11,152 research outputs found
Wavelet-based fluid motion estimation
International audienceBased on a wavelet expansion of the velocity field, we present a novel optical flow algorithm dedicated to the estimation of continuous motion fields such as fluid flows. This scale-space representation, associated to a simple gradient-based optimization algorithm, naturally sets up a well-defined multi-resolution analysis framework for the optical flow estimation problem, thus avoiding the common drawbacks of standard multi-resolution schemes. Moreover, wavelet properties enable the design of simple yet efficient high-order regularizers or polynomial approximations associated to a low computational complexity. Accuracy of proposed methods is assessed on challenging sequences of turbulent fluids flows
Self-similar prior and wavelet bases for hidden incompressible turbulent motion
This work is concerned with the ill-posed inverse problem of estimating
turbulent flows from the observation of an image sequence. From a Bayesian
perspective, a divergence-free isotropic fractional Brownian motion (fBm) is
chosen as a prior model for instantaneous turbulent velocity fields. This
self-similar prior characterizes accurately second-order statistics of velocity
fields in incompressible isotropic turbulence. Nevertheless, the associated
maximum a posteriori involves a fractional Laplacian operator which is delicate
to implement in practice. To deal with this issue, we propose to decompose the
divergent-free fBm on well-chosen wavelet bases. As a first alternative, we
propose to design wavelets as whitening filters. We show that these filters are
fractional Laplacian wavelets composed with the Leray projector. As a second
alternative, we use a divergence-free wavelet basis, which takes implicitly
into account the incompressibility constraint arising from physics. Although
the latter decomposition involves correlated wavelet coefficients, we are able
to handle this dependence in practice. Based on these two wavelet
decompositions, we finally provide effective and efficient algorithms to
approach the maximum a posteriori. An intensive numerical evaluation proves the
relevance of the proposed wavelet-based self-similar priors.Comment: SIAM Journal on Imaging Sciences, 201
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
Stochastic representation of the Reynolds transport theorem: revisiting large-scale modeling
We explore the potential of a formulation of the Navier-Stokes equations
incorporating a random description of the small-scale velocity component. This
model, established from a version of the Reynolds transport theorem adapted to
a stochastic representation of the flow, gives rise to a large-scale
description of the flow dynamics in which emerges an anisotropic subgrid
tensor, reminiscent to the Reynolds stress tensor, together with a drift
correction due to an inhomogeneous turbulence. The corresponding subgrid model,
which depends on the small scales velocity variance, generalizes the Boussinesq
eddy viscosity assumption. However, it is not anymore obtained from an analogy
with molecular dissipation but ensues rigorously from the random modeling of
the flow. This principle allows us to propose several subgrid models defined
directly on the resolved flow component. We assess and compare numerically
those models on a standard Green-Taylor vortex flow at Reynolds 1600. The
numerical simulations, carried out with an accurate divergence-free scheme,
outperform classical large-eddies formulations and provides a simple
demonstration of the pertinence of the proposed large-scale modeling
Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders
In this paper we present an extended version of Hilbert-Huang transform,
namely arbitrary-order Hilbert spectral analysis, to characterize the
scale-invariant properties of a time series directly in an amplitude-frequency
space. We first show numerically that due to a nonlinear distortion,
traditional methods require high-order harmonic components to represent
nonlinear processes, except for the Hilbert-based method. This will lead to an
artificial energy flux from the low-frequency (large scale) to the
high-frequency (small scale) part. Thus the power law, if it exists, is
contaminated. We then compare the Hilbert method with structure functions (SF),
detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing
fractional Brownian motion and synthesized multifractal time series. For the
former simulation, we find that all methods provide comparable results. For the
latter simulation, we perform simulations with an intermittent parameter {\mu}
= 0.15. We find that the SF underestimates scaling exponent when q > 3. The
Hilbert method provides a slight underestimation when q > 5. However, both DFA
and WL overestimate the scaling exponents when q > 5. It seems that Hilbert and
DFA methods provide better singularity spectra than SF and WL. We finally apply
all methods to a passive scalar (temperature) data obtained from a jet
experiment with a Taylor's microscale Reynolds number Relambda \simeq 250. Due
to the presence of strong ramp-cliff structures, the SF fails to detect the
power law behavior. For the traditional method, the ramp-cliff structure causes
a serious artificial energy flux from the low-frequency (large scale) to the
high-frequency (small scale) part. Thus DFA and WL underestimate the scaling
exponents. However, the Hilbert method provides scaling exponents
{\xi}{\theta}(q) quite close to the one for longitudinal velocity.Comment: 13 pages, 10 figure
Steady-state simulation of reflected Brownian motion and related stochastic networks
This paper develops the first class of algorithms that enable unbiased
estimation of steady-state expectations for multidimensional reflected Brownian
motion. In order to explain our ideas, we first consider the case of compound
Poisson (possibly Markov modulated) input. In this case, we analyze the
complexity of our procedure as the dimension of the network increases and show
that, under certain assumptions, the algorithm has polynomial-expected
termination time. Our methodology includes procedures that are of interest
beyond steady-state simulation and reflected processes. For instance, we use
wavelets to construct a piecewise linear function that can be guaranteed to be
within distance (deterministic) in the uniform norm to Brownian
motion in any compact time interval.Comment: Published at http://dx.doi.org/10.1214/14-AAP1072 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Methods for characterising microphysical processes in plasmas
Advanced spectral and statistical data analysis techniques have greatly
contributed to shaping our understanding of microphysical processes in plasmas.
We review some of the main techniques that allow for characterising fluctuation
phenomena in geospace and in laboratory plasma observations. Special emphasis
is given to the commonalities between different disciplines, which have
witnessed the development of similar tools, often with differing terminologies.
The review is phrased in terms of few important concepts: self-similarity,
deviation from self-similarity (i.e. intermittency and coherent structures),
wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres
Wavelet analysis of magnetic turbulence in the Earth's plasma sheet
Recent studies provide evidence for the multi-scale nature of magnetic
turbulence in the plasma sheet. Wavelet methods represent modern time series
analysis techniques suitable for the description of statistical characteristics
of multi-scale turbulence. Cluster FGM (fluxgate magnetometer) magnetic field
high-resolution (~67 Hz) measurements are studied during an interval in which
the spacecraft are in the plasma sheet. As Cluster passes through different
plasma regions, physical processes exhibit non-steady properties on
magnetohydrodynamic (MHD) and small, possibly kinetic scales. As a consequence,
the implementation of wavelet-based techniques becomes complicated due to the
statistically transitory properties of magnetic fluctuations and finite size
effects. Using a supervised multi-scale technique which allows existence test
of moments, the robustness of higher-order statistics is investigated. On this
basis the properties of magnetic turbulence are investigated for changing
thickness of the plasma sheet.Comment: 17 pages, 5 figure
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