Search results for "Fractal"
showing 10 items of 329 documents
Axial behaviour of Cantor ring diffractals
2003
Cantor ring diffractals describe rotationally symmetric pupils constructed from a one-dimensional polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors of such pupils, including fractal dimension, number of gaps and lacunarity, are investigated. It is shown that, contrary to their transversal response, the axial behaviour of these pupils does not resemble the fractal structure of the aperture. The sensitivity of such pupils to the spherical aberration is also analysed.
On the Multifractal Character of the Lorenz Attractor
1992
A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character
Does the galaxy correlation length increase with the sample depth?
2001
We have analyzed the behavior of the correlation length, $r_0$, as a function of the sample depth by extracting from the CfA2 redshift survey volume--limited samples out to increasing distances. For a fractal distribution, the value of $r_0$ would increase with the volume occupied by the sample. We find no linear increase for the CfA2 samples of the sort that would be expected if the Universe preserved its small scale fractal character out to the distances considered (60--100$\hmpc$). The results instead show a roughly constant value for $r_0$ as a function of the size of the sample, with small fluctuations due to local inhomogeneities and luminosity segregation. Thus the fractal picture ca…
Fractals and multifractals in the description of the cosmic structure
1990
Abstract The concepts of fractals and multifractals are applied to describe the large scale galaxy distribution. It is shown how the Universe fits the fractal geometry on small scales (several Mpc), but that there exists some cut-off where the scale invariance is broken. Even in the scaling region the cosmic structure is not a simple fractal, and the task is to introduce more complex and complete clustering descriptors. At this stage, the concept of multifractals appears to be more efficient to describe the texture of the Universe.
A transfer matrix method for the analysis of fractal quantum potentials
2005
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential.
Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization
1996
The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.
Influencia del modelo de ojo teórico en la evaluación numérica de lentes intraoculares fractales
2020
In this work we present the numerical evaluation of a new design of fractal intraocular lens studied through a ray-tracing program. To determine the monochromatic and polychromatic performance of these lenses in different theoretical model eyes the Modulation Transfer Function (MTF) and the area above the MTF (AMTF) have been used. These merit functions show the same behavior for different values of asphericity (Q), independently from the theoretical model eye, even though there are differences due to the Spherical Aberration (SA) considered in each model.
Surface tension and interfacial fluctuations in d-dimensional Ising model
2005
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…
Fragmentation of fractal random structures.
2014
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.
MULTIFRACTAL ELECTRONIC WAVE FUNCTIONS IN THE ANDERSON MODEL OF LOCALIZATION
1992
Investigations of the multifractal properties of electronic wave functions in disordered samples are reviewed. The characteristic mass exponents of the multifractal measure, the generalized dimensions and the singularity spectra are discussed for typical cases. New results for large 3D systems are reported, suggesting that the multifractal properties at the mobility edge which separates localized and extended states are independent of the microscopic details of the model.