Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Radiation from a Charge Supported in a Gravitational Field

We examine whether a charge supported statically in a gravitational field radiates, and find the answer to this question to be positive. Based on our earlier results we find that the important condition for the creation of radiation is the existence of a relative acceleration between the charge and its electric field, where such an acceleration causes the curving of the electric field and the creation of a stress force due to this curvature. This stress force is the reaction force, which creates the radiation. Later we find that this condition do exist for a charge supported statically in a gravitational field, where the electric field of the charge falls in the gravitational field, it curves, and the stress force raised in this curved field, creates electromagnetic radiation.     

Crystal and molecular structure of hydroxyjatrophone C

The structure of the title compound has been established by means of the x-ray diffraction method on a single crystal. The crystals are othorhombic, space groupP2₁2₁2₁ (No. 19) witha=10.222(4),b=10.622(2),c=16.434(3) Å,z=4. Full-matrix least squares refinement led toR=4.9%. The molecular stereochemistry, bond distances, bond angles, torsion angles, and hydrogen bond scheme have all been determined.Camille and Henry Dreyfus Teacher Scholar, 1978–1983; National Institutes of Health (National Cancer Institute) Career Development Award, 1980–1985.     

A Time of Flight Model for Cloud’s Radiative Transfer

A model for fast calculation of path radiance of finite clouds is presented. The calculations are simplified by using the reciprocity principle and the homogenousness property of the incident light. Comparisons with reasonably accurate calculations for spherical cloud and two-dimensional infinite layer were made.Presented at the 7th International Workshop on Multiple Scattering Lidar/Light Experiments (MUSCLE7), July 21–23 1994, Chiba, Japan.     

A short story of SIN!

A brief overview is given of the theory of surface-ion neutralization (SIN) by highlighting studies from the pioneering days to the present time. Emphasis is placed on the 1-electron time-dependent Newns-Anderson (TDNA) model, which has played such a key role in studying resonance charge transfer. Recently, a many-electron (ME) version of the TDNA approach has been formulated to treat two or more electron processes, such as Auger transitions. The equation-of-motion technique is used to obtain the TD coefficients from which the required SIN probabilities can be found. After outlining the ME method, two applications are described. The first deals with the Li⁺-Cs/W(110) system, while the second addresses the laser enhancement of SIN, in the case of Li⁺-KBr, and revises some earlier results.     

STOCHASTIC ENERGY DEMAND AND THE STABILIZATION VALUE OF ENERGY STORAGE

The economic value of energy storage to meet peak electricity demand is analyzed with an emphasis on the role of demand uncertainty. The concept of the stabilization value, which measures that part of the benefit of the storage project which is due solely to the stochastic demand components, is defined. The magnitude of the stabilization value, relative to the overall value of energy storage, is evaluated in terms of a simple model that accounts for the relevant characteristics of the electric power utility's production mix. It is found that neglecting the demand uncertainty can seriously bias the benefit assessment of the storage project as well as the determination of the optimal storage capacity.     

Recurrence relations for Tchebycheffian B-splines

Four-term recurrence relations with constant coefficients are derived for a wide class of T chebycheffian B-splines, LB-splines and complex B-splines. Such a relation exists whenever the differential operator defining the underlying “polynomial” space can be factored in two essentially different ways. The four lower order B-splines in the recurrence relation appear in two pairs, each pair corresponding to one of these factorization. It is shown that the two-term recurrence relations for polynomial, trigonometric and hyperbolic B-splines as well as other known two-term recurrence relations are obtained directly from the four-term recurrence relations in a unified and systematic way. The above derivation also yields two different two-term recurrence relations for Green’s functions of these “polynomial” spaces In this context the special examples of exponential functions and rational functions are analyzed in detail.     

The spectrum of a one-dimensional hierarchical model

The spectrum of a discrete Schrödinger operator with a hierarchically distributed potential is studied both by a renormalization group technique and by numerical analysis. A suitable choice of the potential makes it possible to reduce the original problem to a two-dimensional map. Scaling laws for the band-edge energyE _be and for the integrated density of states are predicted together with the global properties of the spectrum. Different scaling regimes are obtained depending on a hierarchy positive parameterR: for R<1/2 the usual scaling laws for the periodic case are obtained, while forR>1/2 the scaling behavior depends explicitly onR.