51 research outputs found
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
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
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
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)
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
Spatio-Temporal Continuous Wavelet Transforms for Motion-Based Segmentation in Real Image Sequences. *
The purpose of this paper is to develop a motion-based segmentation for digital image sequences that is based on continuous wavelet transform. Continu-ous wavelet transform allows estimating the motion parameters on all the moving discontinuities, edges and boundaries in the image sequence. The impor-tant fact an our case is that this technique provides all the information of motion parameter estimates and edge locations at once without going back and forth refining the segmentation and the motion parameter estimation. Also, this is achieved without involving any point/block corresponding techniques in our al-gorithm. The edges and the motion parameter es-timates are calculated locally on small windows or pixels in the image planes by maximizing the square of the modulus of the wavelet transform. A clustering procedure allows separating all the detected edges into clusters of homogeneous motion. Building a ridge-skeleton on the reconstructed edges in each cluster provides the ultimate motion-based segments or par-tition. The algorithm was simulated using real traf-fic image sequences acquired by a mobile camera and proved to be accurate and robust.
Hardware Accelerated Wavelet Transformations
. Wavelets and related multiscale representations are important means for edge detection and processing as well as for segmentation and registration. Due to the computational complexity of these approaches no interactive visualization of the extraction process is possible nowadays. By using the hardware of modern graphics workstations for accelerating wavelet decomposition and reconstruction we realize a first important step for removing lags in the visualization cycle. 1 Introduction Feature extraction has been proven to be a useful utility for segmentation and registration in volume visualization [7, 13]. Many edge detection algorithms used in this step employ wavelets or related basis functions for the internal representation of the volume. Additionally, wavelets can be used for fast volume visualization [5] using the Fourier rendering approach [8, 12]. Wavelet analysis is a mainly memory bound problem. Graphics hardware on the other hand regularly has memory systems that can be ad..
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