125,277 research outputs found
Transport Coefficients from Large Deviation Functions
We describe a method for computing transport coefficients from the direct
evaluation of large deviation function. This method is general, relying on only
equilibrium fluctuations, and is statistically efficient, employing trajectory
based importance sampling. Equilibrium fluctuations of molecular currents are
characterized by their large deviation functions, which is a scaled cumulant
generating function analogous to the free energy. A diffusion Monte Carlo
algorithm is used to evaluate the large deviation functions, from which
arbitrary transport coefficients are derivable. We find significant statistical
improvement over traditional Green-Kubo based calculations. The systematic and
statistical errors of this method are analyzed in the context of specific
transport coefficient calculations, including the shear viscosity, interfacial
friction coefficient, and thermal conductivity.Comment: 11 pages, 5 figure
Transport Coefficients from Large Deviation Functions
We describe a method for computing transport coefficients from the direct
evaluation of large deviation function. This method is general, relying on only
equilibrium fluctuations, and is statistically efficient, employing trajectory
based importance sampling. Equilibrium fluctuations of molecular currents are
characterized by their large deviation functions, which is a scaled cumulant
generating function analogous to the free energy. A diffusion Monte Carlo
algorithm is used to evaluate the large deviation functions, from which
arbitrary transport coefficients are derivable. We find significant statistical
improvement over traditional Green-Kubo based calculations. The systematic and
statistical errors of this method are analyzed in the context of specific
transport coefficient calculations, including the shear viscosity, interfacial
friction coefficient, and thermal conductivity.Comment: 11 pages, 5 figure
Racing Multi-Objective Selection Probabilities
In the context of Noisy Multi-Objective Optimization, dealing with
uncertainties requires the decision maker to define some preferences about how
to handle them, through some statistics (e.g., mean, median) to be used to
evaluate the qualities of the solutions, and define the corresponding Pareto
set. Approximating these statistics requires repeated samplings of the
population, drastically increasing the overall computational cost. To tackle
this issue, this paper proposes to directly estimate the probability of each
individual to be selected, using some Hoeffding races to dynamically assign the
estimation budget during the selection step. The proposed racing approach is
validated against static budget approaches with NSGA-II on noisy versions of
the ZDT benchmark functions
Broad Histogram: An Overview
The Broad Histogram is a method allowing the direct calculation of the energy
degeneracy . This quantity is independent of thermodynamic concepts such
as thermal equilibrium. It only depends on the distribution of allowed (micro)
states along the energy axis, but not on the energy changes between the system
and its environment. Once one has obtained , no further effort is needed
in order to consider different environment conditions, for instance, different
temperatures, for the same system.
The method is based on the exact relation between and the
microcanonical averages of certain macroscopic quantities and
. For an application to a particular problem, one needs to choose
an adequate instrument in order to determine the averages , as functions of energy. Replacing the usual
fixed-temperature canonical by the fixed-energy microcanonical ensemble, new
subtle concepts emerge. The temperature, for instance, is no longer an external
parameter controlled by the user, all canonical averages being functions of
this parameter. Instead, the microcanonical temperature is a
function of energy defined from itself, being thus an {\bf internal}
(environment independent) characteristic of the system. Accordingly, all
microcanonical averages are functions of .
The present text is an overview of the method. Some features of the
microcanonical ensemble are also discussed, as well as some clues towards the
definition of efficient Monte Carlo microcanonical sampling rules.Comment: 32 pages, tex, 3 PS figure
Precipitation and latent heating distributions from satellite passive microwave radiometry. Part I: improved method and uncertainties
A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5°-resolution range from approximately 50% at 1 mm h−1 to 20% at 14 mm h−1. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%–80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5° resolution is relatively small (less than 6% at 5 mm day−1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%–35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%–15% at 5 mm day−1, with proportionate reductions in latent heating sampling errors
Errors in particle tracking velocimetry with high-speed cameras
Velocity errors in particle tracking velocimetry (PTV) are studied. When
using high-speed video cameras, the velocity error may increase at a high
camera frame rate. This increase in velocity error is due to particle-position
uncertainty, which is one of two sources of velocity errors studied here. The
other source of error is particle acceleration, which has the opposite trend of
diminishing at higher frame rates. Both kinds of errors can propagate into
quantities calculated from velocity, such as the kinetic temperature of
particles or correlation functions. As demonstrated in a dusty plasma
experiment, the kinetic temperature of particles has no unique value when
measured using PTV, but depends on the sampling time interval or frame rate. It
is also shown that an artifact appears in an autocorrelation function computed
from particle positions and velocities, and it becomes more severe when a small
sampling-time interval is used. Schemes to reduce these errors are
demonstrated.Comment: 6 pages, 5 figures, Review of Scientific Instruments, 2011 (In Press
Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space
High angular resolution diffusion imaging data is the observed characteristic
function for the local diffusion of water molecules in tissue. This data is
used to infer structural information in brain imaging. Nonparametric scalar
measures are proposed to summarize such data, and to locally characterize
spatial features of the diffusion probability density function (PDF), relying
on the geometry of the characteristic function. Summary statistics are defined
so that their distributions are, to first-order, both independent of nuisance
parameters and also analytically tractable. The dominant direction of the
diffusion at a spatial location (voxel) is determined, and a new set of axes
are introduced in Fourier space. Variation quantified in these axes determines
the local spatial properties of the diffusion density. Nonparametric hypothesis
tests for determining whether the diffusion is unimodal, isotropic or
multi-modal are proposed. More subtle characteristics of white-matter
microstructure, such as the degree of anisotropy of the PDF and symmetry
compared with a variety of asymmetric PDF alternatives, may be ascertained
directly in the Fourier domain without parametric assumptions on the form of
the diffusion PDF. We simulate a set of diffusion processes and characterize
their local properties using the newly introduced summaries. We show how
complex white-matter structures across multiple voxels exhibit clear
ellipsoidal and asymmetric structure in simulation, and assess the performance
of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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