
The validity of different available contact models is tested against experimental data for contact normal loading of artificially shaped granite stones. Three elastic models and two plastic models were tested with different combinations of contact shape (spherical, conical and flat) and roughnesses. It was found that the deviation from the Hertz mo...
Quantum Cosmology describes the nature of the universe from a perspective of an unobserved and largely unseen microcosm forming the basis for an experienced and observed macrocosm. It so presents a cosmogenesis, a description of the origins as an ontology for cosmological models. The building blocks of an experienced physical reality in atomic, mol...
It has been found that fractal-like patterns are present in the temporal structure of the variability of healthy biological rhythms, while pathology and disease lead to their deterioration. Interestingly, it has recently been suggested that these patterns in biological rhythms are related with each other, reflecting overall health or lack of it, du...
C/SiC composites are high-temperature structural materials with excellent properties, such as high-temperature resistance and light weight, and are widely used in aerospace fields as advanced materials. Pores are common and unavoidable defects inside composite components, especially affecting mechanical properties and further affecting the safety a...
The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals. The conditions of existence for the Riemann definite integrals over non-rectifiable curves and fractals are provided. We give a definition of a singular integral over non-r...
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, nonhomogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between nonconsecutively visited pairs of nearest-neighboring sites (contacts). It captures the main features of a semi-fl...
We study the entropy production in a fractal system composed of two subsystems, each of which is subjected to an external force. This is achieved by using the H-theorem on the nonlinear Fokker–Planck equations (NFEs) characterizing the diffusing dynamics of each subsystem. In particular, we write a general NFE in terms of Hausdorff derivatives to t...
Leaky urban drainage networks (UDNs) exfiltrating wastewater can contaminate aquifers. Detailed knowledge on spatiotemporal distributions of water-dissolved, sewer-borne contaminants in groundwater is essential to protect urban aquifers and to optimize monitoring systems. We evaluated the effect of UDN layouts on the spreading of sewer-borne contam...
Self-similar structures of river networks have been quantified as diverse scaling laws. Among them we investigated a power functional relationship between the apparent drainage density ρa and the pruning area Ap with an exponent η. We analytically derived the relationship between η and other scaling exponents known for fractal river networks. The a...
In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors’ problems of rational contraction maps in the framework of dislocated metric spaces is also established. Moreover, the generalized c...
Hyperelastic materials like gels and rubbers have numerous applications in daily life and industrial production. However, most traditional contact models for rough solids do not include the hyperelastic deformation mechanism. This paper extends the linear-elastic incremental equivalent contact model to study the contact processes of hyperelastic ro...
The improvement in the insulation material performance is one of the recent crucial problems. The energy consumption in the construction and buildings field has a significant impact on the society and the environment. For these reasons, researchers have focused on studying their thermal behaviour in order to improve fabrication methods and material...
An interesting feature of the brain is its ability to respond to disparate sensory signals from the environment in unique ways depending on the environmental context or current brain state. In dynamical systems, this is an example of multi-stability, the ability to switch between multiple stable states corresponding to specific patterns of brain ac...
A miniaturized antenna based on fractal method and Tapered-feeder technique for ultra-wideband (UWB) applications is developed in this research. The structure of the component cell monopole antenna is designed by using a half circle-shaped fractal method and merging material implementation with the L-stub shape. These techniques provide a wide impe...
Objectives
The aim of this study was to analyse the radiomorphometric parameters of trabecular bone of the mandible in celiac patients.
Materials and Methods
A total of 37 patients (30 females and 7 males) celiac disease patients and 37 age and gender-matched healthy individuals (control group) were included in this study. The analyzed radiomorpho...
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A passive dynamic walker is a mechanical system that walks down a slope without any control, and gives useful insights into the dynamic mechanism of stable walking. This system shows specific attractor characteristics depending on the slope angle due to nonlinear dynamics, such as period-doubling to chaos and its disappearance by a boundary crisis....
La secuencia de Jacobsthal (OEIS A001045) [1] ; está basada en la sucesión generalizada de Fibonacci (OEIS A000045) [2] ; aplicando el principio de recurrencia de la sucesión de Pell (OEIS A000129) [3] ; siendo un caso particular de la secuencia de Lucas (OEIS A000204) [4] ; definida por el matemático alemán Ernst Jacobsthal (1882-1965); comenzando...
Root fractal analysis is instrumental in comprehending the intricate structures of plant root systems, offering insights into root morphology, branching patterns, and resource acquisition efficiency. We conducted a field experiment on paddy–wheat root systems under varying nitrogen fertilizer strategies to address the need for quantitative standard...
The acoustic characteristics of the rock failure process can reflect the evolution of crack development and expansion. To study the evolution of different types of internal cracks during the rock failure process, the acoustic emission (AE) signal of the yellow sandstone under uniaxial compression was collected with AE monitoring technology, and the...
This article presents a dual-band fractal-based Bandpass Filter (BPF) for Substrate-Integrated Waveguides (SIWs) for the first time. The suggested filter is built by cutting a slit into the structure's top layer, Koch Snowflake fractal style. The Fractional Bandwidth (FBW) at 7.7 GHz for the first band of the downsized BPF is 9.45 percent, while th...
Archives of composite weather radar images represent an invaluable resource to study the predictability of precipitation. In this paper, we compare two distinct approaches to construct empirical low-dimensional attractors from radar precipitation fields. In the first approach, the phase space dimensions of the attractor are defined using the domain...
With the deepening of urbanization in China, the coordinated development of cities in different regions is an important part of the sustainable development of the country, and the reasonable quantification of the unbalanced development of cities in different regions is an important issue facing the society nowadays. Previous studies usually use pop...
