Search results for "Fractal dimension"
showing 10 items of 78 documents
Reproducibility and accuracy in the morphometric and mechanical quantification of trabecular bone from 3Tesla magnetic resonance images
2014
Abstract Objective We used an animal model to analyze the reproducibility and accuracy of certain biomarkers of bone image quality in comparison to a gold standard of computed microtomography (μCT). Materials and methods We used magnetic resonance (MR) imaging and μCT to study the metaphyses of 5 sheep tibiae. The MR images (3 T) were acquired with a T1-weighted gradient echo sequence and an isotropic spatial resolution of 180 μm. The μCT images were acquired using a scanner with a spatial resolution of 7.5 μm isotropic voxels. In the preparation of the images, we applied equalization, interpolation, and thresholding algorithms. In the quantitative analysis, we calculated the percentage of …
Characterizing cavity-like spaces in active-site models of zeolites
2003
A method for the calculation of fractal surfaces of crystals is presented. The fractal dimension of fragments of zeolites is computed. Results compare well with reference calculations performed with program GEPOL. The active site of Bronsted acid zeolites is modelled by sets of Al–OH–Si units. These units form 2–12-membered rings. Topological indices for the different active-site models are computed. The comparison of calculations performed with programs GEPOL and SURMO2 allows computing the model indices. The cavity-like globularity and rugosity show sharp discontinuities for the ring with 6 units. Most cavity-like spaces show no fractal character. However, the 6–8-ring cavity-like spaces …
Fractal geometry for measuring and modelling urban patterns
2007
Urban growth generates nowadays patterns, which look rather irregular. Planning policy regrets the lack of compactness and density of these agglomerations, but controlling urban sprawl turns out to be difficult. Obviously a new type of spatial organisation emerges, which is rather the result of a self-organisation process to which a high number of social agents contribute. In the present contribution we focus on the use of fractal geometry which turned out to be a powerful instrument for describing the morphology of these patterns. After an introduction about the context of research, fractal models are presented, which serve as reference models for better understanding the spatial organisat…
Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature
2010
By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. F…
Fractal eigenstates in disordered systems
1990
Abstract The wave functions of the non-interacting electrons in disordered systems described by a tight-binding model with site-diagonal disorder are investigated by means of the inverse participation ratio. The wave functions are shown to be fractal objects. In three-dimensional samples, a critical fractal dimension can be defined for the mobility edge in the band centre, which yields the mobility edge trajectory in the whole energy range in good agreement with previous calculations based on the investigation of the exponentially decaying transmission coefficient.
Hybrid approach to surface roughness evaluation in multistage machining processes
2003
Abstract An assessment of surface quality in turned, ground and honed specimens is made by means of a computer-based processing of digitised surface profiles. Three different methods of surface finish characterisation, i.e. statistical, fractal and neural network-based approaches are examined and compared. Correlations between some representative roughness parameters and the fractal dimension (D) values estimated were found. Consequently, they can be converted to their corresponding roughness parameters, i.e. Ra, Rz and RΔa. Finally, a set of parameters including the minimum surface finish data for machining of external cylindrical surfaces when using complex technological process, is propo…
Vectorized ‘‘TOPO’’ Program for the Theoretical Simulation of Molecular Shape
1991
The TOPO program for theoretical simulation of molecular shape is presented here. Molecular shape is characterized by a set of electrostatic and geometrical descriptors and topological indices including the fractal dimension of the accessible surface. An atom-atom analysis of all descriptors has been implemented. The program has been adapted for the realization of high-performance computing. Results are reported for porphine and phthalocyanine molecules.
Application of fractal geometry to dissolution kinetic study of a sweetener excipient
2001
Abstract In the context of relationship study between dissolution kinetic and particle morphology using the fractal geometry tool, we use a commercially available quality of saccharin powder. The characterization of molecular feature and image analysis study allows us to conclude to the statistic self-similarity of particles of four sieved particles size fractions, permitting the fractal approach. Calculation of reactive fractal dimension is performed using two forms of mass transfer equation: −d Q /d t = kQ D R /3 Δ C and −d Q /d t = k′R D R −3 Δ C , with Δ C ={ C f /[ln C s /( C s − C f )]}. Based on comparison of the surface fractal dimension D S on the two values of reactive fractal di…
Canopy Architecture Appraisal by Fractal Dimension of 'Flordastar' Peach Trees Grafted onto Different Rootstocks
2007
The objective of this research was to evaluate the modification of canopy architecture of ''Flordastar'' peach (Prunus persica L. Batsch) grafted onto rootstocks with different vigour, by the use of fractal dimension (D). The hypothesis was that different vigour rootstocks are able to modify the complexity of the branching pattern and that this effect can be assessed by a geometric parameter such as the fractal dimension (D) of the 2D projection of tree branching structure. The observations were carried out in a four-year-old experimental orchard of cv. ''Flordastar'' peach trees grafted onto Ishtara, Barrier, GF677 and MrS 2/5 rootstocks. On digital pictures of leafless, dormant peach tree…
Fractal approach in petrology: Small-angle neutron scattering experiments with volcanic rocks.
1988
Following Mandelbrot's pioneering work in 1977, we attempt to use the concept of fractal dimension in petrology. Fractal dimension is an intensive property of matter which offers a quantitative measure of the degree of surface roughness. Neutron scattering experiments have been performed on 18 volcanic rocks from different localities. The scattered intensity as a function of the momentum transfer obeys a power law whose exponent varies, for the rock samples presented, between -3 and -4. We conclude that, at the molecular level, our volcanic rocks are not fractal volumes. With regard to the particle-matrix interface, it is not possible to provide a determination at the present stage of resea…