5,047 research outputs found
Structural Studies of Decaying Fluid Turbulence: Effect of Initial Conditions
We present results from a systematic numerical study of structural properties
of an unforced, incompressible, homogeneous, and isotropic three-dimensional
turbulent fluid with an initial energy spectrum that develops a cascade of
kinetic energy to large wavenumbers. The results are compared with those from a
recently studied set of power-law initial energy spectra [C. Kalelkar and R.
Pandit, Phys. Rev. E, {\bf 69}, 046304 (2004)] which do not exhibit such a
cascade. Differences are exhibited in plots of vorticity isosurfaces, the
temporal evolution of the kinetic energy-dissipation rate, and the rates of
production of the mean enstrophy along the principal axes of the strain-rate
tensor. A crossover between non-`cascade-type' and `cascade-type' behaviour is
shown numerically for a specific set of initial energy spectra.Comment: 9 pages, 27 figures, Accepted for publication in Physical Review
Two-point velocity average of turbulence: statistics and their implications
For turbulence, although the two-point velocity difference u(x+r)-u(x) at
each scale r has been studied in detail, the velocity average [u(x+r)+u(x)]/2
has not thus far. Theoretically or experimentally, we find interesting features
of the velocity average. It satisfies an exact scale-by-scale energy budget
equation. The flatness factor varies with the scale r in a universal manner.
These features are not consistent with the existing assumption that the
velocity average is independent of r and represents energy-containing
large-scale motions alone. We accordingly propose that it represents motions
over scales >= r as long as the velocity difference represents motions at the
scale r.Comment: 8 pages, accepted by Physics of Fluids (see http://pof.aip.org/
New algorithms for the dual of the convex cost network flow problem with application to computer vision
Motivated by various applications to computer vision, we consider an integer convex optimization problem which is the dual of the convex cost network flow problem. In this
paper, we first propose a new primal algorithm for computing an optimal solution of the problem. Our primal algorithm iteratively updates primal variables by solving associated
minimum cut problems. The main contribution in this paper is to provide a tight bound for the number of the iterations. We show that the time complexity of the primal algorithm is K ¢ T(n;m) where K is the range of primal variables and T(n;m) is the time needed to compute a minimum cut in a graph with n nodes and m edges.
We then propose a primal-dual algorithm for the dual of the convex cost network flow problem. The primal-dual algorithm can be seen as a refined version of the primal algorithm by maintaining dual variables (flow) in addition to primal variables. Although its time complexity is the same as that for the primal algorithm, we can expect a better performance
practically.
We finally consider an application to a computer vision problem called the panoramic stitching problem. We apply several implementations of our primal-dual algorithm to some
instances of the panoramic stitching problem and test their practical performance.
We also show that our primal algorithm as well as the proofs can be applied to the L\-convex function minimization problem which is a more general problem than the dual of the convex cost network flow problem
"Locally homogeneous turbulence" Is it an inconsistent framework?
In his first 1941 paper Kolmogorov assumed that the velocity has increments
which are homogeneous and independent of the velocity at a suitable reference
point. This assumption of local homogeneity is consistent with the nonlinear
dynamics only in an asymptotic sense when the reference point is far away. The
inconsistency is illustrated numerically using the Burgers equation.
Kolmogorov's derivation of the four-fifths law for the third-order structure
function and its anisotropic generalization are actually valid only for
homogeneous turbulence, but a local version due to Duchon and Robert still
holds. A Kolomogorov--Landau approach is proposed to handle the effect of
fluctuations in the large-scale velocity on small-scale statistical properties;
it is is only a mild extension of the 1941 theory and does not incorporate
intermittency effects.Comment: 4 pages, 2 figure
Entropy and Area in Loop Quantum Gravity
Black hole thermodynamics suggests that the maximum entropy that can be
contained in a region of space is proportional to the area enclosing it rather
than its volume. I argue that this follows naturally from loop quantum gravity
and a result of Kolmogorov and Bardzin' on the the realizability of networks in
three dimensions. This represents an alternative to other approaches in which
some sort of correlation between field configurations helps limit the degrees
of freedom within a region. It also provides an approach to thinking about
black hole entropy in terms of states inside rather than on its surface.
Intuitively, a spin network complicated enough to imbue a region with volume
only lets that volume grow as quickly as the area bounding it.Comment: 7 pages, this essay received an Honourable Mention in the Gravity
Research Foundation Essay Competition 2005; reformatted for IJMP (accepted
for publication) with minor typographical corrections and some extended
discussio
Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows
Studies of the relation between the shear parameter S^* and the Reynolds
number Re are presented for a nearly homogeneous and statistically stationary
turbulent shear flow. The parametric investigations are in line with a
generalized perspective on the return to local isotropy in shear flows that was
outlined recently [Schumacher, Sreenivasan and Yeung, Phys. Fluids, vol.15, 84
(2003)]. Therefore, two parameters, the constant shear rate S and the level of
initial turbulent fluctuations as prescribed by an energy injection rate
epsilon_{in}, are varied systematically. The investigations suggest that the
shear parameter levels off for larger Reynolds numbers which is supported by
dimensional arguments. It is found that the skewness of the transverse
derivative shows a different decay behavior with respect to Reynolds number
when the sequence of simulation runs follows different pathways across the
two-parameter plane. The study can shed new light on different interpretations
of the decay of odd order moments in high-Reynolds number experiments.Comment: 9 pages, 9 Postscript figure
Analogy between turbulence and quantum gravity: beyond Kolmogorov's 1941 theory
Simple arguments based on the general properties of quantum fluctuations have
been recently shown to imply that quantum fluctuations of spacetime obey the
same scaling laws of the velocity fluctuations in a homogeneous incompressible
turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less
noted, however, is the fact that this analogy rules out the possibility of a
fractal quantum spacetime, in contradiction with growing evidence in quantum
gravity research. In this Note, we show that the notion of a fractal quantum
spacetime can be restored by extending the analogy between turbulence and
quantum gravity beyond the realm of K41 theory. In particular, it is shown that
compatibility of a fractal quantum-space time with the recent Horava-Lifshitz
scenario for quantum gravity, implies singular quantum wavefunctions. Finally,
we propose an operational procedure, based on Extended Self-Similarity
techniques, to inspect the (multi)-scaling properties of quantum gravitational
fluctuations.Comment: Sliglty modified version of the article about to appear in IJMP
Shear Effects in Non-Homogeneous Turbulence
Motivated by recent experimental and numerical results, a simple unifying
picture of intermittency in turbulent shear flows is suggested. Integral
Structure Functions (ISF), taking into account explicitly the shear intensity,
are introduced on phenomenological grounds. ISF can exhibit a universal scaling
behavior, independent of the shear intensity. This picture is in satisfactory
agreement with both experimental and numerical data. Possible extension to
convective turbulence and implication on closure conditions for Large-Eddy
Simulation of non-homogeneous flows are briefly discussed.Comment: 4 pages, 5 figure
Scaling Relations of Compressible MHD Turbulence
We study scaling relations of compressible strongly magnetized turbulence. We
find a good correspondence of our results with the Fleck (1996) model of
compressible hydrodynamic turbulence. In particular, we find that the
density-weighted velocity, i.e. , proposed in Kritsuk et
al. (2007) obeys the Kolmogorov scaling, i.e. for the
high Mach number turbulence. Similarly, we find that the exponents of the third
order structure functions for stay equal to unity for the all the Mach
numbers studied. The scaling of higher order correlations obeys the She-Leveque
(1994) scalings corresponding to the two-dimensional dissipative structures,
and this result does not change with the Mach number either. In contrast to
which exhibits different scaling parallel and perpendicular to the local
magnetic field, the scaling of is similar in both directions. In addition,
we find that the peaks of density create a hierarchy in which both physical and
column densities decrease with the scale in accordance to the Fleck (1996)
predictions. This hierarchy can be related ubiquitous small ionized and neutral
structures (SINS) in the interstellar gas. We believe that studies of
statistics of the column density peaks can provide both consistency check for
the turbulence velocity studies and insight into supersonic turbulence, when
the velocity information is not available.Comment: 4 pages, 5 figure
The Kelvin-wave cascade in the vortex filament model
The energy transfer mechanism in zero temperature superfluid turbulence of
helium-4 is still a widely debated topic. Currently, the main hypothesis is
that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently
small scales such that energy is dissipated as heat via phonon excitations.
Theoretically, there are at least two proposed theories for Kelvin-wave
interactions. We perform the most comprehensive numerical simulation of weakly
nonlinear interacting Kelvin-waves to date and show, using a specially designed
numerical algorithm incorporating the full Biot-Savart equation, that our
results are consistent with nonlocal six-wave Kelvin wave interactions as
proposed by L'vov and Nazarenko.Comment: 6 pages, 6 figure
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