“…By means of near-field scattering we measure the time-dependent density-density correlation function as the aggregation process evolves, and we determine the ratio of the hydrodynamic and gyration radius to elucidate the aggregate's internal structure as a function of its fractal dimension. Surprisingly, we find that despite the large variation of particle interactions, the mass is always evenly distributed in all objects with fractal dimension ranging from 2.55 for shallow potentials to 1.78 for deep ones.…”
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“…This paper attempts to reveal the friction adaptive mechanism. Based on the fractal theory, two fractal parameters of fractal dimension and scale coefficient are used to characterize the surface morphology of the slipper mathematically, and the adaptive friction mechanism model is established by combining the friction coefficient equation. …”
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“…The results show that the synergy of the three nanomaterials promotes the generation of hydration products such as calcium silicate hydrate (C–S–H) and ettringite (AFt), improves the total pore fractal dimension (D(w)) and seepage pore fractal dimension (D(s)), and optimizes the microscopic pore structure. …”
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“…This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. …”
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“…Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. …”
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“…Objectives: The aims of this study were to explore how image compression affects density, fractal dimension, linear and angular measurements on digital panoramic images and assess inter and intra-observer repeatability of these measurements. …”
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“…Interestingly, these MoS(2) dendritic crystals on SiC exhibit an average fractal dimension 1.76, which is slightly larger than the classical Diffusion-limited-Aggregation fractal dimension 1.66. …”
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“…The relationship between the fractal dimensions (D(s1), D(s2), and D(g1)) and CPT could be divided into two distinct stages: a decrease in the CPT with increasing fractal dimensions (2.6–2.85), and then an in increase in the CPT. …”
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“…One of the most important features, especially of real networks, is their complexity, which often manifests itself in a fractal or even multifractal structure. As a generalization of fractal analysis, the multifractal analysis of complex networks is a useful tool for identifying and quantitatively describing the spatial hierarchy of both theoretical and numerical fractal patterns. …”
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“…This behavior is attributed to the presence of a majority of non-propagating vibrational modes, resulting from the nanoscale fractal structure of the material. By examining the fractal geometry of porous Si and its fractal dimensionality, which was smaller than two for the specific porous Si material used, we propose that a band of fractons (the localized vibrational excitations of a fractal lattice) is responsible for the observed plateau. …”
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“…In particular, it is known that linear analysis and fractal parameters of heart rate variability (HRV) are able to indirectly measure cardiac autonomic activity. …”
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“…CONCLUSIONS: It is concluded that this new formulation has two parameters that are directly estimated from the experiment, describes well the growth kinetics of unperturbed Ehrlich and fibrosarcoma Sa-37 tumors, and confirms the fractal origin of the Gompertz formulation and the fractal property of tumors.…”
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“…To study the polydispersity and irregularity of CGPCA, the CGPCA surface fractal dimension was calculated using fractal dimension combined with scanning electron microscopy. …”
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“…The equation is based on a fractal viewpoint of proteins, on a generalization of the Landau-Peierls instability, and on a marginal stability criterion. …”
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“…The article investigates the effect of thermal modification of porous carbon material (PCM), obtained from plant feedstock, on its morphology and fractal structure by small-angle X-ray scattering (SAXS) method. …”
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“…Here we used two open-access datasets to assess the intersession reliability of three cortical measures (thickness, gyrification, and fractal dimensionality) and two subcortical measures (volume and fractal dimensionality). …”
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“…First, the fractal method is employed to analyze the features of the machined surfaces of different materials and examine the relationship between the surface roughness and fractal dimension of different materials. …”
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“…It is shown that the fractal dimension of the adsorption process is larger than the fractal dimension of the desorption branch, meaning that the phase state of the adsorbate is more symmetric during the adsorption step than in the desorption process.…”
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“…All examined W microstructures show a direct correlation between the fractal dimension and irradiation energy. Analyses establish an empirical relation expressing a change in the microstructure as a function of the irradiation energy based on the changes in the fractal dimension of the microstructures. …”
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