1,167 research outputs found
Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium
Multifractal scaling (MFS) refers to structures that can be described as a
collection of interwoven fractal subsets which exhibit power-law spatial
scaling behavior with a range of scaling exponents (concentration, or
singularity, strengths) and dimensions. The existence of MFS implies an
underlying multiplicative (or hierarchical, or cascade) process. Panoramic
column density images of several nearby star- forming cloud complexes,
constructed from IRAS data and justified in an appendix, are shown to exhibit
such multifractal scaling, which we interpret as indirect but quantitative
evidence for nested hierarchical structure. The relation between the dimensions
of the subsets and their concentration strengths (the "multifractal spectrum'')
appears to satisfactorily order the observed regions in terms of the mixture of
geometries present: strong point-like concentrations, line- like filaments or
fronts, and space-filling diffuse structures. This multifractal spectrum is a
global property of the regions studied, and does not rely on any operational
definition of "clouds.'' The range of forms of the multifractal spectrum among
the regions studied implies that the column density structures do not form a
universality class, in contrast to indications for velocity and passive scalar
fields in incompressible turbulence, providing another indication that the
physics of highly compressible interstellar gas dynamics differs fundamentally
from incompressible turbulence. (Abstract truncated)Comment: 27 pages, (LaTeX), 13 figures, 1 table, submitted to Astrophysical
Journa
Scaling in the Bombay Stock Exchange Index
In this paper we study BSE Index financial time series for fractal and
multifractal behaviour. We show that Bombay stock Exchange (BSE)Index time
series is mono-fractal and can be represented by a fractional Brownian motion.Comment: 11 pages,3 figure
Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension
We study the abelian sandpile model on decorated one dimensional chains. We
determine the structure and the asymptotic form of distribution of
avalanche-sizes in these models, and show that these differ qualitatively from
the behavior on a simple linear chain. We find that the probability
distribution of the total number of topplings on a finite system of size
is not described by a simple finite size scaling form, but by a linear
combination of two simple scaling forms , for large , where and are some scaling functions of
one argument.Comment: 10 pages, revtex, figures include
Multifractal analysis of the metal-insulator transition in anisotropic systems
We study the Anderson model of localization with anisotropic hopping in three
dimensions for weakly coupled chains and weakly coupled planes. The eigenstates
of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes
up to , show multifractal behavior at the metal-insulator transition even
for strong anisotropy. The critical disorder strength determined from the
system size dependence of the singularity spectra is in a reasonable agreement
with a recent study using transfer matrix methods. But the respective spectrum
at deviates from the ``characteristic spectrum'' determined for the
isotropic system. This indicates a quantitative difference of the multifractal
properties of states of the anisotropic as compared to the isotropic system.
Further, we calculate the Kubo conductivity for given anisotropies by exact
diagonalization. Already for small system sizes of only sites we observe
a rapidly decreasing conductivity in the directions with reduced hopping if the
coupling becomes weaker.Comment: 25 RevTeX pages with 10 PS-figures include
Correlation Exponent and Anomalously Localized States at the Critical Point of the Anderson Transition
We study the box-measure correlation function of quantum states at the
Anderson transition point with taking care of anomalously localized states
(ALS). By eliminating ALS from the ensemble of critical wavefunctions, we
confirm, for the first time, the scaling relation z(q)=d+2tau(q)-tau(2q) for a
wide range of q, where q is the order of box-measure moments and z(q) and
tau(q) are the correlation and the mass exponents, respectively. The influence
of ALS to the calculation of z(q) is also discussed.Comment: 6 pages, 3 figure
Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis
We compare different partitioning schemes for the box-counting algorithm in
the multifractal analysis by computing the singularity spectrum and the
distribution of the box probabilities. As model system we use the Anderson
model of localization in two and three dimensions. We show that a partitioning
scheme which includes unrestricted values of the box size and an average over
all box origins leads to smaller error bounds than the standard method using
only integer ratios of the linear system size and the box size which was found
by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most
reliable results.Comment: 10 pages, 13 figure
Flow induced by a sphere settling in an aging yield-stress fluid
We have studied the flow induced by a macroscopic spherical particle settling
in a Laponite suspension that exhibits a yield-stress, thixotropy and
shear-thinning. We show that the fluid thixotropy (or aging) induces an
increase with time of both the apparent yield stress and shear-thinning
properties but also a breaking of the flow fore-aft symmetry predicted in
Hershel-Bulkley fluids (yield-stress, shear-thinning fluids with no
thixotropy). We have also varied the stress exerted by the particles on the
fluid by using particles of different densities. Although the stresses exerted
by the particles are of the same order of magnitude, the velocity field
presents utterly different features: whereas the flow around the lighter
particle shows a confinement similar to the one observed in shear-thinning
fluids, the wake of the heavier particle is characterized by an upward motion
of the fluid ("negative wake"), whatever the fluid's age. We compare the
features of this negative wake to the one observed in viscoelastic
shear-thinning fluids (polymeric or micelle solutions). Although the flows
around the two particles strongly differ, their settling behaviors display no
apparent difference which constitutes an intriguing result and evidences the
complexity of the dependence of the drag factor on flow field
Multifractality of the quantum Hall wave functions in higher Landau levels
To probe the universality class of the quantum Hall system at the
metal-insulator critical point, the multifractality of the wave function
is studied for higher Landau levels, , for various range of
random potential. We have found that, while the multifractal spectrum
(and consequently the fractal dimension) does vary with , the
parabolic form for indicative of a log-normal distribution of
persists in higher Landau levels. If we relate the multifractality with
the scaling of localization via the conformal theory, an asymptotic recovery of
the single-parameter scaling with increasing is seen, in agreement
with Huckestein's irrelevant scaling field argument.Comment: 10 pages, revtex, 5 figures available on request from
[email protected]
Multifractality of Drop Breakup in Air-blast Nozzle Atomization Process
The multifractal nature of drop breakup in air-blast nozzle atomization
process has been studied. We apply the multiplier method to extract the
negative and the positive parts of the f(alpha) curve with the data of drop
size distribution measured using Dual PDA. A random multifractal model with the
multiplier triangularly distributed is proposed to characterize the breakup of
drops. The agreement of the left part of the multifractal spectra between the
experimental result and the model is remarkable. The cause of the distinction
of the right part of the f(alpha) curve is argued. The fact that negative
dimensions arise in the current system means that the spatial distribution of
the drops yielded by the high-speed jet fluctuates from sample to sample. On
other words, the spatial concentration distribution of the disperse phase in
the spray zone fluctuates momentarily showing intrinsic randomness
Self-Organized States in Cellular Automata: Exact Solution
The spatial structure, fluctuations as well as all state probabilities of
self-organized (steady) states of cellular automata can be found (almost)
exactly and {\em explicitly} from their Markovian dynamics. The method is shown
on an example of a natural sand pile model with a gradient threshold.Comment: 4 pages (REVTeX), incl. 2 figures (PostScript
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