1,742 research outputs found

    Growth Models and Models of Turbulence : A Stochastic Quantization Perspective

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    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

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    Nonextensive statistics, characterized by a nonextensive parameter qq, 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 qq increases, and the result converges to Benford's law exactly as qq 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

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    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 y2=f(x)y^2 = f(x) with genus gg.Comment: AMS-Tex, 14 page

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

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    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

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    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)P(s) and the spectral rigidity Δ3(L)\Delta_3(L) do not follow Poisson statistics. In particular, P(s)P(s) shows a sharp peak at s=1s=1 while Δ3(L)\Delta_3(L) for small values of LL 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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