1,476 research outputs found
A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem
This paper is the second in a series exploring the properties of a functor
which assigns a homotopy double groupoid with connections to a Hausdorff space.
We show that this functor satisfies a version of the van Kampen theorem, and
so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems.
The methods are analogous to those developed by Brown and Higgins for similar
theorems for other higher homotopy groupoids.
An integral part of the proof is a detailed discussion of commutative cubes
in a double category with connections, and a proof of the key result that any
composition of commutative cubes is commutative. These results have recently
been generalised to all dimensions by Philip Higgins.Comment: 19 pages, uses picte
An exact relation between Eulerian and Lagrangian velocity increment statistics
We present a formal connection between Lagrangian and Eulerian velocity
increment distributions which is applicable to a wide range of turbulent
systems ranging from turbulence in incompressible fluids to magnetohydrodynamic
turbulence. For the case of the inverse cascade regime of two-dimensional
turbulence we numerically estimate the transition probabilities involved in
this connection. In this context we are able to directly identify the processes
leading to strongly non-Gaussian statistics for the Lagrangian velocity
increments.Comment: 5 pages, 3 figure
The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
We present an overview of recent works on the statistical description of
turbulent flows in terms of probability density functions (PDFs) in the
framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework,
evolution equations for the PDFs are derived from the basic equations of fluid
motion. The closure problem arises either in terms of a coupling to multi-point
PDFs or in terms of conditional averages entering the evolution equations as
unknown functions. We mainly focus on the latter case and use data from direct
numerical simulations (DNS) to specify the unclosed terms. Apart from giving an
introduction into the basic analytical techniques, applications to
two-dimensional vorticity statistics, to the single-point velocity and
vorticity statistics of three-dimensional turbulence, to the temperature
statistics of Rayleigh-B\'enard convection and to Burgers turbulence are
discussed.Comment: Accepted for publication in C. R. Acad. Sc
Lagrangian statistics in forced two-dimensional turbulence
We report on simulations of two-dimensional turbulence in the inverse energy
cascade regime. Focusing on the statistics of Lagrangian tracer particles,
scaling behavior of the probability density functions of velocity fluctuations
is investigated. The results are compared to the three-dimensional case. In
particular an analysis in terms of compensated cumulants reveals the transition
from a strong non-Gaussian behavior with large tails to Gaussianity. The
reported computation of correlation functions for the acceleration components
sheds light on the underlying dynamics of the tracer particles.Comment: 8 figures, 1 tabl
Third workshop on exploiting semantic annotations in information retrieval (ESAIR):CIKM 2010 workshop
Third workshop on exploiting semantic annotations in information retrieval (ESAIR):CIKM 2010 workshop
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