1,919 research outputs found
Burgers Turbulence
The last decades witnessed a renewal of interest in the Burgers equation.
Much activities focused on extensions of the original one-dimensional
pressureless model introduced in the thirties by the Dutch scientist J.M.
Burgers, and more precisely on the problem of Burgers turbulence, that is the
study of the solutions to the one- or multi-dimensional Burgers equation with
random initial conditions or random forcing. Such work was frequently motivated
by new emerging applications of Burgers model to statistical physics,
cosmology, and fluid dynamics. Also Burgers turbulence appeared as one of the
simplest instances of a nonlinear system out of equilibrium. The study of
random Lagrangian systems, of stochastic partial differential equations and
their invariant measures, the theory of dynamical systems, the applications of
field theory to the understanding of dissipative anomalies and of multiscaling
in hydrodynamic turbulence have benefited significantly from progress in
Burgers turbulence. The aim of this review is to give a unified view of
selected work stemming from these rather diverse disciplines.Comment: Review Article, 49 pages, 43 figure
Application of remote sensing to study nearshore circulation
Immediate use of drogued buoy tracking was made when the Virginia State Highway Department requested assistance in selecting the best route for a new bridge-tunnel complex across the James River at Newport News. The result was that the Highway Department acted and chose a preferred route from several alternatives. It was also observed that the drogues did not follow the channel as predicted by the James River hydraulic model. This permitted telling the Navy why it is that part of their channel always silts up. The Hampton Roads Sanitation District asked help locate the best route and position of an ocean sewer outfall. Biological activities are focused primarily on delineating biological interaction between the marsh and continental shelf waters on Virginia's Eastern Shore. Information derived is helpful in categorizing the relative biological value of different marsh areas so that meaningful use and management decisions can be made concerning their eventual disposition
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
We consider linear inverse problems where the solution is assumed to have a
sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that
replacing the usual quadratic regularizing penalties by weighted l^p-penalties
on the coefficients of such expansions, with 1 < or = p < or =2, still
regularizes the problem. If p < 2, regularized solutions of such l^p-penalized
problems will have sparser expansions, with respect to the basis under
consideration. To compute the corresponding regularized solutions we propose an
iterative algorithm that amounts to a Landweber iteration with thresholding (or
nonlinear shrinkage) applied at each iteration step. We prove that this
algorithm converges in norm. We also review some potential applications of this
method.Comment: 30 pages, 3 figures; this is version 2 - changes with respect to v1:
small correction in proof (but not statement of) lemma 3.15; description of
Besov spaces in intro and app A clarified (and corrected); smaller pointsize
(making 30 instead of 38 pages
Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification
Multi-element uncertainty quantification approaches can robustly resolve the high sensitivities caused by discontinuities in parametric space by reducing the polynomial degree locally to a piecewise linear approximation. It is important to extend the higher degree interpolation in the smooth regions up to a thin layer of linear elements that contain the discontinuity to maintain a highly accurate solution. This is achieved here by introducing Essentially Non-Oscillatory (ENO) type stencil selection into the Simplex Stochastic Collocation (SSC) method. For each simplex in the discretization of the parametric space, the stencil with the highest polynomial degree is selected from the set of candidate stencils
to construct the local response surface approximation. The application of the resulting SSC–ENO method to a discontinuous test function shows a sharper resolution of the jumps and a higher order approximation of the percentiles near the singularity. SSC–ENO is also applied to a chemical model problem and a shock tube problem to study the impact of uncertainty both on the formation of discontinuities in time and on the location of discontinuities in space
Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals
We demonstrate that the global fields of temperature, humidity and
geopotential heights admit a nearly sparse representation in the wavelet
domain, offering a viable path forward to explore new paradigms of
sparsity-promoting data assimilation and compressive recovery of land
surface-atmospheric states from space. We illustrate this idea using retrieval
products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave
Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the
sparsity of the fields of temperature is relatively pressure-independent while
atmospheric humidity and geopotential heights are typically sparser at lower
and higher pressure levels, respectively. We provide evidence that these
land-atmospheric states can be accurately estimated using a small set of
measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl
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