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Fractal dimension
About: Fractal dimension is a research topic. Over the lifetime, 14764 publications have been published within this topic receiving 329050 citations.
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TL;DR: The surface fractal dimension of yttria stabilized zirconia nanopowders has been determined by the fractal Frenkel-Halsay-Hill equation and Neimark's equation as mentioned in this paper.
Abstract: Yttria stabilized zirconia nanopowders have been prepared by co-precipitation method with using a microwave radiation in the process of drying with followed calcination at different temperatures (400–900 °C). Porosity and the surface fractal dimension of zirconia nanopowders have been studied by the nitrogen isotherms at 77 K. The fractal dimension of yttria stabilized zirconia was determined by the fractal Frenkel–Halsay–Hill equation and Neimark’s equation. We found that for samples calcined at temperatures in the range of 400–900 °C the surface fractal dimension is nearly constant (2.5–2.6). This indicates that the surfaces of yttria stabilized zirconia calcined at different temperatures are indeed irregular and may be described by fractal geometry in a certain range of length scale.
3 citations
TL;DR: In this article, a modified growth rule was proposed to simulate the growth anisotropy along the axes of symmetry. But the growth in the anisotropic regime was not considered.
Abstract: Diffusion-limited particle aggregation is simulated with a modified growth rule. By means of a parameter the growth anisotropy along the axes of symmetry can be varied continually from isotropic to strongly anisotropic. For weak anisotropy one initially observes an isotropic structure with a fractal dimension D = 1.7 which crosses over to an anisotropic structure with two different scaling exponents Daxial = 1.5 and Ddiagonal = 2.0 along the axes, respectively, along the diagonals, on a square lattice. One can understand the growth in the anisotropic regime in terms of classical aggregation, where the fluctuations are neglected.
3 citations
3 citations
TL;DR: This quantitative rather than qualitative comparison done by fractal dimension numerical analysis helps to decrease the quality assurance errors in IMRT dosimetry verification.
Abstract: Purpose. This study describes how to identify the coincidence of desired planning isodose curves with film experimental results by using a mathematical fractal dimension characteristic method to avoid the errors caused by visual inspection in the intensity modulation radiation therapy (IMRT). Methods and Materials. The isodose curves of the films delivered by linear accelerator according to Plato treatment planning system were acquired using Osiris software to aim directly at a single interested dose curve for fractal characteristic analysis. The results were compared with the corresponding planning desired isodose curves for fractal dimension analysis in order to determine the acceptable confidence level between the planning and the measurement. Results. The film measured isodose curves and computer planning curves were deemed identical in dose distribution if their fractal dimensions are within some criteria which suggested that the fractal dimension is a unique fingerprint of a curve in checking the planning and film measurement results. The dose measured results of the film were presumed to be the same if their fractal dimension was within 1%. Conclusions. This quantitative rather than qualitative comparison done by fractal dimension numerical analysis helps to decrease the quality assurance errors in IMRT dosimetry verification.
3 citations
TL;DR: In this paper, the authors analyzed the amorphous/solid to disordered liquid structural phase transitions of an anomalous confined fluid in terms of their fractal dimensions, where the model studied is composed by particles interaction through a two-length scales potential confined by two infinite plates.
Abstract: In this paper we analyze the amorphous/solid to disordered liquid structural phase transitions of an anomalous confined fluid in terms of their fractal dimensions. The model studied is composed by particles interaction through a two-length scales potential confined by two infinite plates. This fluid that in the bulk exhibits water-like anomalies under confinement forms layers of particles. We show that the fluid at the contact layer forms at high densities structures and transitions that can be mapped into fractal dimensions. The multi-fractal singularity spectrum is obtained in all these cases and it is used as the order parameter to quantify the structural transitions for each stage on the confined liquid. This mapping shows that the fractal dimension increases with the density and with the temperature.
3 citations