Search results for "fractal dimension"
showing 10 items of 78 documents
LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY
2002
We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.
Two-Length-Scale Structure in Some Computer-Generated Aggregates Grown by Diffusion-Limited Aggregation
1994
AbstractThe properties of some aggregates “grown” on a computer by diffusion-limited aggregation have been investigated. Calculations showed that the intensity of the small-angle x-ray and neutron scattering from the aggregates was proportional to q−D for qL ≫ 1, where D > 0, L is a length that characterizes the large-scale structure of the aggregate, q = 4πλ−1 sin(θ/2), γ is the wavelength, and θ is the scattering angle. The magnitude of the exponent D was appreciably smaller than the fractal dimensions that many simulations have shown to be typical of the mass fractal aggregates grown by diffusion-limited aggregation. The calculations suggest that the aggregates have structure on two d…
Diagnostic Performance of Muscle Echo Intensity and Fractal Dimension for the Detection of Frailty Phenotype
2021
To determine the relationship between muscle echo intensity (EI) and fractal dimension (FD), and the diagnostic performance of both ultrasound parameters for the identification of frailty phenotype. A retrospective interpretation of ultrasound scans from a previous cohort (November 2014–February 2015) was performed. The sample included healthy participants <60 years old, and participants ≥60 divided into robust, pre-frail, and frail groups according to Fried frailty criteria. A region of interest of the rectus femoris from the ultrasound scan was segmented, and histogram function was applied to obtain EI. For fractal analysis, images were processed using two-dimensional box-counting techniq…
Fractal analyses reveal independent complexity and predictability of gait
2017
Locomotion is a natural task that has been assessed since decades and used as a proxy to highlight impairments of various origins. Most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular…
Wavelet and fractal approach to surface roughness characterization after finish turning of different workpiece materials
2009
In this paper, the surface profiles generated in longitudinal turning operations were characterized using continuous wavelet transform (CWT) and normalized fractal dimension Dn. In the comparative analysis, some characteristic roughness profiles after the turning of different workpiece materials, such as C45 medium carbon steel, nodular cast iron and hardened (55 HRC) high-strength alloy steel were selected. For wavelet characterization, both Morlet and ‘Mexican hat’ analyzing wavelets, which allow the assessment of extrema and frequency distribution, were utilized. The results of the CWT as a function of profile and momentary wavelet length are presented. It is concluded that CWT can be us…
Fractal dimension of zeolite catalysts
2002
Atom—atom analyses of the geometric descriptors, topological indices and fractal dimension D are applied to active-site models of Br⊘nsted acid zeolites. The results are compared with those from the literature for rings and cavities. A method is tested similar to that used in previous works for crystal fragments. The results obtained are encouraging and the good quality of the analysis is clear from a comparison with cavity results. The active sites are modelled by sets of Al—OH—Si units. These bridges form 2–12 membered rings. Indices for the models are calculated. An analysis shows that the maximal Dsi contribution corresponds to the 6-ring, matching the maximal Dcavity. It is suggested t…
Direct observation of polar nanostructures in PLZT ceramics for electrooptic applications
2004
ABSTRACTTransparent Pb1-yLay(Zr1-xTix)1-y/4O3(PLZT, y=0.0975, x=0.35) ceramics prepared via hot pressing techniques were studied via piezoelectric force microscopy (PFM). Clear piezoelectric contrast is observed in a cubic relaxor phase indicating spatial distribution of polarization with an average cluster size of about 50 nm. The irregular polarization pattern is associated with the formation of a glassy state, where random electric and stress fields are responsible for the disruption of the long-range ferroelectric order. Local poling of the ceramics resulted in the formation of a stable micron-size domain that could be continuously switched under varying dc bias (local hysteresis loop).…
Comparative evaluation of the swelling and degrees of cross-linking in three organic gel packings for SEC through some geometric parameters.
2003
Abstract The size exclusion chromatographic (SEC) behavior of five solvent/polymer systems in three organic column packings based on polystyrene/divinylbenzene (PS/DVB) copolymer, TSK-Gel H HR , μ-styragel and TSK-Gel H XL , has been compared. All the packings offer similar characteristics (pore size, particle size and efficiency) but some differences have been found when eluting the same systems. The different elution behavior observed in both polymeric gels has been analyzed in terms of their swelling and cross-linking degrees and of the fractal parameters. From the Universal Calibration plots, values of the chromatographic partition coefficient, K p , have been obtained and using some eq…
Study of Morphology of Reactive Dissolution Interface Using Fractal Geometry
1996
J. Pharm. Sci. ISI Document Delivery No.: VF662 Times Cited: 7 Cited Reference Count: 15 Tromelin, A Gnanou, JC Andres, C Pourcelot, Y Chaillot, B; International audience; The determination of reactive fractal dimension was carried out using two forms of the Noyes-Whitney equation, -dQ/dt = K(Q/Q(0))(DR/3) and -d Q/dt = K' R(DR-3) using the Richardson plot on the basis of previous data obtained by dissolution of an orthoboric acid powder. The correlation of the results provided by the two ways of calculation allows proposal of the hypothesis that dissolution begins on a specific population of reactive sites and probably promotes the formation of microporous volumes or cracks.
Fractal approach in petrology: combining ultra small angle, small angle and intermediate angle neutron scattering
2000
Ultra small angle neutron scattering (USANS) instruments have recently covered the gap between the size resolution available with conventional intermediate angle neutron scattering and small angle neutron scattering (SANS) instruments on one side and optical microscopy on the other side. New fields of investigations are now open and important areas of material science (ceramics, glass fibers, natural materials) and fundamental physics (phase transition, phase separation and critical phenomena) can be studied in bulk samples with an accuracy previously unobtainable owing to a combination of favourable features of the neutron-matter interaction: high penetrability of neutrons, even cold neutr…