Analysis of Velocity Derivatives in Turbulence based on Generalized Statistics

A theoretical formula for the probability density function (PDF) of velocity derivatives in a fully developed turbulent flow is derived with the multifractal aspect based on the generalized measures of entropy, i.e., the extensive Renyi entropy or the non-extensive Tsallis entropy, and is used, successfully, to analyze the PDF's observed in the direct numerical simulation (DNS) conducted by Gotoh et al.. The minimum length scale r_d/eta in the longitudinal (transverse) inertial range of the DNS is estimated to be r_d^L/eta = 1.716 (r_d^T/eta = 2.180) in the unit of the Kolmogorov scale eta.Comment: 6 pages, 1 figur

Analysis of Velocity Fluctuation in Turbulence based on Generalized Statistics

The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity fluctuations. These formulae are derived by the present authors with the multifractal aspect based on the statistics that are constructed on the generalized measures of entropy, i.e., the extensive R\'{e}nyi's or the non-extensive Tsallis' entropy. It is revealed that there exist two scaling regions separated by a crossover length, i.e., a definite length approximately of the order of the Taylor microscale. It indicates that the multifractal distribution of singularities in velocity gradient in turbulent flow is robust enough to produce scaling behaviors even for the phenomena out side the inertial range.Comment: 10 Pages, 5 figure

Finite-temperature form factors in the free Majorana theory

We study the large distance expansion of correlation functions in the free massive Majorana theory at finite temperature, alias the Ising field theory at zero magnetic field on a cylinder. We develop a method that mimics the spectral decomposition, or form factor expansion, of zero-temperature correlation functions, introducing the concept of "finite-temperature form factors". Our techniques are different from those of previous attempts in this subject. We show that an appropriate analytical continuation of finite-temperature form factors gives form factors in the quantization scheme on the circle. We show that finite-temperature form factor expansions are able to reproduce expansions in form factors on the circle. We calculate finite-temperature form factors of non-interacting fields (fields that are local with respect to the fundamental fermion field). We observe that they are given by a mixing of their zero-temperature form factors and of those of other fields of lower scaling dimension. We then calculate finite-temperature form factors of order and disorder fields. For this purpose, we derive the Riemann-Hilbert problem that completely specifies the set of finite-temperature form factors of general twist fields (order and disorder fields and their descendants). This Riemann-Hilbert problem is different from the zero-temperature one, and so are its solutions. Our results agree with the known form factors on the circle of order and disorder fields.Comment: 40 pp.; v2: 42 pp., refs and acknowledgment added, typos corrected, description of general matrix elements corrected and extended; v3: 47 pp., appendix adde

Metastability, negative specific heat and weak mixing in classical long-range many-rotator system

We perform a molecular dynamical study of the isolated $d=1$ classical Hamiltonian ${\cal H} = {1/2} \sum_{i=1}^N L_i^2 + \sum_{i \ne j} \frac{1-cos(\theta_i-\theta_j)}{r_{ij}^\alpha} ;(\alpha \ge 0)$, known to exhibit a second order phase transition, being disordered for $u \equiv U/N{\tilde N} \ge u_c(\alpha,d)$ and ordered otherwise ($U\equiv$ total energy and ${\tilde N} \equiv \frac{N^{1-\alpha/d}-\alpha/d}{1-\alpha/d}$). We focus on the nonextensive case $\alpha/d \le 1$ and observe that, for $u<u_c$, a basin of attraction exists for the initial conditions for which the system quickly relaxes onto a longstanding metastable state (whose duration presumably diverges with $N$ like ${\tilde N}$) which eventually crosses over to the microcanonical Boltzmann-Gibbs stable state. The temperature associated with the (scaled) average kinetic energy per particle is lower in the metastable state than in the stable one. It is exhibited for the first time that the appropriately scaled maximal Lyapunov exponent $\lambda_{u<u_c}^{max}(metastable) \propto N^{-\kappa_{metastable}} ;(N \to \infty)$, where, for all values of $\alpha/d$, $\kappa_{metastable}$ numerically coincides with {\it one third} of its value for $u>u_c$, hence decreases from 1/9 to zero when $\alpha/d$ increases from zero to unity, remaining zero thereafter. This new and simple {\it connection between anomalies above and below the critical point} reinforces the nonextensive universality scenario.Comment: 9 pages and 4 PS figure

Pure Stationary States of Open Quantum Systems

Using Liouville space and superoperator formalism we consider pure stationary states of open and dissipative quantum systems. We discuss stationary states of open quantum systems, which coincide with stationary states of closed quantum systems. Open quantum systems with pure stationary states of linear oscillator are suggested. We consider stationary states for the Lindblad equation. We discuss bifurcations of pure stationary states for open quantum systems which are quantum analogs of classical dynamical bifurcations.Comment: 7p., REVTeX

Joint spatiotemporal models to predict seabird densities at sea

Introduction: Seabirds are abundant, conspicuous members of marine ecosystems worldwide. Synthesis of distribution data compiled over time is required to address regional management issues and understand ecosystem change. Major challenges when estimating seabird densities at sea arise from variability in dispersion of the birds, sampling effort over time and space, and differences in bird detection rates associated with survey vessel type. Methods: Using a novel approach for modeling seabirds at sea, we applied joint dynamic species distribution models (JDSDM) with a vector-autoregressive spatiotemporal framework to survey data collected over nearly five decades and archived in the North Pacific Pelagic Seabird Database. We produced monthly gridded density predictions and abundance estimates for 8 species groups (77% of all birds observed) within Cook Inlet, Alaska. JDSDMs included habitat covariates to inform density predictions in unsampled areas and accounted for changes in observed densities due to differing survey methods and decadal-scale variation in ocean conditions. Results: The best fit model provided a high level of explanatory power (86% of deviance explained). Abundance estimates were reasonably precise, and consistent with limited historical studies. Modeled densities identified seasonal variability in abundance with peak numbers of all species groups in July or August. Seabirds were largely absent from the study region in either fall (e.g., murrelets) or spring (e.g., puffins) months, or both periods (shearwaters). Discussion: Our results indicated that pelagic shearwaters (Ardenna spp.) and tufted puffin (Fratercula cirrhata) have declined over the past four decades and these taxa warrant further investigation into underlying mechanisms explaining these trends. JDSDMs provide a useful tool to estimate seabird distribution and seasonal trends that will facilitate risk assessments and planning in areas affected by human activities such as oil and gas development, shipping, and offshore wind and renewable energy

Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

We consider nonequilibrium probabilistic dynamics in logistic-like maps $x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W>>1$ intervals partitioning the phase space and focus on the unique value $q_{sen}<1$ for which the entropic form $S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like $t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.Comment: Final version with new Title and small modifications. REVTeX, 8 pages and 4 eps figure

Acceleration and vortex filaments in turbulence

We report recent results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present some results concerning acceleration statistics and the statistics of trapping by vortex filaments.Comment: 10 pages, 5 figure

From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states

The self-consistent propagation of generalized $D_{1}$ [coherent-product] states and of a class of gaussian density matrix generalizations is examined, at both zero and finite-temperature, for arbitrary interactions between the localized lattice (electronic or vibronic) excitations and the phonon modes. It is shown that in all legitimate cases, the evolution of $D_{1}$ states reduces to the disentangled evolution of the component $D_{2}$ states. The self-consistency conditions for the latter amount to conditions for decoherence-free propagation, which complement the $D_{2}$ Davydov soliton equations in such a way as to lift the nonlinearity of the evolution for the on-site degrees of freedom. Although it cannot support Davydov solitons, the coherent-product ansatz does provide a wide class of exact density-matrix solutions for the joint evolution of the lattice and phonon bath in compatible systems. Included are solutions for initial states given as a product of a [largely arbitrary] lattice state and a thermal equilibrium state of the phonons. It is also shown that external pumping can produce self-consistent Frohlich-like effects. A few sample cases of coherent, albeit not solitonic, propagation are briefly discussed.Comment: revtex3, latex2e; 22 pages, no figs.; to appear in Phys.Rev.E (Nov.2001

Self-energy-part resummed quark and gluon propagators in a spin-polarized quark matter and generalized Boltzmann equations

We construct perturbative frameworks for studying nonequilibrium spin-polarized quark matter. We employ the closed-time-path formalism and use the gradient approximation in the derivative expansion. After constructing self-energy-part resummed quark and gluon propagators, we formulate two kind of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the initial-particle distribution function, and the second one is formulated on the basis of `` physical''-particle distribution function. In the course of construction of the second framework, the generalized Boltzmann equations and their relatives {\em directly} come out, which describe the evolution of the system. The frameworks are relevant to the study of a magnetic character of quark matters, e.g., possible quark stars.Comment: 57 page