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