2,849 research outputs found
Statistics of spatial averages and optimal averaging in the presence of missing data
We consider statistics of spatial averages estimated by weighting
observations over an arbitrary spatial domain using identical and independent
measuring devices, and derive an account of bias and variance in the presence
of missing observations. We test the model relative to simulations, and the
approximations for bias and variance with missing data are shown to compare
well even when the probability of missing data is large. Previous authors have
examined optimal averaging strategies for minimizing bias, variance and mean
squared error of the spatial average, and we extend the analysis to the case of
missing observations. Minimizing variance mainly requires higher weights where
local variance and covariance is small, whereas minimizing bias requires higher
weights where the field is closer to the true spatial average. Missing data
increases variance and contributes to bias, and reducing both effects involves
emphasizing locations with mean value nearer to the spatial average. The
framework is applied to study spatially averaged rainfall over India. We use
our model to estimate standard error in all-India rainfall as the combined
effect of measurement uncertainty and bias, when weights are chosen so as to
yield minimum mean squared error
The structure of particle cloud premixed flames
The aim of this study is to provide a numerical and asymptotic description of the structure of planar laminar flames, propagating in a medium containing a uniform cloud of fuel-particles premixed with air. Attention is restricted here to systems where the fuel-particles first vaporize to form a known gaseous fuel, which is then oxidized in the gas-phase. This program is supported for the period September 14, 1991 to September 13, 1992. Some results of the study is shown in Ref. 1. The work summarized in Ref. 1 was initiated prior to September 14, 1991 and was completed on February 1992. Research performed in addition to that described in Ref. 1 in collaboration with Professor A. Linan, is summarized here
Edge states, spin transport and impurity induced local density of states in spin-orbit coupled graphene
We study graphene which has both spin-orbit coupling (SOC), taken to be of
the Kane-Mele form, and a Zeeman field induced due to proximity to a
ferromagnetic material. We show that a zigzag interface of graphene having SOC
with its pristine counterpart hosts robust chiral edge modes in spite of the
gapless nature of the pristine graphene; such modes do not occur for armchair
interfaces. Next we study the change in the local density of states (LDOS) due
to the presence of an impurity in graphene with SOC and Zeeman field, and
demonstrate that the Fourier transform of the LDOS close to the Dirac points
can act as a measure of the strength of the spin-orbit coupling; in addition,
for a specific distribution of impurity atoms, the LDOS is controlled by a
destructive interference effect of graphene electrons which is a direct
consequence of their Dirac nature. Finally, we study transport across junctions
which separates spin-orbit coupled graphene with Kane-Mele and Rashba terms
from pristine graphene both in the presence and absence of a Zeeman field. We
demonstrate that such junctions are generally spin active, namely, they can
rotate the spin so that an incident electron which is spin polarized along some
direction has a finite probability of being transmitted with the opposite spin.
This leads to a finite, electrically controllable, spin current in such
graphene junctions. We discuss possible experiments which can probe our
theoretical predictions.Comment: 21 pages, 19 figures; added some discussion and references; this is
the final published versio
Note on Coherent States and Adiabatic Connections, Curvatures
We give a possible generalization to the example in the paper of Zanardi and
Rasetti (quant-ph/9904011). For this generalized one explicit forms of
adiabatic connection, curvature and etc. are given.Comment: Latex file, 12 page
Convergent estimators of variance of a spatial mean in the presence of missing observations
In the geosciences, a recurring problem is one of estimating spatial means of
a physical field using weighted averages of point observations. An important
variant is when individual observations are counted with some probability less
than one. This can occur in different contexts: from missing data to estimating
the statistics across subsamples. In such situations, the spatial mean is a
ratio of random variables, whose statistics involve approximate estimators
derived through series expansion. The present paper considers truncated
estimators of variance of the spatial mean and their general structure in the
presence of missing data. To all orders, the variance estimator depends only on
the first and second moments of the underlying field, and convergence requires
these moments to be finite. Furthermore, convergence occurs if either the
probability of counting individual observations is larger than 1/2 or the
number of point observations is large. In case the point observations are
weighted uniformly, the estimators are easily found using combinatorics and
involve Stirling numbers of the second kind
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