122 research outputs found
Turbulent luminance in impassioned van Gogh paintings
We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation
Hamiltonian structure of Hamiltonian chaos
From a kinematical point of view, the geometrical information of hamiltonian
chaos is given by the (un)stable directions, while the dynamical information is
given by the Lyapunov exponents. The finite time Lyapunov exponents are of
particular importance in physics. The spatial variations of the finite time
Lyapunov exponent and its associated (un)stable direction are related. Both of
them are found to be determined by a new hamiltonian of same number of degrees
of freedom as the original one. This new hamiltonian defines a flow field with
characteristically chaotic trajectories. The direction and the magnitude of the
phase flow field give the (un)stable direction and the finite time Lyapunov
exponent of the original hamiltonian. Our analysis was based on a
degree of freedom hamiltonian system
Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence
Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and
R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different
approaches that have the Navier-Stokes equations as the common starting point,
a set of steady-state dynamic equations for structure functions of arbitrary
order in hydrodynamic turbulence. These equations are not closed. Yakhot
proposed a "mean field theory" to close the equations for locally isotropic
turbulence, and obtained scaling exponents of structure functions and an
expression for the tails of the probability density function of transverse
velocity increments. At high Reynolds numbers, we present some relevant
experimental data on pressure and dissipation terms that are needed to provide
closure, as well as on aspects predicted by the theory. Comparison between the
theory and the data shows varying levels of agreement, and reveals gaps
inherent to the implementation of the theory.Comment: 16 pages, 23 figure
Yakhot's model of strong turbulence: A generalization of scaling models of turbulence
We report on some implications of the theory of turbulence developed by V.
Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on
the expression for the scaling exponents . We show that Yakhot's
result contains three well known scaling models as special cases, namely K41,
K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys.
Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical
justification for the method of extended self--similarity (ESS).Comment: 8 page
Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations
The connection between anomalous scaling of structure functions
(intermittency) and numerical methods for turbulence simulations is discussed.
It is argued that the computational work for direct numerical simulations (DNS)
of fully developed turbulence increases as , and not as
expected from Kolmogorov's theory, where is a large-scale Reynolds number.
Various relations for the moments of acceleration and velocity derivatives are
derived. An infinite set of exact constraints on dynamically consistent subgrid
models for Large Eddy Simulations (LES) is derived from the Navier-Stokes
equations, and some problems of principle associated with existing LES models
are highlighted.Comment: 18 page
Modeling of graphene-based NEMS
The possibility of designing nanoelectromechanical systems (NEMS) based on
relative motion or vibrations of graphene layers is analyzed. Ab initio and
empirical calculations of the potential relief of interlayer interaction energy
in bilayer graphene are performed. A new potential based on the density
functional theory calculations with the dispersion correction is developed to
reliably reproduce the potential relief of interlayer interaction energy in
bilayer graphene. Telescopic oscillations and small relative vibrations of
graphene layers are investigated using molecular dynamics simulations. It is
shown that these vibrations are characterized with small Q-factor values. The
perspectives of nanoelectromechanical systems based on relative motion or
vibrations of graphene layers are discussed.Comment: 19 pages, 4 figure
Model Flames in the Boussinesq Limit: The Effects of Feedback
We have studied the fully nonlinear behavior of pre-mixed flames in a
gravitationally stratified medium, subject to the Boussinesq approximation. Key
results include the establishment of criterion for when such flames propagate
as simple planar flames; elucidation of scaling laws for the effective flame
speed; and a study of the stability properties of these flames. The simplicity
of some of our scalings results suggests that analytical work may further
advance our understandings of buoyant flames.Comment: 11 pages, 14 figures, RevTex, gzipped tar fil
Can Barrier to Relative Sliding of Carbon Nanotube Walls Be Measured?
Interwall interaction energies, as well as barriers to relative sliding of
the walls along the nanotube axis, are first calculated for pairs of both
armchair or both zigzag adjacent walls of carbon nanotubes with a wide range of
radiuses. It is found that for the pairs with the radius of the outer wall
greater than 5 nm both the interwall interaction energy and barriers to the
relative sliding per one atom of the outer wall only slightly depends on the
wall radius. A wide set of the measurable physical quantities determined by
these barriers are estimated as a function of the wall radius: shear strengths
and diffusion coefficients for relative sliding of the walls along the axis, as
well as frequencies of relative axial oscillations of the walls. For
nonreversible telescopic extension of the walls, maximum overlap of the walls
for which threshold static friction forces are greater than capillary forces is
estimated. Possibility of experimental verification of the calculated barriers
by measurements of the estimated physical quantities is discussed.Comment: 16 pages, 8 figure
Strong Universality in Forced and Decaying Turbulence
The weak version of universality in turbulence refers to the independence of
the scaling exponents of the th order strcuture functions from the
statistics of the forcing. The strong version includes universality of the
coefficients of the structure functions in the isotropic sector, once
normalized by the mean energy flux. We demonstrate that shell models of
turbulence exhibit strong universality for both forced and decaying turbulence.
The exponents {\em and} the normalized coefficients are time independent in
decaying turbulence, forcing independent in forced turbulence, and equal for
decaying and forced turbulence. We conjecture that this is also the case for
Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte
Local properties of extended self-similarity in 3D turbulence
Using a generalization of extended self-similarity we have studied local
scaling properties of 3D turbulence in a direct numerical simulation. We have
found that these properties are consistent with lognormal-like behavior of
energy dissipation fluctuations with moderate amplitudes for space scales
beginning from Kolmogorov length up to the largest scales, and in the
whole range of the Reynolds numbers: . The
locally determined intermittency exponent varies with ; it has a
maximum at scale , independent of .Comment: 4 pages, 5 figure
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