3,814 research outputs found
Contour lines of the discrete scale invariant rough surfaces
We study the fractal properties of the 2d discrete scale invariant (DSI)
rough surfaces. The contour lines of these rough surfaces show clear DSI. In
the appropriate limit the DSI surfaces converge to the scale invariant rough
surfaces. The fractal properties of the 2d DSI rough surfaces apart from
possessing the discrete scale invariance property follow the properties of the
contour lines of the corresponding scale invariant rough surfaces. We check
this hypothesis by calculating numerous fractal exponents of the contour lines
by using numerical calculations. Apart from calculating the known scaling
exponents some other new fractal exponents are also calculated.Comment: 9 Pages, 12 figure
Thermodynamic interpretation of the uniformity of the phase space probability measure
Uniformity of the probability measure of phase space is considered in the
framework of classical equilibrium thermodynamics. For the canonical and the
grand canonical ensembles, relations are given between the phase space
uniformities and thermodynamic potentials, their fluctuations and correlations.
For the binary system in the vicinity of the critical point the uniformity is
interpreted in terms of temperature dependent rates of phases of well defined
uniformities. Examples of a liquid-gas system and the mass spectrum of nuclear
fragments are presented.Comment: 11 pages, 2 figure
Zipf's law in Nuclear Multifragmentation and Percolation Theory
We investigate the average sizes of the largest fragments in nuclear
multifragmentation events near the critical point of the nuclear matter phase
diagram. We perform analytic calculations employing Poisson statistics as well
as Monte Carlo simulations of the percolation type. We find that previous
claims of manifestations of Zipf's Law in the rank-ordered fragment size
distributions are not born out in our result, neither in finite nor infinite
systems. Instead, we find that Zipf-Mandelbrot distributions are needed to
describe the results, and we show how one can derive them in the infinite size
limit. However, we agree with previous authors that the investigation of
rank-ordered fragment size distributions is an alternative way to look for the
critical point in the nuclear matter diagram.Comment: 8 pages, 11 figures, submitted to PR
Wealth Condensation in Pareto Macro-Economies
We discuss a Pareto macro-economy (a) in a closed system with fixed total
wealth and (b) in an open system with average mean wealth and compare our
results to a similar analysis in a super-open system (c) with unbounded wealth.
Wealth condensation takes place in the social phase for closed and open
economies, while it occurs in the liberal phase for super-open economies. In
the first two cases, the condensation is related to a mechanism known from the
balls-in-boxes model, while in the last case to the non-integrable tails of the
Pareto distribution. For a closed macro-economy in the social phase, we point
to the emergence of a ``corruption'' phenomenon: a sizeable fraction of the
total wealth is always amassed by a single individual.Comment: 4 pages, 1 figur
Extreme values and fat tails of multifractal fluctuations
In this paper we discuss the problem of the estimation of extreme event
occurrence probability for data drawn from some multifractal process. We also
study the heavy (power-law) tail behavior of probability density function
associated with such data. We show that because of strong correlations,
standard extreme value approach is not valid and classical tail exponent
estimators should be interpreted cautiously. Extreme statistics associated with
multifractal random processes turn out to be characterized by non
self-averaging properties. Our considerations rely upon some analogy between
random multiplicative cascades and the physics of disordered systems and also
on recent mathematical results about the so-called multifractal formalism.
Applied to financial time series, our findings allow us to propose an unified
framemork that accounts for the observed multiscaling properties of return
fluctuations, the volatility clustering phenomenon and the observed ``inverse
cubic law'' of the return pdf tails
How fundamental is the character of thermal uncertainty relations?
We show that thermodynamic uncertainties do not preserve their form if the
underlying probability distribution is transformed into an escort one.
Heisenberg's relations, on the other hand, are not affected by such
transformation. We conclude therefore that the former uncertainty cannot be as
fundamental as the quantum one.Comment: 4 pages, no figure
Hurst Coefficient in long time series of population size: Model for two plant populations with different reproductive strategies
Can the fractal dimension of fluctuations in population size be used to estimate extinction risk? The problem with estimating this fractal dimension is that the lengths of the time series are usually too short for conclusive results. This study answered this question with long time series data obtained from an iterative competition model. This model produces competitive extinction at different perturbation intensities for two different germination strategies: germination of all seeds vs. dormancy in half the seeds. This provided long time series of 900 years and different extinction risks. The results support the hypothesis for the effectiveness of the Hurst coefficient for estimating extinction risk
spectra in elementary cellular automata and fractal signals
We systematically compute the power spectra of the one-dimensional elementary
cellular automata introduced by Wolfram. On the one hand our analysis reveals
that one automaton displays spectra though considered as trivial, and on
the other hand that various automata classified as chaotic/complex display no
spectra. We model the results generalizing the recently investigated
Sierpinski signal to a class of fractal signals that are tailored to produce
spectra. From the widespread occurrence of (elementary) cellular
automata patterns in chemistry, physics and computer sciences, there are
various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included
Fractal geometry of critical Potts clusters
Numerical simulations on the total mass, the numbers of bonds on the hull,
external perimeter, singly connected bonds and gates into large fjords of the
Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at
criticality are presented. The data are found consistent with the recently
derived corrections-to-scaling theory. However, the approach to the asymptotic
region is slow, and the present range of the data does not allow a unique
identification of the exact correction exponentsComment: 7 pages, 8 figures, Late
Punctuation effects in English and Esperanto texts
A statistical physics study of punctuation effects on sentence lengths is
presented for written texts: {\it Alice in wonderland} and {\it Through a
looking glass}. The translation of the first text into esperanto is also
considered as a test for the role of punctuation in defining a style, and for
contrasting natural and artificial, but written, languages. Several log-log
plots of the sentence length-rank relationship are presented for the major
punctuation marks. Different power laws are observed with characteristic
exponents. The exponent can take a value much less than unity ( 0.50 or
0.30) depending on how a sentence is defined. The texts are also mapped into
time series based on the word frequencies. The quantitative differences between
the original and translated texts are very minutes, at the exponent level. It
is argued that sentences seem to be more reliable than word distributions in
discussing an author style.Comment: 13 pages, 7 figures (3x2+1), 60 reference
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