3,507 research outputs found
A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation
Data assimilation obtains improved estimates of the state of a physical system by combining imperfect
model results with sparse and noisy observations of reality. Not all observations used in data assimilation
are equally valuable. The ability to characterize the usefulness of different data points is important
for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future
sensor systems.
In the companion paper (Sandu et al., 2012) we derive an ensemble-based computational procedure
to estimate the information content of various observations in the context of 4D-Var. Here we apply
this methodology to quantify the signal and degrees of freedom for signal information metrics of satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical
transport model. The assimilation of a subset of data points characterized by the highest information
content yields an analysis comparable in quality with the one obtained using the entire data set
Fluctuating hydrodynamics of multi-species, non-reactive mixtures
In this paper we discuss the formulation of the fuctuating Navier-Stokes
(FNS) equations for multi-species, non-reactive fluids. In particular, we
establish a form suitable for numerical solution of the resulting stochastic
partial differential equations. An accurate and efficient numerical scheme,
based on our previous methods for single species and binary mixtures, is
presented and tested at equilibrium as well as for a variety of non-equilibrium
problems. These include the study of giant nonequilibrium concentration
fluctuations in a ternary mixture in the presence of a diffusion barrier, the
triggering of a Rayleigh-Taylor instability by diffusion in a four-species
mixture, as well as reverse diffusion in a ternary mixture. Good agreement with
theory and experiment demonstrates that the formulation is robust and can serve
as a useful tool in the study of thermal fluctuations for multi-species fluids.
The extension to include chemical reactions will be treated in a sequel paper
Optimal Reconstruction of Inviscid Vortices
We address the question of constructing simple inviscid vortex models which
optimally approximate realistic flows as solutions of an inverse problem.
Assuming the model to be incompressible, inviscid and stationary in the frame
of reference moving with the vortex, the "structure" of the vortex is uniquely
characterized by the functional relation between the streamfunction and
vorticity. It is demonstrated how the inverse problem of reconstructing this
functional relation from data can be framed as an optimization problem which
can be efficiently solved using variational techniques. In contrast to earlier
studies, the vorticity function defining the streamfunction-vorticity relation
is reconstructed in the continuous setting subject to a minimum number of
assumptions. To focus attention, we consider flows in 3D axisymmetric geometry
with vortex rings. To validate our approach, a test case involving Hill's
vortex is presented in which a very good reconstruction is obtained. In the
second example we construct an optimal inviscid vortex model for a realistic
flow in which a more accurate vorticity function is obtained than produced
through an empirical fit. When compared to available theoretical vortex-ring
models, our approach has the advantage of offering a good representation of
both the vortex structure and its integral characteristics.Comment: 33 pages, 10 figure
Optimal feeding is optimal swimming for all P\'eclet numbers
Cells swimming in viscous fluids create flow fields which influence the
transport of relevant nutrients, and therefore their feeding rate. We propose a
modeling approach to the problem of optimal feeding at zero Reynolds number. We
consider a simplified spherical swimmer deforming its shape tangentially in a
steady fashion (so-called squirmer). Assuming that the nutrient is a passive
scalar obeying an advection-diffusion equation, the optimal use of flow fields
by the swimmer for feeding is determined by maximizing the diffusive flux at
the organism surface for a fixed rate of energy dissipation in the fluid. The
results are obtained through the use of an adjoint-based numerical optimization
implemented by a Legendre polynomial spectral method. We show that, to within a
negligible amount, the optimal feeding mechanism consists in putting all the
energy expended by surface distortion into swimming - so-called treadmill
motion - which is also the solution maximizing the swimming efficiency.
Surprisingly, although the rate of feeding depends strongly on the value of the
P\'eclet number, the optimal feeding stroke is shown to be essentially
independent of it, which is confirmed by asymptotic analysis. Within the
context of steady actuation, optimal feeding is therefore found to be
equivalent to optimal swimming for all P\'eclet numbers.Comment: 14 pages, 6 figures, to appear in Physics of Fluid
Forward and Adjoint Radiance Monte Carlo Models for Quantitative Photoacoustic Imaging
In quantitative photoacoustic imaging, the aim is to recover physiologically relevant tissue parameters such as chromophore concentrations or oxygen saturation. Obtaining accurate estimates is challenging due to the non-linear relationship between the concentrations and the photoacoustic images. Nonlinear least squares inversions designed to tackle this problem require a model of light transport, the most accurate of which is the radiative transfer equation. This paper presents a highly scalable Monte Carlo model of light transport that computes the radiance in 2D using a Fourier basis to discretise in angle. The model was validated against a 2D finite element model of the radiative transfer equation, and was used to compute gradients of an error functional with respect to the absorption and scattering coefficient. It was found that adjoint-based gradient calculations were much more robust to inherent Monte Carlo noise than a finite difference approach. Furthermore, the Fourier angular discretisation allowed very efficient gradient calculations as sums of Fourier coefficients. These advantages, along with the high parallelisability of Monte Carlo models, makes this approach an attractive candidate as a light model for quantitative inversion in photoacoustic imaging
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