Journal articles: 'Morphologie fractale'

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MOUSSA, R., and C. BOCQUILLON. "Morphologie fractale du réseau hydrographique." Hydrological Sciences Journal 38, no. 3 (June 1993): 187–201. http://dx.doi.org/10.1080/02626669309492662.

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Frankhauser, Pierre. "La formation fractale des tissus urbains." Cahiers de géographie du Québec 42, no. 117 (April 12, 2005): 379–98. http://dx.doi.org/10.7202/022764ar.

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L'article développe la question de savoir dans quelle mesure l'approche fractale représente un apport nouveau permettant de reconstituer la morphologie des tissus agglomérés. L'approche fractale introduit un nouveau paradigme pour concevoir la façon dont de tels tissus répondent à des critères d'optimisation. Sont explicitées les méthodes d'analyses de dilatation et radiale, ainsi que la reconstitution des courbes du comportement scalant. Ces méthodes complémentaires sont appliquées à des études de divers cadres densément bâtis: vastes zones métropolitaines et agglomérations de taille moyenne en Franche-Comté.

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Badariotti, Dominique. "Des fractales pour l’urbanisme?" Cahiers de géographie du Québec 49, no. 137 (March 9, 2006): 133–56. http://dx.doi.org/10.7202/012297ar.

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Résumé À partir de l’analyse de la morphologie de l’agglomération transfrontalière Strasbourg-Kehl, cet article traite de l’apport des analyses fractales dans le domaine de l’urbanisme. Outre quelques résultats d’ensemble désormais classiques, comme le calcul de la dimension fractale ou l’édition de la courbe du comportement scalant, il aborde le sujet des dimensions particulières de certains tissus spécifiques comme le centre-ville, les ensembles pavillonnaires, les grands ensembles et les zones techniques périphériques. Il propose également deux nouveaux indicateurs élaborés à partir des mesures de fractalité et susceptibles d’intéresser l’urbanisme et les recherches urbaines.

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Mitic, Vojislav V., Goran Lazovic, Dragoljub Mirjanic, Hans Fecht, Branislav Vlahovic, and Walter Arnold. "The fractal nature as new frontier in microstructural characterization and relativization of scale sizes within space." Modern Physics Letters B 34, no. 22 (July 30, 2020): 2050421. http://dx.doi.org/10.1142/s0217984920504217.

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Today in the age of advanced ceramic civilization, there are a variety of applications for modern ceramics materials with specific properties. Our up-to date research recognizes that ceramics have a fractal configuration nature on the basis of different phenomena. The key property of fractals is their scale-independence. The practical value is that the fractal objects’ interaction and energy is possible at any reasonable scale of magnitude, including the nanoscale and may be even below. This is a consequence of fractal scale independence. This brings us to the conclusion that properties of fractals are valid on any scale (macro, micro, or nano). We also analyzed these questions with experimental results obtained from a comet, here 67P, and also from ceramic grain and pore morphologies on the microstructure level. Fractality, as a scale-independent morphology, provides significant variety of opportunities, for example for energy storage. From the viewpoint of scaling, the relation between large and small in fractal analysis is very important. An ideal fractal can be magnified endlessly but natural morphologies cannot, what is the new light in materials sciences and space.

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Zhao, Shanrong, Jin Tan, Jiyang Wang, Xiaohong Xu, and Hong Liu. "A Dendrite with "Sierpinski Gasket" Fractal Morphology in Matt Glaze of LiAlSiO4-SiO2 System." Fractals 11, no. 03 (September 2003): 271–76. http://dx.doi.org/10.1142/s0218348x03001525.

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In this paper, we introduce a dendritic crystal, formed in matt glaze of LiAlSiO 4- SiO 2, having "Sierpinski gasket" fractal morphology. The crystal structure of this "Sierpinski gasket" dendrite is β-quartz. β-quartz can grow two kinds of fractal patterns: snow-shaped dendrite and "Sierpinski gasket" dendrite, depending on different supercooling conditions. These two kinds of fractals can develop together in one dendritic crystal. The evolution of the boundary morphologies between these two kinds of fractal dendrites can be described by another fractal — Koch curve. The "Sierpinski gasket" dendrite is a rather new fractal growth pattern which can introduce new opportunities to fractal growth research of nonlinear sciences.

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Chen, Yanguang. "Fractal Modeling and Fractal Dimension Description of Urban Morphology." Entropy 22, no. 9 (August 30, 2020): 961. http://dx.doi.org/10.3390/e22090961.

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The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology.

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PAN, XUEZAI. "RESEARCH ON MORPHOLOGIES OF ROCK FRACTURE SURFACES BASED ON MATHEMATICAL METHODS." Fractals 23, no. 04 (December 2015): 1550039. http://dx.doi.org/10.1142/s0218348x15500395.

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In order to research mechanics of rock fracture instant, it is one of methods that rock fracture mechanics are researched by rock fracture surfaces’ morphology. Some researched results which come from international and domestic researches in decades are described and summarized from mathematics in this paper. For example, fractal dimension method, “Small Island Method”, fractal interpolation method, Multi-fractal method, the accumulation power spectral density method. In addition, advantages and insufficiencies of every method are reviewed and commented. In the end, the future researched expectations are put forward from three aspects of rock fracture surfaces’ morphology.

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Li, Q., A. Wiedenmann, and H. Wollenberger. "Fractal morphologies from decomposition of Fe−Ni−Invar alloys." Journal of Materials Research 12, no. 1 (January 1997): 83–92. http://dx.doi.org/10.1557/jmr.1997.0014.

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Small angle neutron scattering investigations performed on Fe1−x–Nix alloys with 0.26 ≤ x ≤ 0.45 revealed a thermodynamically driven decomposition below 800 °C. The miscibility gap extends at least from 30 at.% Ni to 45 at.% Ni. The diffusioncontrolled decomposition produces fractal morphologies during the early stages of the process. During annealing the structure of the precipitated phase densifies continuously from mass fractals with small dimensionality (1 ≤ dm ≤ 3) to surface fractals with 2 ≤ ds ≤ 3. The results are compared with recent simulations of aggregation and growth as well as with a new analysis of spinodal decomposition, both predicting fractal morphologies.

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HUYNH, HOAI NGUYEN, and LOCK YUE CHEW. "ARC-FRACTAL AND THE DYNAMICS OF COASTAL MORPHOLOGY." Fractals 19, no. 02 (June 2011): 141–62. http://dx.doi.org/10.1142/s0218348x11005178.

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In this paper, we present an idea of creating fractals by using the geometric arc as the basic element. This approach of generating fractals, through the tuning of just three parameters, gives a universal way to obtain many novel fractals including the classic ones. Although this arc-fractal system shares similar features with the well-known Lindenmayer system, such as the same set of invariant points and the ability to tile the space, they do have different properties. One of which is the generation of pseudo-random number, which is not available in the Lindenmayer system. Furthermore, by assuming that coastline formation is based purely on the processes of erosion and deposition, the arc-fractal system can also serve as a dynamical model of coastal morphology, with each level of its construction corresponds to the time evolution of the shape of the coastal features. Remarkably, our results indicate that the arc-fractal system can provide an explanation on the origin of fractality in real coastline.

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Mu, Xiaokai, Wei Sun, Chong Liu, Bo Yuan, Yunlong Wang, and Qingchao Sun. "Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory." Materials 13, no. 18 (September 18, 2020): 4158. http://dx.doi.org/10.3390/ma13184158.

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This paper presents a numerical simulation method to determine the surface morphology characteristics of metallic materials. First, a surface profiler (NV5000 5022s) was used to measure the surface, and the morphology data thereof were characterized. Second, fractal theory was used to simulate the surface profile for different fractal dimensions D and scale coefficients G, and statistical analyses of different surface morphologies were carried out. Finally, the fractal dimension D of the simulated morphology and the actual morphology were compared. The analysis showed that the error of fractal dimension D between the two morphologies was less than 10%; meanwhile, the comparison values of the characterization parameters of the simulated morphology and the actual morphology were approximately equal, and the errors were below 6%. Therefore, the current method used to evaluate the surface morphologies of parts processed by the grinding/milling method can be replaced by the simulated method using the corresponding parameters. This method makes it possible to theorize about the surface morphologies of machined parts, and provides a theoretical basis and reference value for the surface morphology design of materials, with the potential to improve the assembly quality of products.

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Feng, Zhigang, Xuezai Pan, Guoxing Dai, and Hongguang Liu. "Research on Rock Fracture Surface Morphology Characterization under Brazilian Test." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/434898.

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In order to test the differences in the morphology characterization of rock fracture surfaces under different loading directions and rates, the following three steps are operated. Firstly, using Brazilian test, the Brazilian discs are loaded to fracture under different loading modes. Secondly, each rock fracture surface is scanned with a highly accurate laser profilometer and accordingly the coordinates of three lines on every rock fracture surface and three sections of every line are selected to analyze their fracture morphology characterization. Finally, modulus maximum method of wavelet transform, including a new defined power algorithm and signal to noise ratio, and fractal variation method are used to determine the differences in rock fracture surfaces’ morphology characterization under different loading directions and rates. The result illustrates that both modulus maximum and fractal variation method can detect anisotropy of rock fracture failure. Compared to modulus maximum method, fractal variation method shows stronger sensitivity to the change of loading rates, which is more suitable to differentiate the rock fracture surface’s morphology characterization under different loading modes.

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Guerrero Torrenegra, Alejandro. "Periferias espontáneas de Ciudad Bolívar-Bogotá: vista desde la perspectiva fractal. Abordaje metodológico." Procesos Urbanos 3 (December 1, 2016): 89–98. http://dx.doi.org/10.21892/2422085x.269.

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Resumen: Las periferias internas espontáneas de América Latina se caracterizan por sus genes tipológicos informales-invasiones, que identifican a los tejidos informales que se producen como consecuencia de las construcciones y reconstrucciones auto-gestionadas. El objetivo principal de la investigación fue identificar la existencia de patrones o códigos fractales en las manzanas de la periferia interna espontánea de las UPZ, de la localidad de Ciudad Bolívar de Bogotá. La investigación es descriptiva y analítica, sigue pautas fenomenológicas, con matemática (no lineales) y geometría fractal. El resultado originó otra manera de aproximación al problema, en el que la morfología urbana guarda una relación con los tamaños y sus dimensiones: longitud, superficie y volumen, variables que conforman el plan, el diseño o la renovación urbana. ___Palabras clave: Periferias urbanas, fractales, patrones fractales. ___Abstract: The spontaneous internal peripheries of Latin America are characterized by their informal type-invasion genes, which identify informal fabrics that occur because of self-managed constructions and reconstructions. The main objective of the research was to identify the existence of patterns or fractal codes in the blocks of the spontaneous internal periphery of UPZ, in the town of Ciudad Bolívar, Bogotá. The research is descriptive and analytical, follows phenomenological guidelines, with mathematics (non-linear) and fractal geometry. The result originated another way of approaching the problem, in which the urban morphology is related to the sizes and their dimensions: length, surface and volume, variables that make up the plan, the design or the urban renewal.___Keywords: Urban peripheries, fractals, fractal patterns. ___Recibido: 27 de marzo de 2016. Aceptado: 17 de mayo de 2016.

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PAN, XUEZAI, ZHIRONG SHENG, and XUDONG SHANG. "CONTRAST OF ROCK FRACTURE SURFACE’S MORPHOLOGY CHARACTERIZATION BASED ON FRACTAL VARIATION." Fractals 27, no. 05 (August 2019): 1950070. http://dx.doi.org/10.1142/s0218348x19500701.

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In order to research roughness of rock fracture surfaces and interior damaged status of rock, some Brazil discs of white marble and sandstone are loaded to fracture by Brazil Test and the mathematical model of fractal variation is used to distinguish the morphology characterization of fracture surface of white marble from that of sandstone. Through computing the acquired scanned data of rock fracture surfaces, the following three results are obtained. First, the roughness of fracture surface increases with increase of loading angles, furthermore, the anisotropy of white marble fracture surface is more obvious than that of sandstone one. Second, under the same loading mode, by analyzing the mean fractal variation, the fracture surface of white marble is rougher than that of sandstone. Finally, rock disc specimens loaded to 1/2 or 3/4 of mechanics of mean fracture threshold still do not fracture at the first time loading, but their interiors have been badly damaged.

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Hilders, O. A., A. Quintero, L. Berrio, R. Caballero, L. Sáenz, N. Peña, and M. Ramos. "Effects of Aged Conditions on the Fracture Surface Fractal Dimension and Mechanical Behavior of an Austenitic Stainless Steel." Microscopy and Microanalysis 6, S2 (August 2000): 768–69. http://dx.doi.org/10.1017/s1431927600036333.

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There have been several attempts to find a relation between the fractal morphology of the fracture surfaces and the mechanical properties of engineering materials., although the current resuls are inconclusive. If there are correlations between the fractal dimension and such properties, this parameter could be very useful to predict them and to improve the resistance to fracture. The main part of the investigations concerned with the fractal geometry and fracture behavior concentrate on the relations between roughness and fracture toughness . In the present work, the effects of thermal aging at 850°C on the fracture topography developed during the rupture in tension at room temperature of a 304 type stainless steel and their relation with the strength and ductility, were studied using the fractal geometry approach.

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Zhai, Jun, Vikas Tomar, and Min Zhou. "Micromechanical Simulation of Dynamic Fracture Using the Cohesive Finite Element Method." Journal of Engineering Materials and Technology 126, no. 2 (March 18, 2004): 179–91. http://dx.doi.org/10.1115/1.1647127.

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Dynamic fracture in two-phase Al2O3/TiB2 ceramic composite microstructures is analyzed explicitly using a cohesive finite element method (CFEM). This framework allows the effects of microstructural heterogeneity, phase morphology, phase distribution, and size scale to be quantified. The analyses consider arbitrary microstructural phase morphologies and entail explicit tracking of crack growth and arbitrary fracture patterns. The approach involves the use of CFEM models that integrate cohesive surfaces along all finite element boundaries as an intrinsic part of the material description. This approach obviates the need for any specific fracture criteria and assigns models the capability of predicting fracture paths and fracture patterns. Calculations are carried out using idealized phase morphologies as well as real phase morphologies in actual material microstructures. Issues analyzed include the influence of microstructural morphology on the fracture behavior, the influence of phase size on fracture resistance, the effect of interphase bonding strength on failure, and the effect of loading rate on fracture.

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Gordienko, Yuri, Elena Zasimchuk, and Rimma Gontareva. "Heterogeneous Pattern Formation at Aluminum Surface — Fourier, Morphology and Fractal Analysis." Materials Science Forum 567-568 (December 2007): 169–72. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.169.

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Surface analysis of the aluminum thin plates plastically deformed under constrained cyclic deformation was performed by Fourier, morphology and fractal techniques. The plates are used for estimation of deformation damage and fracture in places with a priori known homogeneous and heterogeneous strain distribution. Advantages and disadvantages of Fourier, morphology and fractal techniques for characterization of the intersections and projections are discussed in the context of its applicability to investigation of plastic deformation and fracture (persistent strain planes and directions, strain localization angles and places, etc.).

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Si, Liang, Yijun Cao, and Guixia Fan. "Breakage Characterization of Magnetite under Impact Loads and Cyclic Impact Loading." Energies 13, no. 20 (October 19, 2020): 5459. http://dx.doi.org/10.3390/en13205459.

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A series of impact compression tests were conducted to study the breakage characteristics of magnetite, as well as the impact pressure on its strain rate and dynamic compressive strength. The dynamic mechanical properties and fragmentation size distribution of magnetite under diverse impact loads and cyclic impact were investigated, with fractal theory as a basis and split Hopkinson pressure bar (SHPB). Breakage methods were also employed to analyze the fracture morphology of magnetite. According to the result, the fractal dimension can reflect the distribution of fragments in various sizes. If the strain rate increases, the fractal dimension will be larger, the fragment size will be finer, and the fragmentation degree will be more influential. A micro-analysis of SEM images demonstrates that the fracture morphology is determined by mineral properties. Under low load cyclic impact, intergranular fracture is the main fractography. Besides, the intergranular fracture will be changed to a transgranular one as the impact load increases.

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Patankar, Dhananjay, Timothy Oolman, Steven Johnson, and Michael Berggren. "Ultrasonic Characterization of Mycelial Morphology as a Fractal Structure." Ultrasonic Imaging 14, no. 1 (January 1992): 86–95. http://dx.doi.org/10.1177/016173469201400106.

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Preliminary measurements of scattering of ultrasound from filamentous microorganisms in aqueous-medium suspensions are reported. The data are used to characterize the structuring (morphology) between the organisms quantitatively by modelling the morphology in terms of fractal structures and obtaining the fractal dimension as the characteristic parameter. The fractal dimension is calculated from the slope of a log-log plot of scattered intensity versus the scattering vector magnitude. The intensity is measured over a range of magnitudes of the scattering vector by varying the scattering angle as well as the ultrasonic frequency. Results from microbial suspensions of different species and different morphologies indicate that the fractal dimension can be used to quantify the morphological state of a suspension. The fractal dimension ranges from around 1.5 for suspensions with pelletous morphology to around 2.5 for suspensions with filamentous morphology.

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Sekerešová, Zuzana, and Hynek Lauschmann. "Multi-Fractal Features of Fatigue Crack Surfaces in Relation to Crack Growth Rate." Materials Science Forum 567-568 (December 2007): 129–32. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.129.

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Texture of a fatigue crack surface is strictly related to crack growth rate. Cracks in specimens from aluminum alloy were studied. Two types of information were used: SEM images of fracture surfaces, and 3D reconstructions of fracture surface morphologies. Sets of equidistantly focused images obtained by an optical microscope served as the basis for 3D reconstruction. Multiparametric fractal analysis was applied to characterize crack surfaces. A vector of fractal features represented each image or 3D reconstruction of selected locations of fracture surfaces. For estimating fractal characteristics, the box-counting method in 3D was used in all cases, [1]. Multilinear regression was used to express the relation between crack growth rate and feature vectors, with satisfactory results for both crack surface representations.

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Huang, Jin, Guohua Xu, Heyong Qin, and Lei Zheng. "Correlation between Fracture Morphology and Microstructural Evolution during Long-Term Aging of EK61 Superalloy." Scanning 2020 (April 24, 2020): 1–8. http://dx.doi.org/10.1155/2020/1087024.

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Microstructural evolutions of EK61 superalloy during long-term aging until 1000 h at 700°C and 750°C, respectively, are studied by combination of Scanning Electron Microscope (SEM) and Transmission Electron Microscope (TEM). Impact fracture morphologies after aging for different time are observed by the SEM. The microstructure is found to be relatively stable during aging at 700°C, and the fracture morphologies are characterized by transgranular fracture. At 750°C, the coarsening of γ′ phase leads the reduction of the quantity of dimples, the chainization of carbides on grain boundaries leads to intergranular fracture, and the netting of η phases within grains leads to the formation of lamellar cleavage steps. It is obvious that the destabilization of precipitated phases affects fracture morphology significantly. The relationship between fracture morphology and the microstructure promotes the evaluation of service reliability of EK61 superalloy.

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Kononov, Dmitry, Svetlana Gubenko, Igor Ivanov, and Sergey Urushev. "Using fractal characteristics to analyze the development of whole-rolled wheel destruction." MATEC Web of Conferences 329 (2020): 02009. http://dx.doi.org/10.1051/matecconf/202032902009.

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Purpose: Determination of mechanical characteristics of wheel steel by analyzing the development of destruction of solid-rolled wheels. Methods: Determination of the crack resistance of all-rolled wheels by testing samples from wheel steel for off-center tension with an edge crack, fractal parametrization of the fracture relief by processing the fracture photo using the R/S analysis method for fracture sections, which allows determining both the total fractal dimension of the fracture (the average for all sections), and in a specific area where there are changes in the fracture morphology. Construction of the dependence of the crack resistance parameter on the fractal dimension. Results: The possibility of analyzing wheel steel fractures by studying their fractal dimension is determined. A method of fractal parametrization of the wheel steel fracture relief is developed, which allows to obtain the value of the fractal dimension in different directions of crack growth. The fractal dimension of wheel steel is determined for different hardness values (after annealing and after thermal improvement). The dependence of the fractal dimension on the ductility characteristics of wheel steel is revealed: the lower the ductility characteristics (elongation, relative contraction) and, accordingly, the higher the hardness, the lower the value of the fractal dimension. The dependence of the fractal dimension on the coefficient of crack resistance of wheel steel KIC is determined, which makes it possible to predict the crack resistance of wheel steel depending on the fractal dimension of the fracture, as well as to judge the nature of the fracture – brittle, viscous or fatigue. Practical significance: The use of fractal fracture parameterization avoids time-consuming tests when determining the mechanical characteristics of wheel steel, as well as to determine the mechanical properties in the case when other methods are no longer applicable (small sample sizes).

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DAS, ISHWAR, SMRITI VERMA, SHOEB A. ANSARI, R. S. LALL, and NAMITA R. AGRAWAL. "FRACTAL GROWTH AND MORPHOLOGICAL TRANSITIONS DURING CRYSTALLIZATION OF AMINO ACIDS IN PRESENCE OF GLUCOSE." Fractals 18, no. 02 (June 2010): 215–22. http://dx.doi.org/10.1142/s0218348x10004890.

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Two-dimensional fractal and spherulitic patterns have been developed on microslides during the crystallization of amino acids in the absence and presence of glucose and agar-agar from their aqueous solutions. Lysine crystallized uniformly in the form of ringed spherulite, but in the presence of glucose it crystallized in the form of branched morphologies. Dependence of glucose concentrations on morphology of glutamic acid has also been studied. Morphology of glutamic acid was found to depend on glucose concentration. Due to interaction between glutamic acid and glucose, following morphological transitions were observed depending on glucose concentrations: spherulite → ringed spherulite → Fractal geometry → DLA-like pattern (D ≈ 1.725). Growth morphologies were characterized by measuring the location of bands (xn) as a function of band number n obeying the relation xn = mn + c, where m and n are slope and intercept respectively, and calculating the fractal dimension at different conditions. Influence of agar-agar on the morphology was also studied. Results showed that branched morphologies were more dominant in the presence of agar-agar. In case of glycine, irregular growth patterns were observed. Interaction between amino acids and glucose was studied by viscosity measurements. It has been inferred that interaction is maximum in case of interaction of glucose with glutamic acid (acidic) and minimum in case of glycine (neutral).

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Petford, Nick, Dave Bryon, Michael P. Atherton, and Robert H. Hunter. "Fractal analysis in granitoid petrology: a means of quantifying irregular grain morphologies." European Journal of Mineralogy 5, no. 3 (June 14, 1993): 593–98. http://dx.doi.org/10.1127/ejm/5/3/0593.

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Han, Qing Kai, Hui Ru Li, Bang Chun Wen, Shui Yuan Chen, and Chang Sheng Liu. "Fractal Features of Surface Morphology of Uneven Eroded Hot-Dip Galvanized Steel." Key Engineering Materials 353-358 (September 2007): 1688–91. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.1688.

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The corrosion surface of hot-dip galvanized steel is regarded to be fractal and contains abundant self-similar information. In most cases, the corrosions of surface are not uniform as considered. For such an uneven eroded surface, regional fractals are introduced here in order to improve the analysis accuracy for local corrosions. Basing on the singular value decomposition of surface image, fractal dimensions of the energy norm along with the energy scale are analyzed. Combining energy norm of singular values and wavelet transform, the corrosion surfaces are described in different scales and decomposed levels.

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John, Ann M., Omar Elfanagely, Carlos A. Ayala, Michael Cohen, and Charles J. Prestigiacomo. "The utility of fractal analysis in clinical neuroscience." Reviews in the Neurosciences 26, no. 6 (December 1, 2015): 633–45. http://dx.doi.org/10.1515/revneuro-2015-0011.

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AbstractPhysicians and scientists can use fractal analysis as a tool to objectively quantify complex patterns found in neuroscience and neurology. Fractal analysis has the potential to allow physicians to make predictions about clinical outcomes, categorize pathological states, and eventually generate diagnoses. In this review, we categorize and analyze the applications of fractal theory in neuroscience found in the literature. We discuss how fractals are applied and what evidence exists for fractal analysis in neurodegeneration, neoplasm, neurodevelopment, neurophysiology, epilepsy, neuropharmacology, and cell morphology. The goal of this review is to introduce the medical community to the utility of applying fractal theory in clinical neuroscience.

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Herd, Charles R., Gerard C. McDonald, and William M. Hess. "Morphology of Carbon-Black Aggregates: Fractal Versus Euclidean Geometry." Rubber Chemistry and Technology 65, no. 1 (March 1, 1992): 107–29. http://dx.doi.org/10.5254/1.3538594.

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Abstract A study has been made comparing the utility of fractal and Euclidean geometry in the characterization of carbon-black aggregates. The fractal models used were the perimeter-area relationship, P∼ADp/2, and the mass fractal, M∼RDm. Values of the perimeter fractal, Dp, and the mass fractal, Dm, were determined for nineteen different grades of carbon black from a sampling of 1000 aggregates per grade. The perimeter (P), area (A), mass (M), and size (R) of the aggregates were all measured by on-line transmission-electron-microscopy/automated-image-analysis (TEM/AIA) which enabled rapid sampling. Values of Dp and Dm ranged from 1.05 to 1.23 and 2.85 to 2.47 respectively and were shown to correlate with carbon-black colloidal properties such as dibutyl-phthalate absorption (DBPA) and Euclidean size and shape parameters from TEM/AIA. These parameters were also used to classify aggregates into different shape categories using discrimination analysis techniques. Both perimeter and mass fractals were nearly constant within each shape category. Four carbon blacks of similar particle size and varied DBPA range were also used to show the effects on Dp and Dm upon high-shear mixing of the carbon-black aggregates into rubber and CAB composites.

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Zhang, Xu, Guangming Zheng, Xiang Cheng, Rufeng Xu, Guoyong Zhao, and Yebing Tian. "Fractal Characteristics of Chip Morphology and Tool Wear in High-Speed Turning of Iron-Based Super Alloy." Materials 13, no. 4 (February 24, 2020): 1020. http://dx.doi.org/10.3390/ma13041020.

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Considering that iron-based super alloy is a kind of difficult-to-cut material, it is easy to produce work hardening and serious tool wear during machining. Therefore, this work aims to explore the chip change characteristics and tool wear mechanism during the processing of iron-based super alloy, calculate the fractal dimensions of chip morphology and tool wear morphology, and use fractals to analyze their change trend. Meanwhile, a new cutting tool with a super ZX coating is used for a high-speed dry turning experiment. The results indicate that the morphology of the chip is saw-tooth, and its color changes gradually, due to the oxidation reaction. The main wear mechanisms of the tool involve abrasive wear, adhesive wear, oxidation wear, coating spalling, microcracking and chipping. The fractal dimension of the tool wear surface and chip is increased with the improvement of cutting speed. This work investigates the fractal characteristics of chip morphology and tool wear morphology. The fractal dimension changes regularly with the change of tool wear, which plays an important role in predicting this tool wear. It is also provides some guidance for the efficient processing of an iron-based super alloy.

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Lauschmann, Hynek, Petr Bednařík, Zuzana Sekerešová, and Michal Beneš. "FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY." Image Analysis & Stereology 27, no. 2 (May 3, 2011): 63. http://dx.doi.org/10.5566/ias.v27.p63-71.

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The morphology of fatigue fracture surface (caused by constant cycle loading) is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness). Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.

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Man, Ke, Yang Zhao, and He Fei Li. "Coordinate Transformation and the Volume Covering Fractal Algorithm of Rock Surface Morphology." Applied Mechanics and Materials 580-583 (July 2014): 966–70. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.966.

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The mechanics characteristics of the rock are mainly subjected by the joint and the fractures of the rock mass. For the joint, the surface morphology is especially the dominant influence factor. In order to describe the nature physics of rock surface, the surface morphology embarked on a fractured granite rock is described. And use the fractal dimension to calculate the volume of covering rock fracture surface, the relationship between fractal dimension and physical characteristics of rock surface.

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Konkol, Janusz. "Fracture Toughness and Fracture Surface Morphology of Concretes Modified with Selected Additives of Pozzolanic Properties." Buildings 9, no. 8 (July 26, 2019): 174. http://dx.doi.org/10.3390/buildings9080174.

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Modern methods of designing and testing concrete must be extended to appropriate material engineering approaches. It is then crucial to link the properties of concrete with its structure described in a quantitative way. The aim of the article was to present the results of research on concretes modified with three additives: Silica fume (SF), activated fluidal ash (FA), and metakaolinite (MK). The concretes were tested for compressive strength, fracture toughness (determining critical stress intensity factor KIcS and elastic modulus E). Also, stereological and fractal tests were performed. The research program covered three separate experiment plans, adopting the water/binder ratio and the additive/binder mass ratio as the independent variables. The results of experiments and their analysis proved a statistically significant relationship between fracture morphology (fractal dimension D) and concrete composition and fracture toughness. A higher fractal dimension was found in concretes with a higher content of cement paste and a lower content of additive. No significant effect of the type of additive used in the above dependence was found. An original method enabling the determination of mechanical properties of concrete with no need for destructive testing has been developed.

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Ali, Anam, Umar Ejaz, and Shazaib Khalid. "Leaf Morphology: An Interpretation of Fractals in Architectural Design." Journal of Art Architecture and Built Environment 2, no. 1 (June 2019): 16–29. http://dx.doi.org/10.32350/jaabe.21.02.

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Nature is the primary source of inspiration for human mind. Our world is full of interesting natural phenomena, organisms and systems that are essential for the existence of life on earth. Learning from nature is not a new concept. However, with the passage of time and the advancement of technology, the world has shifted to high tech strategies that are not sustainable in our natural context any more. Hence, scientists and designers are rethinking about sustainable solutions by taking inspiration from nature and with the help of advance technologies. Mathematics of self-similar shapes has existed for centuries. We have now realized that it is a natural phenomenon and is known as fractals. It is found everywhere, from trees to river networks, clouds to coral reefs, lighting to bird’s wings and vascular system of lungs to leaves. Fractals are never ending and infinitely complex patterns that are self-similar across different scales. Fractals create infinite complexity but in mathematics, it can be formulated thorough relatively simple equations. The idea is to study leaf morphology to understand the fractal pattern in leaf. Further, we want to explore the properties of leaf fractals so that we can use these arrangements in our architectural design.

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Nasr, Pedram, Hannah Leung, France-Isabelle Auzanneau, and Michael A. Rogers. "Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks." Gels 7, no. 2 (April 14, 2021): 46. http://dx.doi.org/10.3390/gels7020046.

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Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

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Slámečka, Karel, and Jaroslav Pokluda. "Analysis of Fracture Morphology and Local Loading Modes in Torsional Fatigue." Materials Science Forum 482 (April 2005): 263–66. http://dx.doi.org/10.4028/www.scientific.net/msf.482.263.

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The paper deals with a profile analysis of the fracture surface generated by pure cyclic torsion. Roughness and fractal characteristics studied in two mutually perpendicular directions were found to be sensitive to the crack front position. The investigation of surface topography revealed the presence of the opening Mode I in all investigated crack front locations.

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Petrović, Srdjan P. "Morphology and fractal dimension of TiO₂ thin films." Macedonian Journal of Chemistry and Chemical Engineering 32, no. 1 (December 1, 2013): 309. http://dx.doi.org/10.20450/mjcce.2013.450.

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The influence of annealing temperature on the morphology and surface fractal dimension of titanium dioxide (TiO2) films prepared via the spray deposition process was investigated. Thin films with various morphologies were obtained at different temperatures and characterized by X-ray diffraction and atomic force microscopy (AFM). It was found that the crystalline structure of TiO2 films depends strongly on annealing temperature. At higher temperatures, the partial phase transformation of anatase-to-rutile was observed. The morphology and surface fractal dimensions were evaluated by image analysis methods based on AFM micrographs. The results indicate that the value of surface roughness (the standard deviation of the height values within the given area of AFM image) of TiO2 films increases with increasing annealing temperature. Fractal analysis revealed that the value of the fractal dimension of the samples decreases slowly from 2.23 to 2.15 following the annealing process.

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Zejin, Yang, and Changsuo Zhang. "Mode I Fracture Toughness Test and Fractal Character of Fracture Trajectory of Red Sandstone under Real-Time High Temperature." Advances in Materials Science and Engineering 2019 (October 13, 2019): 1–13. http://dx.doi.org/10.1155/2019/5083947.

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To evaluate the stability and compactness of high-temperature underground construction, it is necessary to test the fracture toughness of surrounding rock (red sandstone) under real-time high temperature. In this paper, SCB specimens recommended by the International Society for Rock Mechanics are used to measure the mode I fracture toughness of red sandstone at real-time high temperatures. Also, to reveal its fracture characteristics and fracture mechanism, the fracture morphology observation (SEM experiment), XRD experiment, mercury intrusion porosimetry testing, and fractal measurement of fracture trajectory are carried out on the red sandstone specimens at various temperatures. The results show that (1) temperature may have a significant impact on the fracture toughness and fracture characteristics of red sandstone. On the whole, the fracture toughness values decrease with the increase in temperature, while the fractal dimensions of fractal trajectories increase with the increase in temperature. (2) Temperature has a significant influence on the fracture mode of red sandstone. At relatively low temperatures (20°C–400°C), the main fracture mode is transgranular failure. At relatively high temperatures (400°C–700°C), the fracture mode is mainly intergranular failure. (3) The weakening mechanism of red sandstone is mainly due to the effect of thermal dehydration when the temperature is between 100°C and 400°C. When the temperature is between 400°C and 700°C, the weakening mechanism is mainly due to thermal cracking and the α-β phase transition of quartz.

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Yin, Dagang, Bin Chen, and Huifen Zhou. "Research on Anisotropic Fracture Mechanical Behavior of Cortical Bone with Combined Method of Fractal and Gray Level Co-Occurrence Matrix." Journal of Biomaterials and Tissue Engineering 11, no. 1 (January 1, 2021): 67–75. http://dx.doi.org/10.1166/jbt.2021.2569.

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The irregular fracture surface of cortical bone, which is caused by complex multilevel micro-nanostructure, reflects the mechanical properties and fracture mechanisms. It is of great significance to characterize some characteristic parameters from the fracture surfaces of bone. In this research, anisotropic fracture mechanical properties of bovine femoral cortical bone along transverse, longitudinal and radial direction are firstly obtained by three-point bend experiment. Then the fracture routes and fracture surfaces are observed by scanning electron microscope. The observation shows that the formed fracture surfaces, which are caused by different crack routes, are extremely rough and have complex textures. Lastly, the combined method of fractal and gray level co-occurrence matrix are adopted to describe the morphology of fracture surface of cortical bone objectively and quantitatively. It is shown that the fracture surface of cortical bone has obvious fractal characteristics and four statistical texture feature parameters (contrast,angular second moment, correlation and entropy) of GLCM of fracture surfaces can describe a certain fracture texture character. The relationship between the characteristic parameters and macroscopic mechanical properties are established. The quantitative analysis and automatic class identification for the fracture surfaces of cortical bone can be achieved.

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Zhou, Yong Zhi, Hao Ran Geng, Mei Li, Chun Jing Sun, and Zhi Ming Wang. "Multirange Fractal Analysis of Discontinuous Microstructure Change of In-40wt.%Sn Melt." Materials Science Forum 704-705 (December 2011): 1055–60. http://dx.doi.org/10.4028/www.scientific.net/msf.704-705.1055.

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Fractal analysis based on results of high temperature X-ray diffraction experiment was used to study the temporal-spatial properties of particles in In-40wt.%Sn melt. Partially-overlapping multirange fractal structure is observed in In-40wt.%Sn melt, and as temperature decreases from 800°C to 130°C, low fractal dimension was found to range between 2.000 and 2.669, high fractal dimension is still 3.000 without alteration. Moreover, low fractal dimension reveals a discontinuous change between 600°C and 700°C. Fractal characteristics of In-40wt.%Sn melt were correlated with the evolution of microstructure. The discussion was made in detail. Multirange fractal model was proposed to calculate transition region curves of multirange fractals. The results show that values of simulation show good agreement with experimental values, the maximum error is less than 1.3%. From the analysis, the range of the transition region between two fractal regions is speculated to be related with structure properties of metal melts. In addition, ultrafine particles’ aggregation mechanism was used to analyze the fractal morphologies. Keywords: multirange fractal; In-40wt.%Sn melt; microstructure change; X-ray diffraction.

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38

Elgohary, Amr. "The Transformation of using Fractal Forms between Islamic and Digital Architecture from a Sustainable Approach." Academic Research Community publication 3, no. 3 (May 5, 2019): 87. http://dx.doi.org/10.21625/archive.v3i3.526.

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Along eras and civilizations, nature as a sustainable reference always has a great role in inspiration of the architectural form by the diversity of its vocabulary, rules, and colors…etc. Consequently, fractals as the main natural elements appeared in the achitectural morphology, since the ancient eras especially in the Islamic architecture in a various levels of forms, details, and patterns. However, nowadays the new architectural theories deal with fractals concept in a different ways depending on the deep understanding of universal and cosmic nature, also the new digital techniques in architectural design and construction that enhanced the appearance of new fractal forms. In this context, the research discusses the transformations of fractal systems, concepts and applications in architecture at the resent architectural theories, focusing on the digital architecture and how it deals with fractal forms, aiming to root the new architectural theories and link it with Islamic heritage to achieve a new Arab architecture that respects and reveals the local heritage and adapt with the latest architectural theories and techniques.

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Konkol, Janusz. "A Fractal Model of Cracking of Cement Matrix Composites." Buildings 10, no. 3 (March 11, 2020): 52. http://dx.doi.org/10.3390/buildings10030052.

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The modern methods of materials (including cement matrix materials) design and testing impose the application of an approach appropriate to materials engineering. A quantitative description of the association between the properties of these materials and their structure is a necessity. What remains the scientific aim, however, is the clarification and description of the occurring phenomena by means of models mapping their actual behavior in the closest way possible. The article presents a cracking fractal model based on tests on the morphology of concrete fracture surfaces. The recorded fractal nature of the cracking of cement matrix materials enabled fractal geometry in the model development to be applied. Owing to the application of statistical analysis, together with an extensive base of data on the profile lines separated out of the real fracture surfaces of concrete, it was possible to develop a cracking fractal model. Not only does this model satisfy the condition of the equality of the fractal dimension of the real and model profile lines, it also offers the possibility of introducing an order to the apparently chaotic phenomena, such as the cracking process. An advantage and novelty of the model is that unlike the other authors’ proposals, there is a possibility of reaching an infinitely large number of solutions for model profile lines, which approximates the model to the real-life scenario. The results of fractal tests were supplemented with strength measurements, identifying concrete’s compressive and fracture toughness (determining the critical stress intensity factor KIcS). A connection between the fractal dimension and the investigated properties of concrete was demonstrated. A higher fractal dimension was observed in the profile lines separated out of the fracture surfaces of concretes of higher water–cement ratio. The advantages of the model include the simplicity and applicability in model studies on other materials of the cement matrix.

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Li, Zhi, and Li Jie Chen. "Feature Recognition of Corrosion Pit for Pre-Corroded AA 2524 and Statistical Analysis." Advanced Materials Research 906 (April 2014): 263–67. http://dx.doi.org/10.4028/www.scientific.net/amr.906.263.

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Corrosion morphology image is one of the most important features for the evaluation of the corrosion damage of materials. By using white light confocal profiler, the corrosion morphologies of AA2524 aluminum alloy specimen are obtained after full immersion to experimental 3.5% salt solution for different time. Through digital image processing, typical corrosion morphology characteristics are extracted, such as the fractal dimension, the depth of pit, the area of pit. By extended 3D box-dimension method, the fractal dimensions of the corrosion surface under immersing time of 24 and 120 hours are determined. The statistical analyses show that the corrosion areas and the characterization parameters ab/2c2 obey Gumma distribution, and the corrosion depth obeys Gumbel, normal, Weibul and log-normal distributions.

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Xian, Yongqiang, Juan Liu, Chonghong Zhang, Jiachao Chen, Yitao Yang, Liqing Zhang, and Yin Song. "Fractal characteristics of fracture morphology of steels irradiated with high-energy ions." Journal of Nuclear Materials 461 (June 2015): 171–77. http://dx.doi.org/10.1016/j.jnucmat.2015.03.022.

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Hilders, O. A., L. Sáenz, N. Peña, M. Ramos, A. Quintero, R. Caballero, and L. Berrío. "Fractal Characterization of the Fractured Surface of a Duplex Stainless Steel and Their Relation with the Strength and Ductility." Microscopy and Microanalysis 6, S2 (August 2000): 766–67. http://dx.doi.org/10.1017/s1431927600036321.

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Due to the very good combination of the most outstanding properties of ferrite and austenite, the microstructure of duplex stainless steels allows them to obtain high strength and toughness levels even at low temperatures . As a result of these combined effects, duplex stainless steels have become very popular for many applications . In practice, the prolonged use of these materials at temperatures below approximately 500°C may cause an embrittlement of the ferrite phase, which has been called 475°C embrittlement. Thus, the isothermal aging at 475°C can be exploited to produce a variety of strength values associated with the corresponding decreases in ductility and variations of the fractal dimension of the fracture surfaces. No experimental measurements of the fractal dimension - tensile properties relationships are available for many commercial metallic alloys, then, the present experiments on a duplex stainless steel were conducted to show that the fractal dimension, D, many be used as a characterization parameter in fracture morphology - mechanical properties studies.

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Du, GuangSheng, ShiJiang Chen, Xiaoyi Chen, Yunfeng Gao, and Hailong Wu. "Study on the Relationship between Fracture Morphology and Splitting Strength of Granite Based on Fabric Distribution." Geofluids 2021 (July 31, 2021): 1–12. http://dx.doi.org/10.1155/2021/9985919.

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Because of the requirement of the mechanical properties of the damaged surrounding granite rock and the existence of the fracture water in hydraulic fracturing engineering, the strength of granite is related to the fabric, and the roughness of the section is also related to the liquid flow rate, a method of roughly determining the strength of the specimen by observing the failure mode of rock is needed. Considering that the physical and mechanical properties of granite are obviously affected by the fabric, the discrete element numerical simulation method was used to reconstruct the granite fabric based on the spatial correlation function to simulate the splitting experiment to investigate the failure mode of the specimen. The relationship between strength, the fractal value of cross-section, and the fabric was analyzed, which was verified through experiment. The results show that (1) the Voronoi GBM model with spatial correlation function of the discrete element can effectively simulate the controllable granite fabric and carry out micromechanical analysis. (2) The strength of the granite specimen and the fractal value of the cross-section have an obvious linear relationship with the fabric; besides, there is also a certain linear relationship between the strength of the specimen and the fractal value, which is influenced by granite fabric. (3) The predicted strength of the specimen according to the fractal value of the section is in good agreement with the actual strength with the error rate of 30%. In a word, this method can predict the strength of the specimen through the failure section and analyze the hydraulic fracture section and water pressure.

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Hwang, Eui-Ho, and Kwan-Sue Jung. "Development of Erosion Fractal-based Interpolation Method of River Morphology." Journal of Korea Water Resources Association 45, no. 9 (September 30, 2012): 943–57. http://dx.doi.org/10.3741/jkwra.2012.45.9.943.

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Maryenko, N. I., and O. Y. Stepanenko. "Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study)." Reports of Morphology 27, no. 2 (June 25, 2021): 16–22. http://dx.doi.org/10.31393/morphology-journal-2021-27(2)-03.

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Fractal analysis is a method of mathematical analysis, which provides quantitative assessment of the spatial configuration complexity of the anatomical structures and may be used as a morphometric method. The purpose of the study was to determine the values of the fractal dimension of the outer linear contour of human cerebellum by studying the magnetic resonance images of the brain using the authors’ modification of the caliper method and compare to the values determined using the box counting method. Brain magnetic resonance images of 30 relatively healthy persons aged 18-30 years (15 men and 15 women) were used in the study. T2-weighted digital magnetic resonance images were studied. The midsagittal MR sections of the cerebellar vermis were investigated. The caliper method in the author’s modification was used for fractal analysis. The average value of the fractal dimension of the linear contour of the cerebellum, determined using the caliper method, was 1.513±0.008 (1.432÷1.600). The average value of the fractal dimension of the linear contour of the cerebellum, determined using the box counting method, was 1.530±0.010 (1.427÷1.647). The average value of the fractal dimension of the cerebellar tissue as a whole, determined using the box counting method, was 1.760±0.006 (1.674÷1.837). The values of the fractal dimension of the outer linear contour of the cerebellum, determined using the caliper method and the box counting method were not statistically significantly different. Therefore, both methods can be used for fractal analysis of the linear contour of the cerebellum. Fractal analysis of the outer linear contour of the cerebellum allows to quantify the complexity of the spatial configuration of the outer surface of the cerebellum, which is difficult to estimate using traditional morphometric methods. The data obtained from this study and the methodology of the caliper method of fractal analysis in the author’s modification can be used for morphometric investigations of the human cerebellum in morphological studies, as well as in assessment of cerebellar MR images for diagnostic purposes.

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Shishulin, A. V. "ON THE TRANSITION BETWEEN FERROMAGNETIC AND PARAMAGNETIC STATES IN MESOPOROUS MATERIALS WITH FRACTAL MORPHOLOGY." Eurasian Physical Technical Journal 18, no. 2 (June 11, 2021): 6–11. http://dx.doi.org/10.31489/2021no2/6-11.

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In this paper, we have shown how the presence of pores and pore morphology influence on magnetic phase transition temperatures in mesoporous ferromagnetic materials. Model calculations have demonstrated the possibility to obtain macroscopic mesoporous samples with notably reduced Curie temperatures which is also further depressed in the case the pore morphology is more complicated. The results have been obtained on the basis of the experimentally verified correlation between the Curie temperature and cohesive energy of the material and illustrated using the examples of pure mesoporous iron, nickel and cobalt while pore morphology has been determined by the methods of fractal geometry. Several practical applications of mesoporous materials with tuned values of the Curie temperature have also been discussed in the final section.

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Kong, Yeo Lee, S. V. Muniandy, M. S. Fakir, and K. Sulaiman. "Fractal Analysis of Morphological Image of Organic Phthalocyanine Tetrasulfonic Acid Tetrasodium (TsNiPc) Film." Advanced Materials Research 895 (February 2014): 407–10. http://dx.doi.org/10.4028/www.scientific.net/amr.895.407.

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Surface morphology of thin films can be efficiently characterized using power spectral density method. Spectral based parameters from surface models can then be linked to electrical conductivity of thin films used for fabricating organic photovoltaic devices. In this study, the surface morphologies of the organic thin films phthalocyanine tetrasulfonic acid tetrasodium (TsNiPc) are investigated using atomic force microscopy. The thin film samples are imaged at 40-minutes and 120-minutes after the solvent treatment. The spectral exponent β is determined from the slope of PSD log-log plot and the fractal dimension D of each film is calculated based on fractal relation β = 8 2D. The relationship between surface roughness and fractal dimension with respect to electrical properties of thin film is discussed.

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Maryenko, N. I., and O. Yu Stepanenko. "Fractal dimension of phylogenetically different parts of the human cerebellum (magnetic resonance imaging study)." Reports of Morphology 26, no. 2 (October 12, 2020): 67–73. http://dx.doi.org/10.31393/morphology-journal-2020-26(2)-10.

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In recent years, fractal analysis has been increasingly used as a morphometric method, which allows to assess the complexity of the organization of quasi-fractal biological structures, including the cerebellum. The aim of the study was to determine the value of fractal dimension of phylogenetically different parts of the cerebellum by studying magnetic resonance imaging of the brain using the method of pixel dilation and to identify gender and age characteristics of individual variability of fractal dimension of the cerebellum and its external linear contour. The study was performed on the magnetic resonance images of the brain of 120 relatively healthy patients in age 18-86 years (65 women, 55 men). T2 weighted tomographic images were investigated. Fractal analysis was performed using the method of pixel dilation in the author’s modification. Fractal dimension (FD) values were determined for cerebellar tomographic images segmented with brightness values of 100 (FD100), 90 (FD90) and in the range of 100-90 (FD100-90 or fractal dimension of the outer cerebellar contour) in its upper and lower lobes, which include phylogenetically different zones. The obtained data were processed using generally accepted statistical methods. The average value of FD100 of the upper lobe of the cerebellum was 1.816±0.005, the lower lobe – 1.855±0.005. The average value of FD90 of the upper lobe of the cerebellum was 1.734±009, the lower lobe – 1.768±0.009. The average value of FD100-90 of the upper lobe of the cerebellum was 1.370±0.009, the lower lobe – 1.431±0.008. All three values of the fractal dimension of the lower lobe, which lobules have a lower phylogenetic age, are statistically significantly higher than the corresponding values of the fractal dimension of the upper lobe, have a more pronounced correlation with age than in the upper lobe. The developed research algorithm can be used to assess the condition of the cerebellum as an additional morphometric method during magnetic resonance imaging study of the brain.

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Hilders, O. A., N. D. Peña, M. Ramos, L. Sáenz, L. Berrío, R. A. Caballero, and A. Quintero. "Stress Triaxiality Dimple Fracture Morphology and Fractal Dimension Relations for Several Aluminum Alloys." Materials Science Forum 396-402 (July 2002): 1321–28. http://dx.doi.org/10.4028/www.scientific.net/msf.396-402.1321.

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Latypova, Renata, Oskari Seppälä, Tun Tun Nyo, Timo Kauppi, Sakari Pallaspuro, Saara Mehtonen, Hannu Hänninen, and Jukka Kömi. "Hydrogen-Induced Cracking of 500 HBW Steels Studied Using a Novel Tuning-Fork Test with Integrated Loadcell System." Corrosion 76, no. 10 (July 20, 2020): 954–66. http://dx.doi.org/10.5006/3592.

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Hydrogen embrittlement is a well-known problem with high-strength steels. An important aspect of hydrogen embrittlement research is the effect of the prior austenite grain (PAG) structure on hydrogen-induced fracture. The microstructural anisotropy of PAG structure depends on the steel manufacturing process. In this study, 500 HBW martensitic steels with different PAG structures are investigated with a novel tuning-fork test that utilizes an integrated loadcell system. The loadcell clamping system is used during hydrogen charging, allowing tracking of the applied force throughout the tests, which enables detection of separate phases of cracking and time-to-fracture. The elongated PAG morphology produces different results depending on the crack path direction in relation to the rolling direction, whereas the equiaxed PAG morphology does not manifest an orientation dependence. Depending on the PAG shape, also the fracture morphology differs. Time-to-fracture results show that elongated grain morphologies with transgranular quasi-cleavage crack propagation are more beneficial against hydrogen-induced fracture than equiaxed grain structure with intergranular crack propagation. These results demonstrate that the shape of the PAG structure plays an important role in the crack propagation mechanism and that it is important to consider the possible direction of hydrogen-induced cracks in the final structural applications.

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Journal articles on the topic 'Morphologie fractale'

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