275 research outputs found
Multifractal PDF analysis for intermittent systems
The formula for probability density functions (PDFs) has been extended to
include PDF for energy dissipation rates in addition to other PDFs such as for
velocity fluctuations, velocity derivatives, fluid particle accelerations,
energy transfer rates, etc, and it is shown that the formula actually explains
various PDFs extracted from direct numerical simulations and experiments
performed in a wind tunnel. It is also shown that the formula with appropriate
zooming increment corresponding to experimental situation gives a new route to
obtain the scaling exponents of velocity structure function, including
intermittency exponent, out of PDFs of velocity fluctuations.Comment: 10 pages, 5 figure
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
Quantum Stochastic Differential Equations in View of Non-Equlibrium Thermo Field Dynamics
Most of the mathematical approaches for quantum Langevin equation are based
on the non-commutativity of the random force operators. Non-commutative random
force operators are introduced in order to guarantee that the equal-time
commutation relation for the stochastic annihilation and creation operators
preserves in time. If it is true, it means that the origin of dissipation is of
quantum mechanical. However, physically, it is hard to believe it. By making
use of the unified canonical operator formalism for the system of the quantum
stochastic differential equations within Non-Equilibrium Thermo Field Dynamics,
it is shown that it is not true in general.Comment: 14 page
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
Quantum stochastic differential equations for boson and fermion systems -- Method of Non-Equilibrium Thermo Field Dynamics
A unified canonical operator formalism for quantum stochastic differential
equations, including the quantum stochastic Liouville equation and the quantum
Langevin equation both of the It\^o and the Stratonovich types, is presented
within the framework of Non-Equilibrium Thermo Field Dynamics (NETFD). It is
performed by introducing an appropriate martingale operator in the
Schr\"odinger and the Heisenberg representations with fermionic and bosonic
Brownian motions. In order to decide the double tilde conjugation rule and the
thermal state conditions for fermions, a generalization of the system
consisting of a vector field and Faddeev-Popov ghosts to dissipative open
situations is carried out within NETFD.Comment: 69 page
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