62 research outputs found
A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows
The fundamental equations that model turbulent flow do not provide much
insight into the size and shape of observed turbulent structures. We
investigate the efficient and accurate representation of structures in
two-dimensional turbulence by applying statistical models directly to the
simulated vorticity field. Rather than extract the coherent portion of the
image from the background variation, as in the classical signal-plus-noise
model, we present a model for individual vortices using the non-decimated
discrete wavelet transform. A template image, supplied by the user, provides
the features to be extracted from the vorticity field. By transforming the
vortex template into the wavelet domain, specific characteristics present in
the template, such as size and symmetry, are broken down into components
associated with spatial frequencies. Multivariate multiple linear regression is
used to fit the vortex template to the vorticity field in the wavelet domain.
Since all levels of the template decomposition may be used to model each level
in the field decomposition, the resulting model need not be identical to the
template. Application to a vortex census algorithm that records quantities of
interest (such as size, peak amplitude, circulation, etc.) as the vorticity
field evolves is given. The multiresolution census algorithm extracts coherent
structures of all shapes and sizes in simulated vorticity fields and is able to
reproduce known physical scaling laws when processing a set of voriticity
fields that evolve over time
Extraction of coherent structures in a rotating turbulent flow experiment
The discrete wavelet packet transform (DWPT) and discrete wavelet transform
(DWT) are used to extract and study the dynamics of coherent structures in a
turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by
strong pumping through tubes at the bottom of a rotating tank (48.4 cm high,
39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence
with increasing height in the tank. Particle Image Velocimetry (PIV)
measurements on the quasi-2D flow reveal many long-lived coherent vortices with
a wide range of sizes. The vorticity fields exhibit vortex birth, merger,
scattering, and destruction. We separate the flow into a low-entropy
``coherent'' and a high-entropy ``incoherent'' component by thresholding the
coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings
using the Fourier transform and JPEG compression together with the Okubo-Weiss
criterion are also tested for comparison. We find that the DWPT and DWT yield
similar results and are much more efficient at representing the total flow than
a Fourier-based method. Only about 3% of the large-amplitude coefficients of
the DWPT and DWT are necessary to represent the coherent component and preserve
the vorticity probability density function, transport properties, and spatial
and temporal correlations. The remaining small amplitude coefficients represent
the incoherent component, which has near Gaussian vorticity PDF, contains no
coherent structures, rapidly loses correlation in time, and does not contribute
significantly to the transport properties of the flow. This suggests that one
can describe and simulate such turbulent flow using a relatively small number
of wavelet or wavelet packet modes.Comment: experimental work aprox 17 pages, 11 figures, accepted to appear in
PRE, last few figures appear at the end. clarifications, added references,
fixed typo
Towards an Inverse Scattering theory for non decaying potentials of the heat equation
The resolvent approach is applied to the spectral analysis of the heat
equation with non decaying potentials. The special case of potentials with
spectral data obtained by a rational similarity transformation of the spectral
data of a generic decaying potential is considered. It is shown that these
potentials describe solitons superimposed by Backlund transformations to a
generic background. Dressing operators and Jost solutions are constructed by
solving a DBAR-problem explicitly in terms of the corresponding objects
associated to the original potential. Regularity conditions of the potential in
the cases N=1 and N=2 are investigated in details. The singularities of the
resolvent for the case N=1 are studied, opening the way to a correct definition
of the spectral data for a generically perturbed soliton.Comment: 22 pages, submitted to Inverse Problem
On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
The unexpectedly rich structure of the multisoliton solutions of the KPII
equation has been explored by using different approaches, running from dressing
method to twisting transformations and to the tau-function formulation. All
these approaches proved to be useful in order to display different properties
of these solutions and their related Jost solutions. The aim of this paper is
to establish the explicit formulae relating all these approaches. In addition
some hidden invariance properties of these multisoliton solutions are
discussed
Quantum algorithm and circuit design solving the Poisson equation
The Poisson equation occurs in many areas of science and engineering. Here we
focus on its numerical solution for an equation in d dimensions. In particular
we present a quantum algorithm and a scalable quantum circuit design which
approximates the solution of the Poisson equation on a grid with error
\varepsilon. We assume we are given a supersposition of function evaluations of
the right hand side of the Poisson equation. The algorithm produces a quantum
state encoding the solution. The number of quantum operations and the number of
qubits used by the circuit is almost linear in d and polylog in
\varepsilon^{-1}. We present quantum circuit modules together with performance
guarantees which can be also used for other problems.Comment: 30 pages, 9 figures. This is the revised version for publication in
New Journal of Physic
Global well-posedness for the KP-I equation on the background of a non localized solution
We prove that the Cauchy problem for the KP-I equation is globally well-posed
for initial data which are localized perturbations (of arbitrary size) of a
non-localized (i.e. not decaying in all directions) traveling wave solution
(e.g. the KdV line solitary wave or the Zaitsev solitary waves which are
localized in and periodic or conversely)
Time localisation of surface defects on optical discs
Abstract — Many have experienced problems with their Compact Disc player when a disc with a scratch or a finger print is tried played. One way to improve the playability of discs with such a defect, is to locate the defect in time and then handle it in a special way. As a consequence this time localisation is needed to be as good as possible. Fang’s algorithm for segmentation of the time axis is used since it has good performance in an application like this. Fang’s algorithm has a clear potential for time localisation for some defects and but not for other defects. Instead the normally used threshold is improved to handle eccentricity and localisation of the end of the defect better. I
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