Weak constraints in four-dimensional variational data assimilation

The formulation of four-dimensional variational data assimilation allows the incorporation of constraints into the cost function which need only be weakly satisfied. In this paper we investigate the value of imposing conservation properties as weak constraints. Using the example of the two-body problem of celestial mechanics we compare weak constraints based on conservation laws with a constraint on the background state.We show how the imposition of conservation-based weak constraints changes the nature of the gradient equation. Assimilation experiments demonstrate how this can add extra information to the assimilation process, even when the underlying numerical model is conserving.

Devolution and the political representation of business interests in the UK

The devolution of political power in Scotland, Wales and Northern Ireland and the developing regional agenda in England are widely read as a significant reconfiguration of the institutions and scales of economic governance. The process is furthest developed in Scotland while Wales and Northern Ireland, in their own distinct ways, provide intermediate cases. Devolution is least developed in England where regional political identities are generally weak and the historical legacy of regional institutions is limited. Within the overall context of devolution government policy has continued to emphasize partnership forms of. governance. Accordingly, the political representation of business interests has a particular salience in the new arrangements. This paper reports on findings from a study designed to examine the relationship between devolution and changes in the political representation of business interests in the territories and regions of the UK. It highlights a number of changes in the nature and extent of business representation. While some of these are significant the evidence suggests that they fail to mark a fundamental shift in the institutional foundation for sub-national business interest representation in the UK. Indeed the political geography of business representation remains dominated by an overarching centralism that is likely to provide a significant check on the further devolution of political power and democratic authority. (c) 2004 Elsevier Ltd. All rights reserved.

Devolution and the political representation of business interests in the UK

The devolution of political power in Scotland, Wales and Northern Ireland and the developing regional agenda in England are widely read as a significant reconfiguration of the institutions and scales of economic governance. The process is furthest developed in Scotland while Wales and Northern Ireland, in their own distinct ways, provide intermediate cases. Devolution is least developed in England where regional political identities are generally weak and the historical legacy of regional institutions is limited. Within the overall context of devolution government policy has continued to emphasize partnership forms of. governance. Accordingly, the political representation of business interests has a particular salience in the new arrangements. This paper reports on findings from a study designed to examine the relationship between devolution and changes in the political representation of business interests in the territories and regions of the UK. It highlights a number of changes in the nature and extent of business representation. While some of these are significant the evidence suggests that they fail to mark a fundamental shift in the institutional foundation for sub-national business interest representation in the UK. Indeed the political geography of business representation remains dominated by an overarching centralism that is likely to provide a significant check on the further devolution of political power and democratic authority. (c) 2004 Elsevier Ltd. All rights reserved.

How to save a bad element with weak boundary conditions

The P-1-P-1 finite element pair is known to allow the existence of spurious pressure (surface elevation) modes for the shallow water equations and to be unstable for mixed formulations. We show that this behavior is strongly influenced by the strong or the weak enforcement of the impermeability boundary conditions. A numerical analysis of the Stommel model is performed for both P-1-P-1 and P-1(NC)-P-1 mixed formulations. Steady and transient test cases are considered. We observe that the P-1-P-1 element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes. (c) 2005 Elsevier Ltd. All rights reserved.

Vibration–rotation variational calculations: precise results on HCN up to 25 000 cm−1

Variation calculations of the vibration–rotation energy levels of many isotopomers of HCN are reported, for J=0, 1, and 2, extending up to approximately 8 quanta of each of the stretching vibrations and 14 quanta of the bending mode. The force field, which is represented as a polynomial expansion in Morse coordinates for the bond stretches and even powers of the angle bend, has been refined by least squares to fit simultaneously all observed data on the Σ and Π state vibrational energies, and the Σ state rotational constants, for both HCN and DCN. The observed vibrational energies are fitted to roughly ±0.5 cm−1, and the rotational constants to roughly ±0.0001 cm−1. The force field has been used to predict the vibration rotation spectra of many isotopomers of HCN up to 25 000 cm−1. The results are consistent with the axis‐switching assignments of some weak overtone bands reported recently by Jonas, Yang, and Wodtke, and they also fit and provide the assignment for recent observations by Romanini and Lehmann of very weak absorption bands above 20 000 cm−1.