Adjoint Methods in Data Assimilation for Estimating Model Error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure. This revised version was published online in July 2006 with corrections to the Cover Date.     

A valuation criterion for normal basis generators in local fields of characteristic p

Let K be a complete local field of characteristic p with perfect residue field, and let L/K be a finite, totally ramified, Galois p-extension with G = Gal(L/K). Let v _L be the normalized valuation with ${v_L(L^{\times})=\mathbb{Z} }Let K be a complete local field of characteristic p with perfect residue field, and let L/K be a finite, totally ramified, Galois p-extension with G = Gal(L/K). Let v _L be the normalized valuation with v_L(L^×)=\mathbbZ {v_L(L^{\times})=\mathbb{Z} }. Let p_L ? L{\pi_L\in L} be a prime element, and let p′ (x) be the derivative of the minimal polynomial for π _L over K. We show that any element r ? L{\rho\in L} with v_L(r) o -v_L(p￠(p_L))-1 mod [L:K]{v_L(\rho)\equiv -v_L(p'(\pi_L))-1\bmod[L:K]} generates a normal basis: K[G]ρ = L. This criterion is tight: Given any integer i with i\not o -v_L(p￠(p_L))-1 mod [L:K]{i\not\equiv -v_L(p'(\pi_L))-1\bmod[L:K]}, there is a r_i ? L{\rho_i\in L} with v _L (ρ _i ) = i such that K[G]r_i\subsetneq L{K[G]\rho_i\subsetneq L}.     

Hypercoordination in triphenyl oxinates of the group 14 elements

The triphenyl oxinates of the group 14 elements (M = Si, Ge, Sn, and Pb) contain the 8-hydroxyquinoline ligand (HOx), which can function in either a bidentate or monodentate fashion. The compounds Ph₃MO_x were prepared by reaction of the triphenylmetal chloride with HOx in the presence of an HCl scavenger triethylamine or, sodium acetate, and in the case of lead, with the sodium salt of 8-hydroxyquinoline. The interaction of the nitrogen with the central atom was studied through the use of the NMR chemical shifts of the central metal atom and the ¹⁵N atom of the ligand. The chemical shifts of the central metal provided evidence that the triphenylgermanium and silicon oxinates are uncoordinated while the triphenyltin and lead oxinates are five-coordinate. These conclusions are confirmed by molecular modeling, ¹⁵N chemical shifts and the metal-¹³C one bond coupling constants at the ipso carbon. The NMR data provides evidence that the strength of the interaction of the nitrogen with the metal increases from silicon and germanium to lead. Two peaks in the 5-coordinate region of the ²⁰⁷Pb NMR spectra can be rationalized with the postulate that strong interaction with lead produces two geometrical isomers. Two peaks were also present in the 5-coordinate region of the ¹¹⁹Sn NMR spectra at low temperatures indicating a rapid exchange between the two geometrical isomers at room temperature.     

A stereodivergent asymmetric approach to difluorinated aldonic acids

A (bromodifluoromethyl)alkyne has been deployed in a stereoselective route to difluorinated aldonic acid analogues, in which a Sharpless asymmetric dihydroxylation reaction and diastereoisomer separation set the stage for phenyl group oxidation.     

Quantifying the reactivity of a remarkably long-lived difluorinated enol in acidic methanol via solution kinetics and electronic structure calculations

A simple enol acetal underwent rapid cleavage in acidic solution to generate a difluorinated enol, which was sufficiently long-lived to be characterized by 2D NMR in a protic solvent at ambient temperature. Density functional theory calculations on a model reaction suggest that there are significant differences in protonation transition state timing between the fluorinated and nonfluorinated enols.     

Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy

Finite element method calculations were carried out to determine extinction spectra and the electromagnetic (EM) contributions to surface-enhanced Raman spectroscopy (SERS) for 90-nm Au nanoparticle dimers modeled after experimental nanotags. The calculations revealed that the EM properties depend significantly on the junction region, specifically the distance between the nanoparticles for spacings of less than 1 nm. For extinction spectra, spacings below 1 nm lead to maxima that are strongly red-shifted from the 600-nm plasmon maximum associated with an isolated nanoparticle. This result agrees qualitatively well with experimental transmission electron microscopy images and localized surface plasmon resonance spectra that are also presented. The calculations further revealed that spacings below 0.5 nm, and especially a slight fusing of the nanoparticles to give tiny crevices, leads to EM enhancements of 10¹⁰ or greater. Assuming a uniform coating of SERS molecules around both nanoparticles, we determined that regardless of the separation, the highest EM fields always dominate the SERS signal. In addition, we determined that for small separations less than 3% of the molecules always contribute to greater than 90% of the signal. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The mechanism of formation of N-formylkynurenine by heme dioxygenases

Heme dioxygenases catalyze the oxidation of L-tryptophan to N-formylkynurenine (NFK), the first and rate-limiting step in tryptophan catabolism. Although recent progress has been made on early stages in the mechanism, there is currently no experimental data on the mechanism of product (NFK) formation. In this work, we have used mass spectrometry to examine product formation in a number of dioxygenases. In addition to NFK formation (m/z = 237), the data identify a species (m/z = 221) that is consistent with insertion of a single atom of oxygen into the substrate during O(2)-driven turnover. The fragmentation pattern for this m/z = 221 species is consistent with a cyclic amino acetal structure; independent chemical synthesis of the 3a-hydroxypyrroloindole-2-carboxylic acid compound is in agreement with this assignment. Labeling experiments with (18)O(2) confirm the origin of the oxygen atom as arising from O(2)-dependent turnover. These data suggest that the dioxygenases use a ring-opening mechanism during NFK formation, rather than Criegee or dioxetane mechanisms as previously proposed.     

Gold-catalyzed rearrangement of substituted allyl aryl ethers

Triphenylphosphinegold(I) complexes catalyze the Claisen-type rearrangement of aryl allyl ethers to the corresponding branched and linear products. The product distribution depends on the olefin geometry of the allylic ether. Stereochemical transfer experiments support an ionic mechanism.     

Investigation of fluid dynamics within a miniature mixed flow blood pump

An oil dot flow visualization method was utilized in conjunction with a traditional light sheet particle tracer method to investigate internal flow dynamics of a miniature mixed-flow blood pump. The effects of the operating condition and impeller design on the internal fluid dynamics and hydrodynamic performance were studied. The oil dot method enabled analysis of separated and disturbed flow within the highly wrapped rotating-blade passages – previously imperceptible with light sheet methods. The blade wrap was found to be critical to providing a favorable fluid dynamics for blood pumping over a range of off-design conditions. The low flow operating conditions were found to have a detrimental effect on blood flow. Received: 13 september 2000 / Accepted: 3 April 2001