A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Microbial relatives of the seed storage proteins of higher plants: conservation of structure and diversification of function during evolution of the cupin superfamily.

This review summarizes the recent discovery of the cupin superfamily (from the Latin term "cupa," a small barrel) of functionally diverse proteins that initially were limited to several higher plant proteins such as seed storage proteins, germin (an oxalate oxidase), germin-like proteins, and auxin-binding protein. Knowledge of the three-dimensional structure of two vicilins, seed proteins with a characteristic beta-barrel core, led to the identification of a small number of conserved residues and thence to the discovery of several microbial proteins which share these key amino acids. In particular, there is a highly conserved pattern of two histidine-containing motifs with a varied intermotif spacing. This cupin signature is found as a central component of many microbial proteins including certain types of phosphomannose isomerase, polyketide synthase, epimerase, and dioxygenase. In addition, the signature has been identified within the N-terminal effector domain in a subgroup of bacterial AraC transcription factors. As well as these single-domain cupins, this survey has identified other classes of two-domain bicupins including bacterial gentisate 1, 2-dioxygenases and 1-hydroxy-2-naphthoate dioxygenases, fungal oxalate decarboxylases, and legume sucrose-binding proteins. Cupin evolution is discussed from the perspective of the structure-function relationships, using data from the genomes of several prokaryotes, especially Bacillus subtilis. Many of these functions involve aspects of sugar metabolism and cell wall synthesis and are concerned with responses to abiotic stress such as heat, desiccation, or starvation. Particular emphasis is also given to the oxalate-degrading enzymes from microbes, their biological significance, and their value in a range of medical and other applications.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

Solar causes of the long-term increase in geomagnetic activity

We analyze the causes of the century-long increase in geomagnetic activity, quantified by annual means of the aa index, using observations of interplanetary space, galactic cosmic rays, the ionosphere, and the auroral electrojet, made during the last three solar cycles. The effects of changes in ionospheric conductivity, the Earth's dipole tilt, and magnetic moment are shown to be small; only changes in near-Earth interplanetary space make a significant contribution to the long-term increase in activity. We study the effects of the interplanetary medium by applying dimensional analysis to generate the optimum solar wind-magnetosphere energy coupling function, having an unprecedentedly high correlation coefficient of 0.97. Analysis of the terms of the coupling function shows that the largest contributions to the drift in activity over solar cycles 20-22 originate from rises in the average interplanetary magnetic field (IMF) strength, solar wind concentration, and speed; average IMF orientation has grown somewhat less propitious for causing geomagnetic activity. The combination of these factors explains almost all of the 39% rise in aa observed over the last three solar cycles. Whereas the IMF strength varies approximately in phase with sunspot numbers, neither its orientation nor the solar wind density shows any coherent solar cycle variation. The solar wind speed peaks strongly in the declining phase of even-numbered cycles and can be identified as the chief cause of the phase shift between the sunspot numbers and the aa index. The rise in the IMF magnitude, the largest single contributor to the drift in geomagnetic activity, is shown to be caused by a rise in the solar coronal magnetic field, consistent with a rise in the coronal source field, modeled from photospheric observations, and an observed decay in cosmic ray fluxes.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Temperature trends derived from Stratospheric Sounding Unit radiances: the effect of increasing CO2 on the weighting function

Stratospheric Sounding Units (SSU) on the NOAA operational satellites have been the main source of near global temperature trend data above the lower stratosphere. They have been used extensively for comparison with model-derived trends. The SSU senses in the 15 micron band of CO2 and hence the weighting function is sensitive to changes in CO2 concentrations. The impact of this change in weighting function has been ignored in all recent trend analyses. We show that the apparent trends in global mean brightness temperature due to the change in weighting function vary from about -0.4 K/decade to 0.4 K/decade depending on the altitude sensed by the different SSU channels. For some channels, this apparent trend is of a similar size to the trend deduced from SSU data but ignoring the change in weighting function. In the mid-stratosphere, the revised trends are now significantly more negative and in better agreement with model-calculated trends.

Carbon suboxide: the vibrational dependence of the v7 bending potential function

Data on the vibrational energy levels and rotational constants of carbon suboxide for the low-wavenumber bending mode ν7 are reviewed, in the ground-state manifold, and in the ν2-, ν3-, ν4-, and ν2 + ν4-state manifolds. Following the procedure developed by Duckett, Mills, and Robiette [J. Mol. Spectrosc. 63, 249 (1976)] the data have been inverted to give the effective bending potential in ν7 for each of these five states. Values are obtained for various other parameters in the effective vibration-rotation Hamiltonian. The potential and rotational constants in ν2 + ν4 are given to a close approximation by linear extrapolation from the ground state through the ν2 and ν4 states.

Rational conversion of substrate and product specificity in a Salvia monoterpene synthase: structural insights into the evolution of terpene synthase function

Terpene synthases are responsible for the biosynthesis of the complex chemical defense arsenal of plants and microorganisms. How do these enzymes, which all appear to share a common terpene synthase fold, specify the many different products made almost entirely from one of only three substrates? Elucidation of the structure of 1,8-cineole synthase from Salvia fruticosa (Sf-CinS1) combined with analysis of functional and phylogenetic relationships of enzymes within Salvia species identified active-site residues responsible for product specificity. Thus, Sf-CinS1 was successfully converted to a sabinene synthase with a minimum number of rationally predicted substitutions, while identification of the Asn side chain essential for water activation introduced 1,8-cineole and alpha-terpineol activity to Salvia pomifera sabinene synthase. A major contribution to product specificity in Sf-CinS1 appears to come from a local deformation within one of the helices forming the active site. This deformation is observed in all other mono- or sesquiterpene structures available, pointing to a conserved mechanism. Moreover, a single amino acid substitution enlarged the active-site cavity enough to accommodate the larger farnesyl pyrophosphate substrate and led to the efficient synthesis of sesquiterpenes, while alternate single substitutions of this critical amino acid yielded five additional terpene synthases.

Phylogeny, function, and evolution of the cupins, a structurally conserved, functionally diverse superfamily of proteins

The cupin superfamily is a group of functionally diverse proteins that are found in all three kingdoms of life, Archaea, Eubacteria, and Eukaryota. These proteins have a characteristic signature domain comprising two histidine- containing motifs separated by an intermotif region of variable length. This domain consists of six beta strands within a conserved beta barrel structure. Most cupins, such as microbial phosphomannose isomerases (PMIs), AraC- type transcriptional regulators, and cereal oxalate oxidases (OXOs), contain only a single domain, whereas others, such as seed storage proteins and oxalate decarboxylases (OXDCs), are bi-cupins with two pairs of motifs. Although some cupins have known functions and have been characterized at the biochemical level, the majority are known only from gene cloning or sequencing projects. In this study, phylogenetic analyses were conducted on the conserved domain to investigate the evolution and structure/function relationships of cupins, with an emphasis on single- domain plant germin-like proteins (GLPs). An unrooted phylogeny of cupins from a wide spectrum of evolutionary lineages identified three main clusters, microbial PMIs, OXDCs, and plant GLPs. The sister group to the plant GLPs in the global analysis was then used to root a phylogeny of all available plant GLPs. The resulting phylogeny contained three main clades, classifying the GLPs into distinct subfamilies. It is suggested that these subfamilies correlate with functional categories, one of which contains the bifunctional barley germin that has both OXO and superoxide dismutase (SOD) activity. It is proposed that GLPs function primarily as SODs, enzymes that protect plants from the effects of oxidative stress. Closer inspection of the DNA sequence encoding the intermotif region in plant GLPs showed global conservation of thymine in the second codon position, a character associated with hydrophobic residues. Since many of these proteins are multimeric and enzymatically inactive in their monomeric state, this conservation of hydrophobicity is thought to be associated with the need to maintain the various monomer- monomer interactions. The type of structure-based predictive analysis presented in this paper is an important approach for understanding gene function and evolution in an era when genomes from a wide range of organisms are being sequenced at a rapid rate.