12,109 research outputs found
Incompressible Turbulence as Nonlocal Field Theory
It is well known that incompressible turbulence is nonlocal in real space
because sound speed is infinite in incompressible fluids. The equation in
Fourier space indicates that it is nonlocal in Fourier space as well. Contrast
this with Burgers equation which is local in real space. Note that the sound
speed in Burgers equation is zero. In our presentation we will contrast these
two equations using nonlocal field theory. Energy spectrum and renormalized
parameters will be discussed.Comment: 7 pages; Talk presented in Conference on "Perspectives in Nonlinear
Dynamics (PNLD 2004)" held in Chennai, 200
Field theoretic calculation of scalar turbulence
The cascade rate of passive scalar and Bachelor's constant in scalar
turbulence are calculated using the flux formula. This calculation is done to
first order in perturbation series. Batchelor's constant in three dimension is
found to be approximately 1.25. In higher dimension, the constant increases as
.Comment: RevTex4, publ. in Int. J. Mod. Phy. B, v.15, p.3419, 200
Quantum mechanical study of molecules - Eigenvalues and eigenvectors of real symmetric matrices
Computer methods for calculating eigenvalue and eigenvectors of real symmetric matrices arising in problems of molecular quantum mechanic
Dynamic Response of Forced Convective Heat Transfer from Cylinders to Low Prandtl Number Fluids
The present paper can be viewed as an extension of the work of Lim and Sleicher (9). They evaluated the frequency response of the heated element submerged in liquid metal by a perturbation method for Peclet numbers of up to 0.4. Velocity fluctuations were assumed small and second-order perturbations neglected. The Oseen approximation was made to the velocity field. Here the velocity configuration has been approximated to that of potential flow and the convection equation has been solved numerically with the aid of a digital computer. The potential flow approximation, as compared with the Oseen approximation, is reasonable over a larger range of Peclet numbers. Also, our scheme is valid for large amplitudes of fluctuation.
The heat response has been studied under sinusoidal variation in the free stream velocity at frequencies ranging from 1 Hz to 100 kHz for Peclet numbers of up to 1.0. The amplitude of fluctuation was 20% of the mean free-stream velocity. The Nusselt number was found to lag behind the velocity variations and the amount of lag increases with frequency and decreases as the Peclet number is increased. The amplitude of fluctuation of Nusselt number is attenuated as the frequency is increased. The attenuation is 10% at a frequency roughly given by: [formula].
Experimental studies to verify the calculated lag and attenuation effects are in progress
Energy fluxes in helical magnetohydrodynamics and dynamo action
Renormalized viscosity, renormalized resistivity, and various energy fluxes
are calculated for helical magnetohydrodynamics using perturbative field
theory. The calculation is to first-order in perturbation. Kinetic and magnetic
helicities do not affect the renormalized parameters, but they induce an
inverse cascade of magnetic energy. The sources for the the large-scale
magnetic field have been shown to be (1) energy flux from large-scale velocity
field to large-scale magnetic field arising due to nonhelical interactions, and
(2) inverse energy flux of magnetic energy caused by helical interactions.
Based on our flux results, a premitive model for galactic dynamo has been
constructed. Our calculations yields dynamo time-scale for a typical galaxy to
be of the order of years. Our field-theoretic calculations also reveal
that the flux of magnetic helicity is backward, consistent with the earlier
observations based on absolute equilibrium theory.Comment: REVTEX4; A factor of 2 corrected in helicit
Interval structure of the Pieri formula for Grothendieck polynomials
We give a combinatorial interpretation of a Pieri formula for double
Grothendieck polynomials in terms of an interval of the Bruhat order. Another
description had been given by Lenart and Postnikov in terms of chain
enumerations. We use Lascoux's interpretation of a product of Grothendieck
polynomials as a product of two kinds of generators of the 0-Hecke algebra, or
sorting operators. In this way we obtain a direct proof of the result of Lenart
and Postnikov and then prove that the set of permutations occuring in the
result is actually an interval of the Bruhat order.Comment: 27 page
Large-Eddy Simulations of Fluid and Magnetohydrodynamic Turbulence Using Renormalized Parameters
In this paper a procedure for large-eddy simulation (LES) has been devised
for fluid and magnetohydrodynamic turbulence in Fourier space using the
renormalized parameters. The parameters calculated using field theory have been
taken from recent papers by Verma [Phys. Rev. E, 2001; Phys. Plasmas, 2001]. We
have carried out LES on grid. These results match quite well with direct
numerical simulations of . We show that proper choice of parameter is
necessary in LES.Comment: 12 pages, 4 figures: Proper figures inserte
Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence
In this paper we analytically compute the strength of nonlinear interactions
in a triad, and the energy exchanges between wavenumber shells in
incompressible fluid turbulence. The computation has been done using
first-order perturbative field theory. In three dimension, magnitude of triad
interactions is large for nonlocal triads, and small for local triads. However,
the shell-to-shell energy transfer rate is found to be local and forward. This
result is due to the fact that the nonlocal triads occupy much less Fourier
space volume than the local ones. The analytical results on three-dimensional
shell-to-shell energy transfer match with their numerical counterparts. In
two-dimensional turbulence, the energy transfer rates to the near-by shells are
forward, but to the distant shells are backward; the cumulative effect is an
inverse cascade of energy.Comment: 10 pages, Revtex
Synthesis and Microstructural Characteristics of Tl-based High Temperature Superconducting Tapes
- …