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Journal articles on the topic 'Variable dimension fractal'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Zhihui, Ni, Wu Lichun, Wang Ming-hui, Yi Jing, and Zeng Qiang. "The Fractal Dimension of River Length Based on the Observed Data." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/327297.

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Although the phenomenon that strictly meets the constant dimension fractal form in the nature does not exist, fractal theory provides a new way and means for the study of complex natural phenomena. Therefore, we use some variable dimension fractal analysis methods to study river flow discharge. On the basis of the flood flow corresponding to the waterline length, the river of the overall and partial dimensions are calculated and the relationships between the overall and partial dimensions are discussed. The law of the length in section of Chongqing city of Yangtze River is calibrated by using

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2

TATOM, FRANK B. "THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS." Fractals 03, no. 01 (1995): 217–29. http://dx.doi.org/10.1142/s0218348x95000175.

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The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-dif

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PRASAD, SRIJANANI ANURAG, and G. P. KAPOOR. "FRACTAL DIMENSION OF COALESCENCE HIDDEN-VARIABLE FRACTAL INTERPOLATION SURFACE." Fractals 19, no. 02 (2011): 195–201. http://dx.doi.org/10.1142/s0218348x11005336.

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In the present paper, the bounds on fractal dimension of Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) in ℝ3 on a equispaced mesh are found. These bounds determine the conditions on the free parameters for fractal dimension of the constructed CHFIS to become close to 3. The results derived here are tested on a tsunami wave surface by computing the lower and upper bounds of the fractal dimension of its CHFIS simulation.

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JÄRVENPÄÄ, ESA, MAARIT JÄRVENPÄÄ, ANTTI KÄENMÄKI, HENNA KOIVUSALO, ÖRJAN STENFLO, and VILLE SUOMALA. "Dimensions of random affine code tree fractals." Ergodic Theory and Dynamical Systems 34, no. 3 (2013): 854–75. http://dx.doi.org/10.1017/etds.2012.168.

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AbstractWe study the dimension of code tree fractals, a class of fractals generated by a set of iterated function systems. We first consider deterministic affine code tree fractals, extending to the code tree fractal setting the classical result of Falconer and Solomyak on the Hausdorff dimension of self-affine fractals generated by a single iterated function system. We then calculate the almost sure Hausdorff, packing and box counting dimensions of a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in

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Tunas, I. Gede, Nadjadji Anwar, and Umboro Lasminto. "Fractal Characteristic Analysis of Watershed as Variable of Synthetic Unit Hydrograph Model." Open Civil Engineering Journal 10, no. 1 (2016): 706–18. http://dx.doi.org/10.2174/1874149501610010706.

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Fractal characteristic of watershed is an important parameter which influences the formation of synthetic unit hydrograph. Based on a previous study, hydrology response of watershed expressed in hydrograph form could be well presented by hydrology network characteristic as a form of fractal characteristic of watershed [1]. Fractal characteristic of watershed was stated as fractal dimension which was presented in three parametersi.e.river branch ratio (RB), river length ratio (RL) and watershed river area ratio (RA). The purpose of this research was to analyze fractal characteristic and to veri

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Fan, Youping, Dai Zhang, and Jingjiao Li. "Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture." Advances in Materials Science and Engineering 2018 (November 1, 2018): 1–10. http://dx.doi.org/10.1155/2018/6019269.

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The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

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Sinclair, Scott E., Steve McKinney, Robb W. Glenny, Susan L. Bernard, and Michael P. Hlastala. "Exercise alters fractal dimension and spatial correlation of pulmonary blood flow in the horse." Journal of Applied Physiology 88, no. 6 (2000): 2269–78. http://dx.doi.org/10.1152/jappl.2000.88.6.2269.

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We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses ( n= 4) by using 15-μm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm3 samples ( n = 1,621–2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) and spatial correlations. On average, the fractal dimension decreased with exercise (trot 1.216 to gallop 1.173; P < 0.05) despite a variable fractal dimension at rest. Spatial correlation of flow to neighb

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Cherny, A. Yu, E. M. Anitas, A. I. Kuklin, M. Balasoiu, and V. A. Osipov. "Scattering from generalized Cantor fractals." Journal of Applied Crystallography 43, no. 4 (2010): 790–97. http://dx.doi.org/10.1107/s0021889810014184.

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A fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set, is considered. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodisper

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9

Wen, Hua. "Quantitative Identification of Reservoir Fracture with the Variable Scale Fractal Technique in Su53 Gas Field, Ordos Basin." Advanced Materials Research 1010-1012 (August 2014): 1723–26. http://dx.doi.org/10.4028/www.scientific.net/amr.1010-1012.1723.

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Typical tight gas reservoirs in the Su53 Gas Field, Ordos Basin, are the demonstration region for deploying horizontal wells. In order to provide foundation for evaluating the volume fracturing adaptability of horizontal wells, through using the amplitude difference data between deep investigate double lateral resistivity (Rd) and shallow investigate double lateral resistivity (Rs), and other conventional logging data, in combination with the response characteristics of fracture in the logging curve, reservoir fracture was quantitatively identified with the variable scale fractal technique, th

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Tian, Shi Min, Xiao Hui Su, Wei Hong Wang, and Rui Xun Lai. "Application of Fractal Theory in the River Regime in the Lower Yellow River." Applied Mechanics and Materials 190-191 (July 2012): 1238–43. http://dx.doi.org/10.4028/www.scientific.net/amm.190-191.1238.

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From 1960 to 1999, the river regime in the Lower Yellow River had been the wandering. After the operation of Xiaolangdi Reservoir, the river regime in the Lower Yellow River has experienced some changes because of the reduced discharge and sediment loads. According to the river regime maps, the wandering features of the Lower Yellow River are inhibited and the river channel is becoming stable. In addition, the fractal dimension method is introduced to discriminate the river regime. The river fractal features are able to reflect the features of river system and the fractal dimension is an impor

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Socoteanu, Radu, Mihai Anastasescu, Anabela Oliveira, Gianina Dobrescu, Rica Boscencu, and Carolina Constantin. "Aggregation Behavior of Some Asymmetric Porphyrins versus Basic Biological Tests Response." International Journal of Photoenergy 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/302587.

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Fractal analysis of free bases porphyrins was computed on atomic force microscopy (AFM) micrographs using two different methods: the correlation function method and the variable length scale method. The correlation function method provides fractal dimension only for short scale range; results indicate that only few images have fractal properties for short ranges; for the rest of them, no fractal dimension was found using the correlation function method. The variable length scale method occur information for long range scaling. All samples have fractal properties at higher scaling range. For th

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BACCHI, O. O. S., K. REICHARDT, and N. A. VILLA NOVA. "FRACTAL SCALING OF PARTICLE AND PORE SIZE DISTRIBUTIONS AND ITS RELATION TO SOIL HYDRAULIC CONDUCTIVITY." Scientia Agricola 53, no. 2-3 (1996): 356. http://dx.doi.org/10.1590/s0103-90161996000200027.

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Fractal scaling has been applied to soils, both for void and solid phases, as an approach to characterize the porous arrangement, attempting to relate particle-size distribution to soil water retention and soil water dynamic properties. One important point of such an analysis is the assumption that the void space geometry of soils reflects its solid phase geometry, taking into account that soil pores are lined by the full range of particles, and that their fractal dimension, which expresses their tortuosity, could be evaluated by the fractal scaling of particle-size distribution. Other authors

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Liew, Gerald, Bamini Gopinath, Andrew J. White, George Burlutsky, Tien Yin Wong, and Paul Mitchell. "Retinal Vasculature Fractal and Stroke Mortality." Stroke 52, no. 4 (2021): 1276–82. http://dx.doi.org/10.1161/strokeaha.120.031886.

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Background and Purpose: Fractal analysis is a method of quantifying the branching complexity and density of the retinal vessels. We hypothesized that reduced fractal dimension, signifying a sparser vascular network, is associated with long-term stroke mortality. Methods: We examined the relationship of fractal dimension and stroke mortality in a prospective, population-based cohort of 3143 participants aged 49 years or older. Fractal dimension was measured from digitized fundus photographs using a computer-automated method. Stroke mortality was documented from Australian National Death Index r

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Mulder, Kenneth, Sophia M. Lee, and Wei Chen. "A triangular model of fractal growth with application to adsorptive spin-coating of polymers." PLOS ONE 19, no. 2 (2024): e0298916. http://dx.doi.org/10.1371/journal.pone.0298916.

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Over the last 40 years, applied mathematicians and physicists have proposed a number of mathematical models that produce structures exhibiting a fractal dimension. This work has coincided with the discovery that objects with fractal dimension are relatively common in the natural and human-produced worlds. One particularly successful model of fractal growth is the diffusion limited aggregation (DLA) model, a model as notable for its simplicity as for its complex and varied behavior. It has been modified and used to simulate fractal growth processes in numerous experimental and empirical context

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Geng, Peng Fei, Lin Zhu Sun, Fang Yang, and Wei Li. "Study on Fractal Characteristics of Acoustic Emission in Circular Double-Layer Stirrup Confined Concrete." Applied Mechanics and Materials 578-579 (July 2014): 359–68. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.359.

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Vertical bearing capacity experiments were conducted with circular double-layer stirrup confined concrete columns as study objects, data acquisition was carried out using acoustic emission (AE) equipment and the AE parameters and graphs acquired during the experiments were analyzed to obtain the damage evolution of steel reinforced concrete columns under compression. The correlation between fractal dimension of AE graphs and curve was studied using the fractal theory, and the results show that the AE parameter graphs have fractal characteristics and the box dimension of each AE parameter graph

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16

Luen Liou, Jeng, and Jen Fin Lin. "A New Microcontact Model Developed for Variable Fractal Dimension, Topothesy, Density of Asperity, and Probability Density Function of Asperity Heights." Journal of Applied Mechanics 74, no. 4 (2006): 603–13. http://dx.doi.org/10.1115/1.2338059.

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In the present study, the fractal theory is applied to modify the conventional model (the Greenwood and Williamson model) established in the statistical form for the microcontacts of two contact surfaces. The mean radius of curvature (R) and the density of asperities (η) are no longer taken as constants, but taken as variables as functions of the related parameters including the fractal dimension (D), the topothesy (G), and the mean separation of two contact surfaces. The fractal dimension and the topothesy varied by differing the mean separation of two contact surfaces are completely obtained

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17

Liu, Xiaoting, Hong-Guang Sun, Mihailo Lazarevic, and Zhuojia Fu. "A variable-order fractal derivative model for anomalous diffusion." Thermal Science 21, no. 1 Part A (2017): 51–59. http://dx.doi.org/10.2298/tsci160415244l.

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This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport) proce

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18

Liou, J. L., and J. F. Lin. "A Microcontact Model Developed for Asperity Heights with a Variable Profile Fractal Dimension, A Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution." Journal of Mechanics 25, no. 1 (2009): 103–15. http://dx.doi.org/10.1017/s1727719100003646.

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AbstractThe cross sections formed by the contact asperities of two rough surfaces at an interference are islandshaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to b

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Deng, Hongwei, Guanglin Tian, Songtao Yu, Zhen Jiang, Zhiming Zhong, and Yanan Zhang. "Research on Strength Prediction Model of Sand-like Material Based on Nuclear Magnetic Resonance and Fractal Theory." Applied Sciences 10, no. 18 (2020): 6601. http://dx.doi.org/10.3390/app10186601.

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Micro-pore structure has a decisive effect on the physical and mechanical properties of porous materials. To further improve the composition of rock-like materials, the internal relationship between microscopic characteristics (porosity, pore size distribution) and macroscopic mechanical properties of materials needs to be studied. This study selects portland cement, quartz sand, silica fume, and water-reducing agent as raw materials to simulate sandstone. Based on the Nuclear magnetic resonance (NMR) theory and fractal theory, the study explores the internal relationship between pore structur

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20

Kapoor, G. P., and Srijanani Anurag Prasad. "Multiresolution Analysis Based on Coalescence Hidden-Variable Fractal Interpolation Functions." International Journal of Computational Mathematics 2014 (December 11, 2014): 1–7. http://dx.doi.org/10.1155/2014/531562.

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Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is developed. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). Our approach consists of introduction of the vector space of CHFIFs, determination of its dimension and construction of Riesz bases of vector subspaces Vk, k∈Z, consisting of c

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Kryvko, Andriy, Claudia del C. Gutiérrez-Torres, José Alfredo Jiménez-Bernal, Orlando Susarrey-Huerta, Eduardo Reyes de Luna, and Didier Samayoa. "Fractal Continuum Maxwell Creep Model." Axioms 14, no. 1 (2025): 33. https://doi.org/10.3390/axioms14010033.

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In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fractal version of Maxwell model is developed. This methodology employs local fractional differential operators on discontinuous properties of fractal sets embedded in the integer space-time so that they behave as analytic envelopes of non-analytic functions in the fractal continuum space-time. Then, creep strain ε(t), creep modulus J(t), and relaxation co

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Son, Minwoo, and Tian-Jian Hsu. "Flocculation model of cohesive sediment using variable fractal dimension." Environmental Fluid Mechanics 8, no. 1 (2008): 55–71. http://dx.doi.org/10.1007/s10652-007-9050-7.

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Maureal, Zeny, Elmer Castillano, and Roberto Padua. "Uniform Minimum Variance Unbiased Estimator of Fractal Dimension." Recoletos Multidisciplinary Research Journal 9, no. 1 (2021): 63–68. http://dx.doi.org/10.32871/rmrj2109.01.06.

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The paper introduced the concept of a fractal distribution using a power-law distribution. It proceeds to determining the relationship between fractal and exponential distribution using a logarithmic transformation of a fractal random variable which turns out to be exponentially distributed. It also considered finding the point estimator of fractional dimension and its statistical characteristics. It was shown that the maximum likelihood estimator of the fractional dimension λ is biased. Another estimator was found and shown to be a uniformly minimum variance unbiased estimator (UMVUE) by Lehm

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Liou, Jeng Luen, and Jen Fin Lin. "A New Method Developed for Fractal Dimension and Topothesy Varying With the Mean Separation of Two Contact Surfaces." Journal of Tribology 128, no. 3 (2006): 515–24. http://dx.doi.org/10.1115/1.2197839.

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Instead of a general consideration of the fractal dimension (D) and the topothesy (G*) as two invariants in the fractal analysis of surface asperities, these two roughness parameters in the present study are varied by changing the mean separation (d*) of two contact surfaces. The relationship between the fractal dimension and the mean separation is found first. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variati

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Xu, Ying, Jinjin Ge, Hailong Li, Rongzhou Yang, Kun Wang, and Shi Hu. "Relationship between Fractal Dimension of Fragmentation Degree and Energy Dissipation of Rock-Like Materials under Initial Stress." Shock and Vibration 2020 (November 28, 2020): 1–10. http://dx.doi.org/10.1155/2020/8861971.

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In order to obtain the relationship between fractal dimension and energy dissipation of rock-like materials under initial stress state, a variable cross-section split Hopkinson pressure bar (SHPB) test system with active confining pressure loading device was used to carry out impact compression and splitting tests on cemented sand specimens. The impact test results show that (1) the prediction value on the fragmentation degree of cemented sand specimens by using the fractal model is basically consistent with the screening results of actual test, which verifies the applicability of the fractal

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Dong, Hong Zhao, Jian Jun Xu, and Shuai Ma. "A Traffic Flow Forecasting Model Based on Variable Dimension Fractal Combined with Weekly Similarity." Applied Mechanics and Materials 44-47 (December 2010): 3427–32. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3427.

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It’s important that the short-time traffic flow forecasting has good real-time performance and high accuracy. In order to satisfy this demand, weekly similarity is imported and an improved fractal forecast model is established. In order to improve forecast accuracy furthermore, one-rank local-region forecasting principle is referenced to determine parameters which influence weekly similarity degree. Finally, the improved fractal model based on variable dimension is employed to predict the traffic flow in Hangzhou city. The experiment result shows that the improved fractal method proposed here

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Atangana, Abdon, and Ali Akgül. "Analysis of a derivative with two variable orders." AIMS Mathematics 7, no. 5 (2022): 7274–93. http://dx.doi.org/10.3934/math.2022406.

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<abstract><p>In this paper, we investigate a derivative with the two variable orders. The first one shows the variable order fractal dimension and the second one presents the fractional order. We consider these derivatives with the power law kernel, exponential decay kernel and Mittag-Leffler kernel. We give the theory of this derivative in details. We also present the numerical approximation. The results we obtained in this work are very useful for researchers to improve many things for fractal fractional derivative with two variable orders.</p></abstract>

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KITAMURA, T., and H. HONJO. "A NEW METHOD TO DESCRIBE BRANCHING PATTERNS AS ONE-VARIABLE ARRAY." Fractals 14, no. 02 (2006): 77–85. http://dx.doi.org/10.1142/s0218348x06003106.

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In nature, especially in non-equilibrium physics, we can see many branching growth patterns. We devised a new method for easily analyzing such pattern structures. A pattern growing in real space is transformed into a one-variable array without destroying the essence of its structure. To validate the method, we analyzed a fractal pattern as an example. By comparing the fractal dimension of the pattern with several exponents of the transformed one-variable array, we discuss the effectiveness of transformation into one-variable arrays.

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WU, JUNRU, and CHENGYUAN WANG. "FRACTAL STOKES’ THEOREM BASED ON INTEGRALS ON FRACTAL MANIFOLDS." Fractals 28, no. 01 (2020): 2050010. http://dx.doi.org/10.1142/s0218348x20500103.

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In this paper, with the Hausdorff measure, the Hausdorff integral on fractal sets with one or lower dimension is firstly introduced via measure theory. Then the definition of the integral on fractal sets in [Formula: see text] is given. With the variable substitution theorem in the Riemann integral generalized to the integral on fractal sets, the integral on fractal manifolds is defined. As a result, with the generalization of Gauss’ theorem, Stokes’ theorem is generalized to the integral on fractal manifolds in [Formula: see text].

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Pratsiovytyi, M. V., I. M. Lysenko, S. P. Ratushniak, and O. A. Tsokolenko. "Distribution of unit mass on one fractal self-similar web-type curve." Matematychni Studii 62, no. 1 (2024): 21–30. http://dx.doi.org/10.30970/ms.62.1.21-30.

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In the article, we study structural, spectral, topological, metric and fractal properties of distribution of complex-valued random variable$\tau=\sum\nolimits_{n=1}^{\infty}\frac{2\varepsilon_{\tau}}{3^n}\equiv\Delta^g_{\tau_1...\tau_n...}$, where $(\tau_n)$ is a~sequence of independent random variables taking the values $0,1,\cdots,6$ with the probabilities $p_{0n}$, $p_{1n},\cdots,p_{6n}$; $\varepsilon_{6}=0$, $\varepsilon_0$, $\varepsilon_1,\cdots,\varepsilon_5$ are 6th roots of unity. We prove that the set of values of random variable $\tau$ is self-similar six petal snowflake which is a f

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Yang, Jie, Yanna Zheng, and Huijing Wang. "Modifications and Statistical Analysis of Acoustic Emission Models Based on the Damage and Fractal Characteristics." Advances in Materials Science and Engineering 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/1898937.

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The damage process is accompanied by the acoustic emission for quasibrittle materials. And in the process of material damage evolution, the length of microcracks satisfies the fractal distribution. Research on their relationship in theory is helpful to reveal the law of material damage evolution and acoustic emission activities. Damage variable expressions are proposed based on the damage and fractal characteristics firstly. Then, the statistical models for acoustic emission considering damage and fractal characteristics are established by deducing the relationship between acoustic emission pa

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Martinez, Francisco, Hermann Manriquez, Alberto Ojeda, and Gabriel Olea. "Organization Patterns of Complex River Networks in Chile: A Fractal Morphology." Mathematics 10, no. 11 (2022): 1806. http://dx.doi.org/10.3390/math10111806.

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River networks are spatially complex systems difficult to describe by using simple morphological indices. To this concern, fractal theory arises as an interesting tool for quantifying such complexity. In this case of study, we have estimated for the first time the fractal dimension of Chilean networks distributed across the country, analysed at two different scales. These networks insert into variable environments, not only from a climatic and hydrological point of view, but also from a morphological point of view. We investigate to which extent the fractal dimension is able to describe the ap

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Wang, Ji Zhe, and Yan Guo. "Fractal Dimension and Characteristic of Tree Branch Growth." Applied Mechanics and Materials 610 (August 2014): 246–50. http://dx.doi.org/10.4028/www.scientific.net/amm.610.246.

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Fractal analysis of plant spatial patterns has been used to characterize the regressive ecological succession. The fractal dimension is used as a variable to help in charactering specific patterns in different kind of trees. A computational program was developed to process, analyze and extract the features of images of tree branch structure. Results are presented from four experiments to determine plant species from the color image of tree branch growth.

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Landis, Eric N. "Damage variables based on three-dimensional measurements of crack geometry." Strength, Fracture and Complexity: An International Journal 3, no. 2-4 (2005): 163–73. https://doi.org/10.3233/sfc-2005-056.

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Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this work, using three-dimensional measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties (surface area, volume, and fractal dimension) of internal cracks were measured through 3D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined f

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Attia, Najmeddine. "Note on fractal interpolation function with variable parameters." AIMS Mathematics 9, no. 9 (2024): 25834–48. http://dx.doi.org/10.3934/math.20241262.

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<p>This paper presents a detailed procedure for determining the probability of return for random walks on $ \mathbb{Z} $, whose increment is given by a generalization of a well-known Fibonacci sequence, namely the $ k $-Fibonacci-like sequence $ (G_{k, n})_n $. Also, we study the size of the set of these walks that return to the origin an infinite number of times, in term of fractal dimension. In addition, we investigate the limiting distribution of an adequate Markov chain that encapsulates the entire Tribonacci sequence $ ({\mathsf T}_n) $ to provide the limiting behavior of this seque

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Zhixin Shao, Yanqi Song, Fuxin Shen, Hongfa Ma, Junjie Zheng, and Juntao Yang. "Study on the freeze-thaw damage characteristics of skarn based on CT three-dimensional reconstruction." Mining Science 31 (2024): 39–59. http://dx.doi.org/10.37190/msc243103.

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To study the mesoscopic damage evolution characteristics of skarn under freeze-thaw cycles, based on CT technology, the skarn samples under freeze-thaw action were scanned by CT, and the image data of skarn were segmented by Avizo software. The digital model of the three-dimensional structure of skarn was established, and the evolution law of the internal structure of skarn during the freeze-thaw cycle was quantitatively analyzed. The box dimension algorithm calculates the fractal dimension of the pore structure under freeze-thaw conditions. The relationship between fractal dimension, pore vol

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Shao, Peng, Yong Nian He, Li Fen Zhou, and Qing Feng Zhang. "Application of Percolation Theory to Rock Damage and Fracture." Key Engineering Materials 353-358 (September 2007): 1117–20. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.1117.

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Rock is a kind of complex and high-disordered geological material, its damage and fracture process usually shows obvious criticality. In this paper, percolation theory is applied to analyze and describe this critical property. First, we discuss the critical fracture probability of rock through percolation and renormalization analysis, and present the equivalence between fracture probability and damage variable. Based on scaling law and the relationship between critical exponents, a critical fractal dimension is obtained. Furthermore, according to the analysis of relationship between damage and

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Selvi, S. S., and A. Makur. "Variable dimension range and domain block-based fractal image coding." IEEE Transactions on Circuits and Systems for Video Technology 13, no. 4 (2003): 343–47. http://dx.doi.org/10.1109/tcsvt.2003.811428.

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Pei, Liang, Jiankang Chen, Jingren Zhou, et al. "A Fractal Prediction Method for Safety Monitoring Deformation of Core Rockfill Dams." Mathematical Problems in Engineering 2021 (January 21, 2021): 1–11. http://dx.doi.org/10.1155/2021/6655657.

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Deformation mechanism in the core rockfill dams with heavy load and high-stress level is difficult to predict and control, which is one of the key problems to be solved in the dam operation safety management and control. Aiming at the large error problems obtained by the parameter-based functional models (regression model, grey theory model, etc.) in the deformation prediction of the core rockfill dams, a fractal prediction method and its technical process by combining the variable dimension fractal dimension and the "metabolism" of prediction data are proposed through analyzing the fractal ad

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Liu, Xiu Ying, and Guo Ping Di. "Experimental Study of Damage Variable Law of Bridge and Tunnel with Underlying Goaf during Expressway." Advanced Materials Research 243-249 (May 2011): 3062–66. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.3062.

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This paper takes geological conditions of the Li—Jun expressway by Kang JiaGou and Tong De coal mine goaf as prototype, using the simulation experiment of similar material, simulates the formation process and distribution of the mined rock fracture and the damage variable of the mined rock by using the simulation experiment of similar material, At the same time, It researches the evolvement law of rock’s fracture network in caving zone, fractured zone over goaf using fractal geometry theory. It analyses the damage variable law in caving zone, fractured zone using the damage mechanical theory,

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Chai, Zhaoyun, Jinbo Bai, Haiyang Zhang, and Pan Yang. "Evolution Rules of Fractures for Mudstone under Compression Shear Load and the Fractal Characteristics of Broken Blocks." Advances in Civil Engineering 2019 (February 3, 2019): 1–7. http://dx.doi.org/10.1155/2019/2489218.

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Failure of rocks is commonly induced by compressive and shear coupling loading. Knowledge of the mechanism and process of deformation and failure of rocks under compressive shear loading condition is an important basis for the study of stability in rock engineering. Based on the nonlinear fractal theory, it is possible to examine the evolution rules of fractures in mudstone under compression shear load and the fractal characteristics of broken blocks using the shear compression test with variable angles of mudstone specimens in natural conditions. This research shows that the cohesion and fric

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Lyu, Lihua, Yingjie Liu, Jihong Bi, and Jing Guo. "Sound Absorption Properties of DFs/EVA Composites." Polymers 11, no. 5 (2019): 811. http://dx.doi.org/10.3390/polym11050811.

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Using discarded feather fibers (DFs) and ethylene vinyl acetate (EVA) copolymer, the DFs/EVA composites with good sound absorption performance were prepared by hot-pressing method. The effects of hot-pressing temperature, mass fraction of DFs, density and thickness of composites on the sound absorption properties were studied by the controlling variable method. The sound absorption properties of the composites were studied by the transfer function method, and under the optimized technological conditions, the sound absorption coefficient of the composites was above 0.9 and the sound absorption

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Shi, Rui Xiang, Chi Ai, Wan Chun Zhao, and Xiao Han Feng. "The Damage Mechanics Model of the Wellbore Surrounding Rock Based on Fractal Theory." Applied Mechanics and Materials 423-426 (September 2013): 1623–26. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.1623.

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In order to describe the mechanical characteristics of CBM wellbore surrounding rock more accurately, the article establishes the CBM wellbore surrounding rock mechanics model based on the fractal theory. According to the pores of CBM surrounding rock and the characteristics of mass fractal, people find the macro fracture and micro fracture damage characteristics and build the relationship of any scale coal strength, damage variable and fractal dimension. According to the numerical calculation method of the surrounding rock stress, people find the surrounding rock stress calculation method and

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Mukhopadhyay, Arkadeb, Manik Barman, and Prasanta Sahoo. "Optimization of Fractal Dimension of Turned AISI 1040 Steel Surface Considering Different Cutting Conditions." International Journal of Surface Engineering and Interdisciplinary Materials Science 7, no. 2 (2019): 19–33. http://dx.doi.org/10.4018/ijseims.2019070102.

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The present work examines the effect of turning process parameters, namely depth of cut and feed rate on the fractal dimension of AISI 1040 steel. Machined surfaces have been characterized using fractal dimensions. Apart from the aforesaid conventional turning parameters, cutting condition has been also considered as a design variable. Three cutting conditions have been considered, e.g. dry, water lubricated, and commercially available water-soluble emulsion lubricated condition. The depth of cut and feed rate has been also been varied at three levels. Experiments were performed following Tagu

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Wang, Min, Yakun Tian, Zhijun Zhang, Qifeng Guo, and Lingling Wu. "Dynamic Evolution of Coal Pore-Fracture Structure and Its Fractal Characteristics under the Action of Salty Solution." Mathematics 12, no. 1 (2023): 72. http://dx.doi.org/10.3390/math12010072.

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The instability and failure of coal pillars is one of the important factors leading to the catastrophic consequences of coal mine goaf collapse. Coal mine water has the characteristics of high salinity. Long-term mine water erosion can easily deform the coal pillar structure, eventually leading to instability and damage. This study carried out tests on coal samples soaked in salt solutions with different concentrations, and the nuclear magnetic resonance (NMR) method was used to obtain the dynamic evolution of the pore-fracture structure of coal. On the basis of fractal theory, the changes in

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Jia, Yufei, Yuxin Bai, Dong Xia, Fuping Li, and Bing Liang. "Energy Dissipation and Damage Evolution during Dynamic Fracture of Muddy Siltstones Containing Initial Damage under the Freeze Thaw Effect." Materials 16, no. 1 (2022): 120. http://dx.doi.org/10.3390/ma16010120.

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This research aims to evaluate the influences of the freeze–thaw (F-T) effect on the energy dissipation mechanism and damage evolution characteristics of muddy siltstones containing initial damage. At first, four initial damage levels were achieved by applying different impact loads to the intact rock, and the damage stresses for levels I, II, III, and IV initial damage were 9.80 Mpa, 17.00 Mpa, 23.34 Mpa, and 32.54 Mpa, respectively. Then dynamic compression tests were conducted on the muddy siltstones containing initial damage after 0, 5, 10, 15, 20, 25, 30, and 40 F-T cycles in the temperat

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Koshovy, G. I. "Electromagnetic Wave Scattering by Strip Systems with a Variable Fractal Dimension." Telecommunications and Radio Engineering 67, no. 15 (2008): 1321–31. http://dx.doi.org/10.1615/telecomradeng.v67.i15.10.

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Ehrl, Lyonel, Miroslav Soos, and Marco Lattuada. "Generation and Geometrical Analysis of Dense Clusters with Variable Fractal Dimension." Journal of Physical Chemistry B 113, no. 31 (2009): 10587–99. http://dx.doi.org/10.1021/jp903557m.

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Qiao, Wei, Shu-Tang Liu, and Jie Sun. "Control of the Thermal Fractal Diffusion of Tightly Compressed Heterogeneous Layers of Thin Plates." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/672547.

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As the thermal conductivity of thin plates composed of tightly compressed heterogeneous layers varies continuously in the form of an exponential function, we present a nonlinear dynamical model of the fractal growth of thermal diffusion. We also analyze the quantitative relationship between the probability of growth and the disturbance term, predict the control action of the environmental disturbance term on fractal growth, and use Matlab simulation to verify the control effectiveness of thermal fractal diffusion. The results facilitate the selection of appropriate control areas and control pa

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Son, M., and T. J. Hsu. "The effect of variable yield strength and variable fractal dimension on flocculation of cohesive sediment." Water Research 43, no. 14 (2009): 3582–92. http://dx.doi.org/10.1016/j.watres.2009.05.016.

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