Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.

The Topological Analysis of the ELFx Localization Function: Quantitative Prediction of Hydrogen Bonds in the Guanine–Cytosine Pair

In this contribution, we recall and test a new methodology designed to identify the favorable reaction pathway between two reactants. Applied to the formation of the DNA guanine (G) –cytosine (C) pair, we successfully predict the best orientation between the base pairs held together by hydrogen bonds and leading to the formation of the typical Watson Crick structure of the GC pair. Beyond the global minimum, some local stationary points of the targeted pair are also clearly identified.

Linarite from Cap Garonne

Linarite, PbCuSO4(OH)2, crystallizes as secondary mineral in form of clusters of crystals in Mine du Pradet at Cap Garonne in France. A tiny single crystal was isolated and its structure was refined from synchrotron diffraction data (λ = 0.049592 nm): P121/m1, a = 467.75(2), b = 563.48(4), c = 967.64(5) pm, β = 102.647(5)°, wR = 0.0544, 819 F 2 values and 56 variables. The proton positions were also refined. The Cu2+ cations are located within Cu(OH)2 ribbons and exhibit pronounced Jahn-Teller distortion (d(Cu–O): 2 × 191.9, 2 × 197.3 and 2 × 252.8 pm). The Cu(OH)2 ribbons are condensed with the sulfate tetrahedra and the lead cations. The latter are coordinated to eight oxygen atoms in a slightly anisotropic manner. Calculations of the electron localization function (ELF) of PbO (litharge), PbSO4 (anglesite) and PbCuSO4(OH)2 (linarite) show pronounced lone-pair character for PbO but rather isotropic ELF values around the lead cations in PbSO4 and PbCuSO4(OH)2.

Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz ’96 system

Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari-Cohn localization function; the within-component localization functions are standard Gaspari-Cohn with different localization radii while the cross-localization function is newly constructed. The functions produce non-negative definite localization matrices, which are suitable for use in variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiment the multivariate Gaspari-Cohn function leads to better performance than any of the other localization functions.

Topological Unraveling the [3+2] Cycloaddition (32CA) Reaction between N-Methylphenylnitrone and Styrene Catalyzed by Chromium Tricarbonyl Complex from Electron Localization Function and Catastrophe Theory.

We have investigated the reaction mechanisms of [3+2] cycloaddition (32CA) between N-methylphenylnitrone and styrene catalyzed by chromium tricarbonyl complex at the MPWB1K/6-311G(d,p) level of approximation. Activation energy analysis reveals that...