Search results for "Fractal"
showing 10 items of 329 documents
Scaling laws in the distribution of galaxies
2004
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale distribution of galaxies in the Universe is far from random: it is highly structured over a vast range of scales. To describe cosmic structures, we need to build mathematically quantifiable descriptions of structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters, superclusters of galaxies and the voids between them. Find…
Is the Universe Fractal?
1999
One of the key issues in cosmology is the question of whether the universe is smooth or fractal at large dimensions. The answer has a bearing on the big bang model of the origin of the universe. MartAnez discusses why recent analyses have come to opposing conclusions regarding this question and looks at how good a case can be made for large-scale smoothness of the universe.
A discrimination technique for extensive air showers based on multiscale, lacunarity and neural network analysis
2011
We present a new method for the identification of extensive air showers initiated by different primaries. The method uses the multiscale concept and is based on the analysis of multifractal behaviour and lacunarity of secondary particle distributions together with a properly designed and trained artificial neural network. In the present work the method is discussed and applied to a set of fully simulated vertical showers, in the experimental framework of ARGO-YBJ, to obtain hadron to gamma primary separation. We show that the presented approach gives very good results, leading, in the 1–10 TeV energy range, to a clear improvement of the discrimination power with respect to the existing figu…
WAVELET ANALYSIS OF THE MULTIFRACTAL CHARACTER OF THE GALAXY DISTRIBUTION
1993
We have determined generalized dimensions of the observed distribution of galaxies. Their different values indicate that this distribution may be described as a multifractal. In order to analyse this distribution further, we have applied local wavelet transforms. Wavelets provide us with an interesting tool to analyse the large-scale structure which can be mathematically quantified and intuitively visualized. Comparing the results of these transforms at different dilation factors helps to visualize more clearly the nearly singular nature of the distribution. This method also allows us to determine the range of the local density power laws
Multifractal fits to the observed main belt asteroid distribution
2002
Dohnanyi's (1969) theory predicts that a collisional system such as the asteroidal population of the main belt should rapidly relax to a power-law stationary size distribution of the kind $N(m)\propto m^{-\alpha}$, with $\alpha$ very close to 11/6, provided all the collisional response parameters are independent on size. The actual asteroid belt distribution at observable sizes, instead, does not exhibit such a simple fractal size distribution. We investigate in this work the possibility that the corresponding cumulative distribution may be instead fairly fitted by multifractal distributions. This multifractal behavior, in contrast with the Dohnany fractal distribution, is related to the re…
Non-equilibrium temperature of well-developed quantum turbulence
2009
Abstract A non-equilibrium effective temperature of quantum vortex tangles is defined as the average energy of closed vortex loops. The resulting thermodynamic expressions for the entropy and the energy in terms of the temperature of the tangle are confirmed by a microscopic analysis based on a potential distribution function for the length of vortex loops. Furthermore, these expressions for the entropy and energy in terms of temperature are analogous to those of black holes: this may be of interest for establishing further connections between topological defects in superfluids and cosmology.
Fractal dimension of superfluid turbulence : A random-walk toy model
2021
This paper deals with the fractal dimension of a superfluid vortex tangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf 43}, 205501 (2010)] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite temperature. This random walk model combines a recent Nemirovskii's proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent pr…
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Acoustic dynamics of network-forming glasses at mesoscopic wavelengths
2013
The lack of long-range structural order in amorphous solids induces well known thermodynamic anomalies, which are the manifestation of distinct peculiarities in the vibrational spectrum. Although the impact of such anomalies vanishes in the long wavelength, elastic continuum limit, it dominates at length scales comparable to interatomic distances, implying an intermediate transition regime still poorly understood. Here we report a study of such mesoscopic domains by means of a broadband version of picosecond photo-acoustics, developed to coherently generate and detect hypersonic sound waves in the sub-THz region with unprecedented sampling efficiency. We identify a temperature-dependent fra…
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
2006
We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.