1,742 research outputs found

### Growth Models and Models of Turbulence : A Stochastic Quantization Perspective

We consider a class of growth models and models of turbulence based on the
randomly stirred fluid. The similarity between the predictions of these models,
noted a decade earlier, is understood on the basis of a stochastic quantization
scheme.Comment: 3 page

### First-Digit Law in Nonextensive Statistics

Nonextensive statistics, characterized by a nonextensive parameter $q$, is a
promising and practically useful generalization of the Boltzmann statistics to
describe power-law behaviors from physical and social observations. We here
explore the unevenness of the first digit distribution of nonextensive
statistics analytically and numerically. We find that the first-digit
distribution follows Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the temperature. The fluctuation
decreases when $q$ increases, and the result converges to Benford's law exactly
as $q$ approaches 2. The relevant regularities between nonextensive statistics
and Benford's law are also presented and discussed.Comment: 11 pages, 3 figures, published in Phys. Rev.

### Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica

In the previous work (J. Geom. Phys. {\bf{39}} (2001) 50-61), the closed loop
solitons in a plane, \it i.e., loops whose curvatures obey the modified
Korteweg-de Vries equations, were investigated for the case related to
algebraic curves with genera one and two. This article is a generalization of
the previous article to those of hyperelliptic curves with general genera. It
was proved that the tangential angle of loop soliton is expressed by the
Weierstrass hyperelliptic al function for a given hyperelliptic curve $y^2 =
f(x)$ with genus $g$.Comment: AMS-Tex, 14 page

### Halo Cores and Phase Space Densities: Observational Constraints on Dark Matter Physics and Structure Formation

We explore observed dynamical trends in a wide range of dark matter dominated
systems (about seven orders of magnitude in mass) to constrain hypothetical
dark matter candidates and scenarios of structure formation. First, we argue
that neither generic warm dark matter (collisionless or collisional) nor
self-interacting dark matter can be responsible for the observed cores on all
scales. Both scenarios predict smaller cores for higher mass systems, in
conflict with observations; some cores must instead have a dynamical origin.
Second, we show that the core phase space densities of dwarf spheroidals,
rotating dwarf and low surface brightness galaxies, and clusters of galaxies
decrease with increasing velocity dispersion like Q ~ sigma^-3 ~ M^-1, as
predicted by a simple scaling argument based on merging equilibrium systems,
over a range of about eight orders of magnitude in Q. We discuss the processes
which set the overall normalization of the observed phase density hierarchy. As
an aside, we note that the observed phase-space scaling behavior and density
profiles of dark matter halos both resemble stellar components in elliptical
galaxies, likely reflecting a similar collisionless, hierarchical origin. Thus,
dark matter halos may suffer from the same systematic departures from homology
as seen in ellipticals, possibly explaining the shallower density profiles
observed in low mass halos. Finally, we use the maximum observed phase space
density in dwarf spheroidal galaxies to fix a minimum mass for relativistically
decoupled warm dark matter candidates of roughly 700 eV for thermal fermions,
and 300 eV for degenerate fermions.Comment: Submitted to the Astrophysical Journal, LaTeX, 26 pages including 4
pages of figure

### Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

The aim of this work is to study the spectral statistics of the asymmetric
rotor model (triaxial rigid rotator). The asymmetric top is classically
integrable and, according to the Berry-Tabor theory, its spectral statistics
should be Poissonian. Surprisingly, our numerical results show that the nearest
neighbor spacing distribution $P(s)$ and the spectral rigidity $\Delta_3(L)$ do
not follow Poisson statistics. In particular, $P(s)$ shows a sharp peak at
$s=1$ while $\Delta_3(L)$ for small values of $L$ follows the Poissonian
predictions and asymptotically it shows large fluctuations around its mean
value. Finally, we analyze the information entropy, which shows a dissolution
of quantum numbers by breaking the axial symmetry of the rigid rotator.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

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