185 research outputs found
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
On observability of Renyi's entropy
Despite recent claims we argue that Renyi's entropy is an observable
quantity. It is shown that, contrary to popular belief, the reported domain of
instability for Renyi entropies has zero measure (Bhattacharyya measure). In
addition, we show the instabilities can be easily emended by introducing a
coarse graining into an actual measurement. We also clear up doubts regarding
the observability of Renyi's entropy in (multi--)fractal systems and in systems
with absolutely continuous PDF's.Comment: 18 pages, 1 EPS figure, REVTeX, minor changes, accepted to Phys. Rev.
Diagonalization of full finite temperature Green's function by quasi-particles
For thermal systems, standard perturbation theory breaks down because of the
absence of stable, observable asymptotic states. We show, how the introduction
of {\it statistical} quasi-particles (stable, but not observable) gives rise to
a consistent description. Statistical and spectral information can be cleanly
separated also for interacting systems.Comment: 9 pages in standard LaTe
Scaling, self-similar solutions and shock waves for V-shaped field potentials
We investigate a (1+1)-dimensional nonlinear field theoretic model with the
field potential It can be obtained as the universal small
amplitude limit in a class of models with potentials which are symmetrically
V-shaped at their minima, or as a continuum limit of certain mechanical system
with infinite number of degrees of freedom. The model has an interesting
scaling symmetry of the 'on shell' type. We find self-similar as well as shock
wave solutions of the field equation in that model.Comment: Two comments and one reference adde
The Delta-Hole model at Finite Temperature
The spectral function of pions interacting with a gas of nucleons and
Delta-33-resonances is investigated using the formalism of Thermo Field
Dynamics. After a discussion of the zero Delta-width approximation at finite
temperature, we take into account a constant width of the resonance. Apart from
a full numerical calculation, we give analytical approximations to the pionic
spectral function including such a width. They are found to be different from
previous approximations, and require an increase of the effective Delta-width
in hot compressed nuclear matter. The results are summarized in an effective
dispersion relation for interacting pions.Comment: 34 pages in standard LaTeX GSI-preprint No. GSI-93-2
Numerical simulation of river channel processes with bank erosion in steep curved channel
River morphodynamics and sediment transportRiver morphology and morphodynamic
Generalizations of the thermal Bogoliubov transformation
The thermal Bogoliubov transformation in thermo field dynamics is generalized
in two respects. First, a generalization of the --degree of freedom to
tilde non--conserving representations is considered. Secondly, the usual
Bogoliubov matrix is extended to a matrix including
mixing of modes with non--trivial multiparticle correlations. The analysis is
carried out for both bosons and fermions.Comment: 20 pages, Latex, Nordita 93/33
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
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
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