636 research outputs found
A method to create disordered vortex arrays in atomic Bose-Einstein condensates
We suggest a method to create turbulence in a trapped atomic Bose-Einstein
condensate (BEC). By replacing in the upper half part of our box the wave
function, Psi, with its complex conjugate, Psi^{*}, new negative vortices are
introduced into the system. The simulations are performed by solving the
two-dimensional Gross-Pitaevskii equation (2D GPE). We study the successive
dynamics of the wave function by monitoring the evolution of density and phase
profile.Comment: 17 pages, 12 figures. Accepted by the Canadian Journal of Physic
The Universal Scaling Exponents of Anisotropy in Turbulence and their Measurement
The scaling properties of correlation functions of non-scalar fields
(constructed from velocity derivatives) in isotropic hydrodynamic turbulence
are characterized by a set of universal exponents. It is explained that these
exponents also characterize the rate of decay of the effects of anisotropic
forcing in developed turbulence. This set has never been measured in either
numerical or laboratory experiments. These exponents are important for the
general theory of turbulence, but also for modeling anisotropic flows. We
propose in this letter how to measure these exponents using existing data bases
of direct numerical simulations and by designing new laboratory experiments.Comment: 10 pages, latex, no figures, online (html) version available at
http://lvov.weizmann.ac.il/EXP/EXP.htm
Geometrical complexity of data approximators
There are many methods developed to approximate a cloud of vectors embedded
in high-dimensional space by simpler objects: starting from principal points
and linear manifolds to self-organizing maps, neural gas, elastic maps, various
types of principal curves and principal trees, and so on. For each type of
approximators the measure of the approximator complexity was developed too.
These measures are necessary to find the balance between accuracy and
complexity and to define the optimal approximations of a given type. We propose
a measure of complexity (geometrical complexity) which is applicable to
approximators of several types and which allows comparing data approximations
of different types.Comment: 10 pages, 3 figures, minor correction and extensio
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
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
Abrégé D'histoire des mathématiques, 1700–1900 Edited by J. Dieudonné. I. Algèbre, analyse classique, théorie des nombres. II. Fonctions elliptiques, analyse fonctionnelle, géométrie différentielle, topologie, probabilités, logique mathématique. Sous la direction de J. Dieudonné, de l'Institut. Avec la collaboration de P. Dugac, W. J. et Fern Ellison, J. Guérindon, M. Guillaume, G. Hirsch, C. Houzel, Paulette Libermann, M. Loève, et J.-L. Verley. Paris (Hermann), 1978. x + 385, vii + 472
Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations
Rigorous estimates for the total - (kinetic) energy plus pressure - flux in
R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds
are used to establish a condition - involving Taylor length scale and the size
of the domain - sufficient for existence of the inertial range and the energy
cascade in decaying turbulence (zero driving force, non-increasing global
energy). Several manifestations of the locality of the flux under this
condition are obtained. All the scales involved are actual physical scales in
R^3 and no regularity or homogeneity/scaling assumptions are made.Comment: 21 pages, 2 figures; accepted to Comm. Math. Phy
ANOMALOUS SCALING OF THE PASSIVE SCALAR
We establish anomalous inertial range scaling of structure functions for a
model of advection of a passive scalar by a random velocity field. The velocity
statistics is taken gaussian with decorrelation in time and velocity
differences scaling as in space, with . The
scalar is driven by a gaussian forcing acting on spatial scale and
decorrelated in time. The structure functions for the scalar are well defined
as the diffusivity is taken to zero and acquire anomalous scaling behavior for
large pumping scales . The anomalous exponent is calculated explicitly for
the 4^{\m\rm th} structure function and for small and it differs
from previous predictions. For all but the second structure functions the
anomalous exponents are nonvanishing.Comment: 8 pages, late
Numerical Investigation of Graph Spectra and Information Interpretability of Eigenvalues
We undertake an extensive numerical investigation of the graph spectra of
thousands regular graphs, a set of random Erd\"os-R\'enyi graphs, the two most
popular types of complex networks and an evolving genetic network by using
novel conceptual and experimental tools. Our objective in so doing is to
contribute to an understanding of the meaning of the Eigenvalues of a graph
relative to its topological and information-theoretic properties. We introduce
a technique for identifying the most informative Eigenvalues of evolving
networks by comparing graph spectra behavior to their algorithmic complexity.
We suggest that extending techniques can be used to further investigate the
behavior of evolving biological networks. In the extended version of this paper
we apply these techniques to seven tissue specific regulatory networks as
static example and network of a na\"ive pluripotent immune cell in the process
of differentiating towards a Th17 cell as evolving example, finding the most
and least informative Eigenvalues at every stage.Comment: Forthcoming in 3rd International Work-Conference on Bioinformatics
and Biomedical Engineering (IWBBIO), Lecture Notes in Bioinformatics, 201
Inequalities for means of chords, with application to isoperimetric problems
We consider a pair of isoperimetric problems arising in physics. The first
concerns a Schr\"odinger operator in with an attractive
interaction supported on a closed curve , formally given by
; we ask which curve of a given length
maximizes the ground state energy. In the second problem we have a loop-shaped
thread in , homogeneously charged but not conducting,
and we ask about the (renormalized) potential-energy minimizer. Both problems
reduce to purely geometric questions about inequalities for mean values of
chords of . We prove an isoperimetric theorem for -means of chords
of curves when , which implies in particular that the global extrema
for the physical problems are always attained when is a circle. The
article finishes with a discussion of the --means of chords when .Comment: LaTeX2e, 11 page
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