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Hydrophobicity classification of polymeric materials based on fractal dimension

THOMAZINI, Daniel; GELFUSO, Maria Virginia; ALTAFIM, Ruy Alberto Corrêa
Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
37.35703%
This study proposes a new method to obtain hydrophobicity classification (HC) in high voltage polymer insulators. In the method mentioned, the HC was analyzed by fractal dimension (fd) and its processing time was evaluated having as a goal the application in mobile devices. Texture images were created from spraying solutions produced of mixtures of isopropyl alcohol and distilled water in proportions, which ranged from 0 to 100% volume of alcohol (%AIA). Based on these solutions, the contact angles of the drops were measured and the textures were used as patterns for fractal dimension calculations.

Texture analysis using volume-radius fractal dimension

Backes, André R.; Bruno, Odemir Martinez
Fonte: Elsevier; Philadelphia Publicador: Elsevier; Philadelphia
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
37.232993%
Texture plays an important role in computer vision. It is one of the most important visual attributes used in image analysis, once it provides information about pixel organization at different regions of the image. This paper presents a novel approach for texture characterization, based on complexity analysis. The proposed approach expands the idea of the Mass-radius fractal dimension, a method originally developed for shape analysis, to a set of coordinates in 3D-space that represents the texture under analysis in a signature able to characterize efficiently different texture classes in terms of complexity. An experiment using images from the Brodatz album illustrates the method performance.; CNPq (306628/2007-4, 484474/2007-3)

"Identificação de correlações usando a Teoria dos Fractais"; Correlation identification using the fractal theory

Sousa, Elaine Parros Machado de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 29/03/2006 PT
Relevância na Pesquisa
37.26412%
O volume de informação manipulada em sistemas apoiados por computador tem crescido tanto no número de objetos que compõem os conjuntos de dados quanto na quantidade e na complexidade dos atributos. Em conjuntos de dados do mundo real, a uniformidade na distribuição de valores e a independência entre atributos são propriedades bastante incomuns. De fato, dados reais são em geral caracterizados pela ampla presença de correlações entre seus atributos. Além disso, num mesmo conjunto podem existir correlações de naturezas diversas, como correlações lineares, não-lineares e não-polinomiais. Todo esse cenário pode degradar a performance dos algoritmos que manipulam e, principalmente, dos que realizam análises dos dados. Além da grande quantidade de objetos a serem tratados e do número elevado de atributos, as correlações nem sempre são conhecidas, o que pode comprometer a eficácia de tais algoritmos. Nesse contexto, as técnicas de redução de dimensionalidade permitem diminuir o número de atributos de um conjunto de dados, minimizando assim os problemas decorrentes da alta dimensionalidade. Algumas delas são baseadas na análise de correlações e, com o objetivo de reduzir a perda de informação relevante causada pela remoção de atributos...

Estimação da dimensão fractal de imagens de SPM; Estimating fractal dimension of SPM images

Pinto, Silvia Cristina Dias
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 26/10/2001 PT
Relevância na Pesquisa
37.905452%
Este trabalho utiliza o método da Salsicha de Minkowski usando dilatação exata para estimação da dimensão fractal em imagens de superfícies de SPM (Microscópio de Varredura por Ponta de prova). Descrevemos uma rotina que permite o cálculo de uma série de dilatações da superfície original em relação a vários raios. O método de dilatação exata considera todas as possíveis salsichas envolvendo um pré-cálculo das distâncias (raios) numa grade ortogonal, que são armazenadas em uma lista junto com suas coordenadas relativas. A partir daí, realizamos um estudo multiescala sobre a curva log-log do volume dilatado em termos dos raios a fim de obter o valor da dimensão fractal para a superfície analisada. Para isso aplicamos dois métodos numéricos exatos, os quais são baseados em: diferenciação da curva por diferenças finitas e, por diferenciação usando uma propriedade da Transformada de Fourier. Os valores da derivada do sinal obtido permitem caracterizar a evolução da dimensão fractal da superfície ao longo de várias escalas espaciais, isto é, a dimensão fractal apresenta um comportamento dinâmico em termos de escalas espaciais definida pelos raios.; This work uses the Minkowski Sausage method using exact dilation for estimating fractal dimension to SPM (Scanning Probe Microscopy) surface images. We describe a routine that permits the calculation of a series of dilations of the original surface...

Fractal character of the SAXS correlation volume in poly(ethylene glycol)/silica hybrid wet gels

Donatti, Dario A.; Vollet, Dimas R.; Ruiz, Alberto Ibanez
Fonte: Springer Publicador: Springer
Tipo: Conferência ou Objeto de Conferência Formato: 243-248
ENG
Relevância na Pesquisa
57.78661%
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Small-angle X-ray scattering (SAXS) was employed to study the nanostructural properties of poly(ethylene glycol)(PEG)/silica hybrid wet gels prepared from hydrolysis of tetraethoxysilane (TEOS) in mixtures with PEG/(PEG + TEOS) molar ratio in the nominal range between 0 and 0.8. The SAXS pattern was found to be well fitted by the scattering from a polymeric particle of radius of gyration R (g) with an internal structure of primary silica particles described by a polymeric constraint of a mass-fractal of dimension D. R (g) increases with the PEG quantity while D first increases from 2.24 for the pure TEOS-derived gel to reach values between 2.46 and 2.40 with the additions of PEG. The correlation volume V (c) as determined by SAXS for such a polymeric structure behaves as a volume-fractal and accordingly scales with R (g) as V (c) similar to R (g) (D) . An overall mean value of about 1 nm could be estimated as an upper limit for the radius of the primary silica particle building up the structure of all the wet gels, independent of the PEG addition.

Hindered motion in highly porous media : steric and fractal approaches

Mota, M.; Yelshin, Alexander
Fonte: Universidade do Minho. Departamento de Engenharia Biológica Publicador: Universidade do Minho. Departamento de Engenharia Biológica
Tipo: Conferência ou Objeto de Conferência
Publicado em /09/2008 ENG
Relevância na Pesquisa
37.50174%
Two-dimensional simulation of porous media using a pore fractal dimension D was performed. Obtained results can be outlined as follows: 1). Starting from large pores with aspect ratio of micro-particle size to pore size λ > 0.001, molecules (or test object) recognise the pore volume as a partially restricted space with reduced fractal dimension. 2). The restriction effect on a molecule depends on pore topology (in the present case on the type of packing). 3). Dramatic reduction of D is observed when λ overcomes 0.01 and approaches λ ~ 0.1 in a 2-D approach, meaning that the test object recognises the pore as one dimensional rather than a 2-D space; in turn, a 3-D system will be recognised by the the test object as a 2-D system. 4). Concerning the hydrodynamic chromatography (HDC) the simulation explains why micro-objects become significantly retarded even at λ ~ 0.01, that is, even when the ratio between the Stokes-Einstein diameter of the diffusing micro-object to the equivalent pore diameter is very small. The developed approach confirms that even for micro-object with a very simple geometry (a square test box) a molecule might be much more sensitive to pore topology than what could be expected by a steric effect. It is possible to expect a more pronounced effect for asymmetric micro-objects in tortuous channels. These results show that the problem of molecular sensitivity towards pore topology may be understood using fractal analysis. Further work will apply this fractal approach to diffusivity behaviour in gel-like and fibre-like or foam structures.

Geometria fractal: propriedades e características de fractais ideais

Assis,Thiago Albuquerque de; Vivas Miranda,José Garcia; Mota,Fernando de Brito; Andrade,Roberto Fernandes Silva; Castilho,Caio Mário Castro de
Fonte: Sociedade Brasileira de Física Publicador: Sociedade Brasileira de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2008 PT
Relevância na Pesquisa
37.232993%
Descobertas recentes revelam que modelos matemáticos euclidianos, de há muito estabelecidos e que procuram reproduzir a geometria da natureza, às vezes se apresentam incompletos e, em determinadas situações, inadequados. Especificamente, muitas das formas encontradas na natureza não são círculos, triângulos, esferas, icosaedros ou retângulos. Enfim, não são simples curvas, superfícies ou sólidos, conforme definidos na geometria clássica de Euclides (300 a.C), cujos teoremas possuem lugar de destaque nos textos de geometria. Neste trabalho apresenta-se uma breve e elementar, mas que busca ser consistente, discussão sobre algumas definições e aplicações relacionadas à geometria fractal, em particular fractais ideais. Caracterizaremos alguns fractais auto-similares que, por sua importância histórica ou riqueza de características, constituem exemplos ilustrativos "clássicos" de propriedades de fractais, propriedades estas que muitas vezes aparecem dispersas numa literatura mais especializada. Mostra-se, por construção, que suas medidas de comprimento, área e volume, nas dimensões euclidianas usuais, dão margem a resultados contraditórios. Estes podem ser explicados pelo fato de que tais objetos só podem ser adequadamente mensurados em espaços de dimensão fracionária.

Hydrophobicity classification of polymeric materials based on fractal dimension

Thomazini,Daniel; Gelfuso,Maria Virginia; Altafim,Ruy Alberto Corrêa
Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2008 EN
Relevância na Pesquisa
37.35703%
This study proposes a new method to obtain hydrophobicity classification (HC) in high voltage polymer insulators. In the method mentioned, the HC was analyzed by fractal dimension (fd) and its processing time was evaluated having as a goal the application in mobile devices. Texture images were created from spraying solutions produced of mixtures of isopropyl alcohol and distilled water in proportions, which ranged from 0 to 100% volume of alcohol (%AIA). Based on these solutions, the contact angles of the drops were measured and the textures were used as patterns for fractal dimension calculations.

Fractal analysis of proton exchange kinetics in lysozyme.

Dewey, T G
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 06/12/1994 EN
Relevância na Pesquisa
27.921448%
Experimental data for the exchange of protons in tritiated lysozyme is reexamined by using a fractal model. The fraction of protons unexchanged, f, is seen to follow a stretched exponential, f infinity exp[(-t/tau)alpha], in the long time limit. Data over a range of temperatures are considered, and accurate fits are obtained with a single, unadjusted scaling exponent, alpha. The time constant, tau, follows an Arrhenius law and gives an activation energy comparable to that obtained for free peptide exchange. A model is proposed where proton exchange occurs as a result of solvent reacting with protein side groups in a restricted volume surrounding the protein. Dynamic fluctuations of the protein allow the protonated groups to enter this volume. Solvent also penetrates this volume, allowing proton exchange to occur. The fluctuations of reactants in this restricted volume dominate the kinetics and result in anomalous behavior. The topology of this reaction volume can be characterized by its fractal dimension. The fractal dimension of the space excluded by the protein is equal to 3-ds, where ds is the fractal dimension of the protein surface. The dimensionality of this "reaction space" can be used to predict the value of the exponent alpha. When the problem is treated as a reaction of the type A + B-->C in a confined region...

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

Goñi, Joaquín; Sporns, Olaf; Cheng, Hu; Aznárez-Sanado, Maite; Wang, Yang; Josa, Santiago; Arrondo, Gonzalo; Mathews, Vincent P; Hummer, Tom A; Kronenberger, William G; Avena-Koenigsberger, Andrea; Saykin, Andrew J.; Pastor, María A.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.938108%
High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure...

Fractal analysis of flocs formed in edible oil -water emulsions by image analysis techniques

Hempoonsert, Jiranun
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
27.84509%
Edible oil is an important contaminant in water and wastewater. Oil droplets smaller than 40 μm may remain in effluent as an emulsion and combine with other contaminants in water. Coagulation/flocculation processes are used to remove oil droplets from water and wastewater. By adding a polymer at proper dose, small oil droplets can be flocculated and separated from water. The purpose of this study was to characterize and analyze the morphology of flocs and floc formation in edible oil-water emulsions by using microscopic image analysis techniques. The fractal dimension, concentration of polymer, effect of pH and temperature are investigated and analyzed to develop a fractal model of the flocs. Three types of edible oil (corn, olive, and sunflower oil) at concentrations of 600 ppm (by volume) were used to determine the optimum polymer dosage and effect of pH and temperature. To find the optimum polymer dose, polymer was added to the oil-water emulsions at concentration of 0.5, 1.0, 1.5, 2.0, 3.0 and 3.5 ppm (by volume). The clearest supernatants obtained from flocculation of corn, olive, and sunflower oil were achieved at polymer dosage of 3.0 ppm producing turbidities of 4.52, 12.90, and 13.10 NTU, respectively. This concentration of polymer was subsequently used to study the effect of pH and temperature on flocculation. The effect of pH was studied at pH 5...

Method of Taylor expansion moment incorporating fractal theories for Brownian coagulation of fine particles

Wan, Z.; You, Z.; Sun, Z.; Yin, W.
Fonte: Walter de Gruyter GmbH & Co KG Publicador: Walter de Gruyter GmbH & Co KG
Tipo: Artigo de Revista Científica
Publicado em //2012 EN
Relevância na Pesquisa
37.50174%
Fine particles aggregating into larger units or flocculation body is a random combination process. Increasing the size and density of flocculation body is the main approach to rapid particle removal or sedimentation in water. Aiming at the Brownian coagulation of fine particles, a new method of Taylor expansion moment construction of fractal flocs has been developed in this paper, incorporating the Taylor expansion approach based on the moment method and the fractal dimension of the floc structure originated from fractal theories. This method successfully overcomes the limit of previous moment methods that require pre-assumed particle size distribution. Results of the zero and second order moments of Brownian flocs from the proposed method are compared with those from the Laguerre method, integral moment method and finite element method. It is found that the higher accuracy and efficiency of computation have been achieved by the new method, compared to the previous ones. Effects of the fractal dimension on the zero and second order moments, geometric average volume and standard deviation are also analyzed using this method. The self-conservation characteristics of particle distribution is observed without presumption of initial distributions.; Zhanhong Wan...

The arterial pattern and fractal dimension of the dog kidney

Gil-García, J.; Gimeno-Domínguez, M.; Murillo-Ferrol, Narciso
Fonte: Murcia : F. Hernández Publicador: Murcia : F. Hernández
Tipo: Artigo de Revista Científica Formato: application/pdf
ENG
Relevância na Pesquisa
37.9022%
A method has been developed by which it is possible to measure the fractal dimension of the arterial tree of the kidney. The objective of this work is to determine a method which permits us to discriminate between the architectures of specific organs by reference to a unique number, namely the fractal dimension of the arterial tree of that organ. This method opens the possibility of a new taxonomy for normal organs and for the pathological injuries related to the vascular morphology of those organs. The method that we have devised uses as its input the volume which is taken up by the arterial tree of the kidney. In order to calculate this volume we first obtained a plastic cast (the arteries were filled with Araldite CY233 plastic resin after which the organic tissues were corroded); thereafter we constructed a theoretical arterial tree having the same volume as the renal one. From this simplified tree, we were able to calculate its fractal dimension. The complete process of constmcting the theoretical arterial tree and the subsequent calculation of its fractal dimension was carried out automatically by way of a computer programrne to which we have given the name fractal program.

Fractal dimension and architecture of trabecular bone

Fazzalari, N.; Parkinson, I.
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Artigo de Revista Científica
Publicado em //1996 EN
Relevância na Pesquisa
37.990688%
The fractal dimension of trabecular bone was determined for biopsies from the proximal femur of 25 subjects undergoing hip arthroplasty. The average age was 67·7 years. A binary profile of the trabecular bone in the biopsy was obtained from a digitized image. A program written for the Quantimet 520 performed the fractal analysis. The fractal dimension was calculated for each specimen, using boxes whose sides ranged from 65 to 1000 μm in length. The mean fractal dimension for the 25 subjects was 1·195+0·064 and shows that in Euclidean terms the surface extent of trabecular bone is indeterminate. The Quantimet 520 was also used to perform bone histomorphometric measurements. These were bone volume/total volume (BV/TV) (per cent)=11·05+4·38, bone surface/total volume (BS/TV) (mm2/mm3)=1·90+0·51, trabecular thickness (Tb.Th) (mm)=0·12+0·03, trabecular spacing (Tb.Sp) (mm)=1·03+0·36, and trabecular number (Tb.N) (number/mm)=0·95+0·25. Pearsons' correlation coefficients showed a statistically significant relationship between the fractal dimension and all the histomorphometric parameters, with BV/TV (r=0·85,P0·0001), BS/TV (r=0·74,P0·0001), Tb.Th (r=0·50,P0·02), Tb.Sp (r=−0·81,P0·0001), and Tb.N (r=0·76,P0·0001). This method for calculating fractal dimension shows that trabecular bone exhibits fractal properties over a defined box size...

Análise da rede fluvial em diferentes escalas utilizando a teoria fractal e produtos de sensoriamento remoto

Schuch, Fernanda Simoni
Fonte: Universidade Federal de Santa Catarina Publicador: Universidade Federal de Santa Catarina
Tipo: Tese de Doutorado Formato: xiii, 141 p.| il., grafs., tabs.
POR
Relevância na Pesquisa
27.816223%
Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Civil, Florianópolis, 2011; Fundamentando-se na teoria dos fractais este volume traz os resultados, análises e novas perspectivas acerca da sua aplicação da referida teoria em análise de redes de drenagem. A área de estudos escolhida para aplicação da metodologia é a Bacia Hidrográfica do Rio Cachoeira, está localizada no município de Joinville no Estado de Santa Catarina, Brasil. Foram utilizados dados da rede de drenagem da área de estudo na forma vetorial obtidas de bases cartográficas, radar (SRTM) e laserscanning. Para gerar a informação fractal dos dados utilizou-se o método Box-counting através do qual se calculou a dimensão fractal dos dados de entrada em 2D e 3D. O método foi aplicado de maneira manual, onde se realizaram etapas passo a passo, em softwares proprietários e em software gerado a partir de ferramentas livres disponíveis na rede mundial de computadores o qual foi denominado 'Bacia Fractal'. Os resultados quantificam as diferenças entre os valores de dimensão fractal obtidas para os dados de entrada provenientes de diferentes produtos do sensoriamento remoto utilizados bem como para os dados planimétricos e planialtimétricos.; Based on the fractal theory this volume presents the results...

Outlining of high quality coking coal by concentration–volume fractal model and turning bands simulation in East-Parvadeh coal deposit, Central Iran

Tokhmechi, Behzad; Madani, Nasser; Wetherelt, Andrew; Ahangaran, Dariush Kaveh; Yasrebi, Amir Bijan; Alhoseini, Seyed Hosein; Afzal, Peyman
Fonte: Elsevier Publicador: Elsevier
Tipo: Artículo de revista
EN
Relevância na Pesquisa
47.711606%
Artículo de publicación ISI; This study aims at identifying the proper parts of C1 and B2 coking coal seams in the North block of East-Parvadeh coal deposit (Central Iran) using the concentration–volume (C–V) fractal modeling according to sulfur and ash values which were calculated by turning bands conditional simulation. The C–V log–log plots were generated based on results of 100 realizations derived via turning bands simulation which show seven different geochemical populations for both sulfur and ash data in B2 seam which has a relatively good quality for coking coal with sulfur and ash values lower than 1.548% and 6.39% respectively. Additionally, C–V log–log plots indicate that there are seven and six for sulfur and ash geochemical populations in C1 seam containing a proper coal quality with respect to sulfur and ash values less than 1.41% and 6.92% respectively. High quality populations are located in the northern and western parts of the studied area which correlated with USGS standard. The logratio matrix was used for the correlation between results obtained by the C–V fractal modeling and geological particulars consisting of pyritic veins and ash coals. Based on the logratio matrix for sulfur values higher than 3.55% and 3.39% for C1 and B2...

Electrostatics in Fractal Geometry: Fractional Calculus Approach

Baskin, Emmanuel; Iomin, Alexander
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/08/2011
Relevância na Pesquisa
27.856316%
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical symmetry case. The method is based on the splitting of a composite volume into a fractal volume $V_d\sim r^d$ with the fractal dimension $d$ and a complementary host volume $V_h=V_3-V_d$. Integrations over these fractal volumes correspond to the convolution integrals that eventually lead to the employment of the fractional integro-differentiation.

The 10 micron amorphous silicate feature of fractal aggregates and compact particles with complex shapes

Min, M.; Dominik, C.; Hovenier, J. W.; de Koter, A.; Waters, L. B. F. M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/09/2005
Relevância na Pesquisa
27.870637%
We model the 10 micron absorption spectra of nonspherical particles composed of amorphous silicate. We consider two classes of particles, compact ones and fractal aggregates composed of homogeneous spheres. For the compact particles we consider Gaussian random spheres with various degrees of non-sphericity. For the fractal aggregates we compute the absorption spectra for various fractal dimensions. The 10 micron spectra are computed for ensembles of these particles in random orientation using the well-known Discrete Dipole Approximation. We compare our results to spectra obtained when using volume equivalent homogeneous spheres and to those computed using a porous sphere approximation. We conclude that, in general, nonspherical particles show a spectral signature that is similar to that of homogeneous spheres with a smaller material volume. This effect is overestimated when approximating the particles by porous spheres with the same volume filling fraction. For aggregates with fractal dimensions typically predicted for cosmic dust, we show that the spectral signature characteristic of very small homogeneous spheres (with a volume equivalent radius r_V<0.5 micron) can be detected even in very large particles. We conclude that particle sizes are underestimated when using homogeneous spheres to model the emission spectra of astronomical sources. In contrast...

Estimation of fractal dimension and fractal curvatures from digital images

Spodarev, Evgeny; Straka, Peter; Winter, Steffen
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/08/2014
Relevância na Pesquisa
27.868804%
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e.\ volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivated by recent results on their limiting behaviour, we use these functionals to estimate the fractal dimension of sets from digital images. Simultaneously, we also obtain estimates of the fractal curvatures of these sets, some fractal counterpart of intrinsic volumes, allowing a finer classification of fractal sets than by means of fractal dimension only. We show the consistency of our estimators and test them on some digital images of self-similar sets.; Comment: 30 pages, 8 Figures

Naturaleza fractal en redes de cristales de grasas; Fractal nature in fat crystal networks

Gómez Herrera, Carlos
Fonte: Consejo Superior de Investigaciones Científicas (España) Publicador: Consejo Superior de Investigaciones Científicas (España)
Tipo: Artículo
SPA
Relevância na Pesquisa
37.905452%
The determination of the mechanical and rheological characteristics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The fractal approach is useful for the characterization of this microstructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G’ in linear region are described. The influence of interesterification on fractal dimension decrease (from 2,46 to 2,15) for butterfat-canola oil blends is notable. This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.; La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su carac­terización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G') dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2...