Flexural waves in drill‐string tubulars with variable loads

We revisit the equations governing the bending motions in thin rods and analyse the filtration of flexural waves in vertical drill strings pre‐stressed by gravity. The aim is to study transverse drill‐string vibrations at seismic frequencies for acoustic communication purposes and provide an algorithm for processing reflected and transmitted bending motions generated by downhole lateral vibrations. We obtain the dispersion equation, including attenuation due to a gravity pre‐stress gradient and frequency‐dependent reflection and transmission coefficients at the interface between subsequent tube intervals. We then develop a propagation‐matrix algorithm to simulate flexural waves in a drill string consisting in an assembly of multiple tube sections of different dimensions. The deflection vibrations are obtained at any arbitrary recording point in the drill string. The modelling is cross‐checked with a full‐wave grid algorithm. The analysis shows that the waves produced by a concentrated force are partitioned in standing and propagating modes, which are calculated by using the flexural impedance of the drill string. Moreover, the reflection coefficients weakly depend on the pre‐stress conditions and pre‐stress has important effects for far‐field signal transmission with variable weight on bit (WOB). We discuss the approximations and limits of the method with respect to realistic drilling conditions.     

A probabilistic approach for the prediction of seismic resilience of bridges

This paper proposes a probabilistic approach for the pre‐event assessment of seismic resilience of bridges, including uncertainties associated with expected damage, restoration process, and rebuilding/rehabilitation costs. A fragility analysis performs the probabilistic evaluation of the level of damage (none, slight, moderate, extensive, and complete) induced on bridges by a seismic event. Then, a probabilistic six‐parameter sinusoidal‐based function describes the bridge functionality over time. Depending on the level of regional seismic hazard, the level of performance that decision makers plan to achieve, the allowable economic impact, and the available budget for post‐event rehabilitation activities, a wide spectrum of scenarios are provided. Possible restoration strategies accounting for the desired level of resilience and direct and indirect costs are investigated by performing a Monte Carlo simulation based on Latin hypercube sampling. Sensitivity analyses show how the recovery parameters affect the resilience assessment and seismic impact. Finally, the proposed approach is applied to an existing highway bridge located along a segment of I‐15, between the cities of Corona and Murrieta, in California. Copyright © 2013 John Wiley & Sons, Ltd.     

Statistical assessment of air quality interventions

This paper presents a general spatio-temporal model for assessing the air quality impact of environmental policies which are introduced as abrupt changes. The estimation method is based on the EM algorithm and the model allows to estimate the impact on air quality over a region and the reduction of human exposure following the considered environmental policy. Moreover, impact testing is proposed as a likelihood ratio test and the number of observations after intervention is computed in order to achieve a certain power for a minimal reduction. An extensive case study is related to the introduction of the congestion charge in Milan city. The consequent estimated reduction of airborne particulate matters and total nitrogen oxides motivates the methods introduced while its derivation illustrates both implementation and inferential issues.     

Unraveling the Schneeberg garnet puzzle: a numerical model of multiple nucleation and coalescence

A quantitative kinetic model for the growth of the different garnet porphyroblast microstructures (type 1 and type 2) of the Western Schneeberg Complex (WSC) is presented. These porphyroblasts formed by a multiple nucleation and coalescence mechanism. Our numerical simulation shows that at constant diffusion rates: (1) low interface reaction rates result in a fully amalgamated porphyroblast (type 2); (2) intermediate reaction rates result in a porphyroblast, where coalescence of grains closer to the margin prevented amalgamation of those in the centre (similar to type 1 porphyroblasts); and (3) high interface reaction rates result in a porphyroblast microstructure with an atoll form. All three microstructures are characterised by distinctive cluster size distributions. A 2-D cluster size distribution analysis of type 1 porphyroblasts of WSC shows that these did not form because of intermediate interface reaction rates, but because the diffusion rate of nutrients was too low to keep pace with the interface reaction rate.Editorial responsibility: T.L. Grove     

EUDOSSO: a space project for solar oscillations and long term variability relevant to climatic changes

The basic design and the scientific aims of the EUDOSSO project are described. EUDOSSO is a space instrument conceived for achieving very high accuracy and long term stability in measuring solar diameter time variations. Therefore it is suitable for measuring long periodg-modes, oblateness and long-term diameter variations possibly relevant to climatic changes.     

On a relation among lie series

In this paper we discuss the relation between the structures of the series expansion for the Dragt and Finn composition of Lie transforms and for a transformation introduced by Giorgilli and Galgani. A recursive algorithm is presented which is used to generate the series expansion for the composition of Lie transforms. This algorithm strongly resembles the algorithm of Giorgilli and Galgani, and differs from it only in an ordering property. The relation with the algorithms of Kamel and Henrard for Deprit's direct and inverse series is also discussed.     

Topological vector spaces of harmonic functions and the trace operator

Many problems in physical geodesy can be formulated in terms of boundary-value problems (BVPs) for the gravitational potential; many of them can be ultimately formulated as a Dirichlet problem. For this reason, there is a flourishing literature of geodetic contributions to potential theory. In this paper, the authors pick up some classical arguments from the mathematical analysis of BVPs and show, by using only Hilbert spaces of harmonic functions, how they can be systematically cast into a functional scheme clarifying the role of duality when dealing with the harmonic subspaces of classical Sobolev spaces, of any real order. The analysis is here restricted to the case of functions harmonic in spherical domains to make the results transparent and more readable by geodesists. A further step is then taken showing how to generalize the Dirichlet problem for the space of all the functions that are harmonic outside a sphere, which exploits the more general theory of Fréchet topological spaces. Basically, the result is that any functions harmonic in the exterior of a sphere can be uniquely identified by a suitably defined trace on the sphere. The paper concludes with comments and discussion of future work.