Search results for "FRACTAL"
showing 10 items of 329 documents
SELF SIMILARITY IN SWELLING SYSTEMS: FRACTAL PROPERTIES OF PEAT
1994
Sphagnum peat gives an example of a swelling system with a self-similar structure in sufficiently wide range of scales. The surface fractal dimension, dfs, has been calculated by means of thermodynamic method on the basis of water adsorption and capillary equilibrium measurements. This method makes possible the exploration of the self-similarity in the scale range over at least 4 decimal orders of magnitude from 1 nm to 10 μm. In a sample explored, two ranges of fractality have been observed: dfs ≈ 2.55 in the range 1.5–80 nm and dfs ≈ 2.42 in the range 0.25–9 µm.
The effect of fractal contact lenses on peripheral refraction in myopic model eyes.
2014
Purpose: To test multizone contact lenses in model eyes: Fractal Contact Lenses (FCLs), designed to induce myopic peripheral refractive error (PRE). Methods: Zemax ray-tracing software was employed to simulate myopic and accommodation-dependent model eyes fitted with FCLs. PRE, defined in terms of mean sphere M and 90–180 astigmatism J180, was computed at different peripheral positions, ranging from 0 to 35 in steps of 5, and for different pupil diameters (PDs). Simulated visual performance and changes in the PRE were also analyzed for contact lens decentration and model eye accommodation. For comparison purposes, the same simulations were performed with another commercially available conta…
Renormalization-group analysis for the transition to chaos in Hamiltonian systems
2002
Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…
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 …
Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
2021
In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, fro…
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 …
Is there any scaling in the cluster distribution?
1994
We apply fractal analysis methods to investigate the scaling properties in the Abell and ACO catalogs of rich galaxy clusters. We also discuss different technical aspects of the method when applied to data sets with small number of points as the cluster catalogs. Results are compared with simulations based on the Zel'dovich approximation. We limit our analysis to scales less than 100 $\hm$. The cluster distribution show a scale invariant multifractal behavior in a limited scale range. For the Abell catalog this range is 15--60$\hm$, while for the ACO sample it extends to smaller scales. Despite this difference in the extension of the scale--range where scale--invariant clustering takes plac…
Generación de fractales a partir del método de Newton
2013
[EN] A large number of fractals known, as Julia fractals and Mandelbrot, can be generated from an iterative method. In this paper we present a virtual laboratory developed as a Graphical User Interface (GUI) of Matlab that allows us to study and visualize in real time the relationship between Newton iterative methods of two variables and the generation of fractals. The main objective is to allow Technical School students in Numerical Computation subjects to acquire the skills to generate fractals and interpret their plots in terms of the convergence or divergence speed of the sequence of iterated.
Geometric rigidity of a class of fractal sets
2017
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally spread out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Dimensione frattale in biologia ed in medicina umana.
2009
Nell’organismo umano, esistono fattori che contribuiscono a rendere stabili i suoi sistemi frattali biologici. Nel presente lavoro di anatomia comparata e di fisiologia, illustro alcuni di questi sistemi ad invarianza di scala; descrivo le principali forze che li determinano, li regolano e stabilizzano. Riporto altresì alcune patologie, collegate alle alterazioni della (FD) dimensione frattale. La ricca bibliografia consultata mi ha dato modo di tracciare importanti correlazioni come quello tra due dimensioni frattali: del sistema nervoso centrale e della circolazione sanguigna cerebrale.