Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity - I. Fundamental solutions

This work examines the propagation of time harmonic, horizontally polarized shear waves through a naturally occurring heterogeneous medium that exhibits viscous behaviour as well as random fluctuations of its elastic modulus about a mean value. As a first step, the governing equation, which is a heterogeneous Helmholtz equation, is solved using algebraic transformations and the relevant Green's function is obtained for two sets of boundary conditions, one corresponding to a finite depth layer and the other to an infinite layer. Viscous material behaviour is introduced by considering the depth-dependent elastic modulus to be a complex quantity. Subsequently, material stochasticity in the medium is handled through the perturbation approach by assuming that the elastic modulus has a small random fluctuation about its mean value. The final results are closed-form expressions for the mean value and covariance matrix of both the wave speed profile in the medium and the corresponding Green's function. In Part II, (Soil Dynam. Earth. Engng, 1996,15, 129-39), two examples concerning seismic wave propagation in soft topsoil and in sandstone serve to illustrate the methodology and comparisons are made with Monte Carlo simulations.     

A SIMPLIFIED APPROACH TO MODELING 3D SEDIMENT-LADEN TURBULENT FLOWS

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Application of particle dynamics to derive a general circulation in low latitudes

Summary In Section 1 are set out the reasons for the use of particle dynamics in this investigation. In Section 2 are solved the equations of motion for particles constrained to move along a horizontal surface under the action of a constant meridional pressure gradient force to obtain (a) velocities in spherical polar co-ordinates with naturally varying Coriolis terms, and (b) velocities and trajectories in plane cartesian co-ordinates in which the Coriolis parameter is assumed constant. Results obtained in each system are compared, showing that the plane co-ordinates as used are not significantly inaccurate, and trajectories of air particles obtained by application significantly inaccurate, and trajectories of air particles obtained by application of this system in steps of 5° of latitude are plotted to show the production of belts of convergence at some distance from the equator under the action of meridional pressure gradient forces.The approximation of these idealised particle trajectories to actual streamlines of the air flow are discussed in Section 3, and the concept of the production of belts of convergence is used to formulate a theory of formation and maintenance of the sub-tropical anticyclones. In Section 4 this theory is applied to observed average temperature data and the calculated results compared with observed average pressure data. A possible synoptic application of the theory is then indicated in Section 5.

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Zusammenfassung Im ersten Abschnitt werden Gründe für die Anwendung der Dynamik von Massenteilchen in der vorliegenden Arbeit dargelegt. Abschnitt 2 enthält die Lösungen der Gleichungen für die Bewegung von Massenteilchen auf horizontalen Flächen unter der Einwirkung eines konstanten meridionalen Druckgradienten. Die Lösungen ergeben a) die Geschwindigkeiten in sphärischen Polarkoordinaten mit variablem Coriolis-Term (entsprechend natürlichen Verhältnissen) und b) Geschwindigkeiten und Trajektorien in ebenen kartesischen Koodinaten in denen der Coriolis-Parameter als konstant angenommen wird. Die Ergebnisse für beide Koordinatensysteme werden verglichen und es zeigt sich, daß bei Verwendung der ebenen Koordinaten keine wesentlichen Ungenauigkeiten auftreten. Zeichnet man schrittweise von 5 zu 5° (Fig. 1) die Trajektorien der Luftteilchen, so ergeben sich als Folge der meridionalen Druckgradienten Konvergenzzonen in einigem Abstand vom Äquator.Die Annäherung dieser idealisierten Trajektorien an tatsächliche Stromlinien der Luft wird in Abschnitt3 diskutiert. An Hand der Vorstellungen von der Entstehung der Konvergenzzonen wird eine Theorie der Entstehung und Erhaltung subtropischer Antizyklonen gegeben. Im vierten Abschnitt wird diese Theorie auf beobachtete Mitteltemperaturen angewendet und die Ergebnisse der Berechnung werden mit beobachteten mittleren Luftdruckwerten verglichen. Auf eine mögliche synoptische Anwendung der vorliegenden Ergebnisse wird in Abschnitt 5 hingewiesen.

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Résumé La première partie contient les motifs de l'emploi de la dynamique de points pesants dans la présente étude. La deuxième partie donne les solutions des équations du mouvement de points pesants sur des surfaces horizontales sous l'effet d'un gradient méridien constant. Ces solutions fournissent les vitesses en coordonnées polaires sphériques avec un terme Coriolis variable, ainsi que les vitesses et les trajectoires en coordonnées cartésiennes planes en admettant un paramètre de Coriolis constant. On compare les résultats pour les deux systèmes de coordonnées et l'on constate que l'emploi des coordonnées planes n'introduit pas d'erreurs appréciables. Si l'on dessine les trajectoires de 5 en 5 degrés on voit apparaître des zones de convergence à quelque distance de l'équateur par suite des gradients méridiens.Dans la troisième partie on discute la similitude plus ou moins grande de ces trajectoires idéalisées avec les lignes de courant réelles. Parant de l'origine possible des zones de convergence, on établit une théorie de l'origine et du maintien des anticyclones subtropicaux. Dans la quatrième partie on applique cette théorie aux températures moyennes observées et l'on compare les résultats avec les valeurs moyennes observées de la pression. Dans la cinquième partie enfin on montre l'application possible des résultats obtenus à la synoptique.

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This paper is published with the permission of the Director of the meteorological Office.     

Lunar behaviour of boron contrasted with the terrestrial boron cycle

Abstract— Fifty-eight lunar rocks have been analysed by prompt gamma neutron activation for B, Gd and Sm. The data were interpreted together with published analyses for Li and other elements. The behaviour of B in lunar rocks is virtually identical to that of Sm, Gd, Li and the other incompatible LIL (Large Ion Lithophile) and HFS (High Field Strength) elements, collectively known as the KREEP component. To a first approximation, the distribution of B concentrations in all lunar rocks can be described as a two-component mixture of KREEP, with ～32 ppm, and B-free mare basalts and anorthositic rocks. The lunar B abundance, estimated from correlations with other KREEP elements, is ～0.14 ppm. Alpha-track images of the analysed lunar rocks were made from thin sections specially prepared to avoid contamination from terrestrial B. They provided surprising evidence that the distributions of B and Li within individual rocks fall into four categories: (1) substitution in mineral structures; (2) in irregular minute particles, disseminated through the rock with no apparent connection with mineralogy; (3) as aggregate properties of rock fragments, acquired prior to assembly in a breccia; and, (4) as aggregate properties of a breccia matrix, distinct from unaffected clasts. Only category (1) is encountered in terrestrial rocks. Categories (2), (3) and (4) become progressively more important as the abundance of KREEP components increases, and it is concluded that the alpha-track images probably show the localisation of not only B and Li but all the KREEP elements. In terrestrial rocks, such textures could be understood in terms of successive episodes of permeation by solutions followed by brecciation, then cementation. It is difficult to adapt such a mechanism to a dry Moon, with brecciation imposed by impact melting. The linear correlation of lunar B and Gd contrasts strongly with the relationship seen in terrestrial rocks, where the presence of water creates a terrestrial B cycle quite different from that of Gd and other lunar incompatible elements.     

Large Magellanic Cloud Planetary Nebula Morphology: Probing Stellar Populations and Evolution

Planetary nebulae (PNe) in the Large Magellanic Cloud (LMC) offer the unique opportunity to study both the population and evolution of low- and intermediate-mass stars, by means of the morphological type of the nebula. Using observations from our LMC PN morphological survey, and including images available in the Hubble Space Telescope Data Archive and published chemical abundances, we find that asymmetry in PNe is strongly correlated with a younger stellar population, as indicated by the abundance of elements that are unaltered by stellar evolution (Ne, Ar, and S). While similar results have been obtained for Galactic PNe, this is the first demonstration of the relationship for extragalactic PNe. We also examine the relation between morphology and abundance of the products of stellar evolution. We found that asymmetric PNe have higher nitrogen and lower carbon abundances than symmetric PNe. Our two main results are broadly consistent with the predictions of stellar evolution if the progenitors of asymmetric PNe have on average larger masses than the progenitors of symmetric PNe. The results bear on the question of formation mechanisms for asymmetric PNe-specifically, that the genesis of PNe structure should relate strongly to the population type, and by inference the mass, of the progenitor star and less strongly on whether the central star is a member of a close binary system.     

The effects of rock uplift and rock resistance on river morphology in a subduction zone forearc,Oregon, USA

Relationships between riverbed morphology, concavity, rock type and rock uplift rate are examined to independently unravel the contribution of along-strike variations in lithology and rates of vertical deformation to the topographic relief of the Oregon coastal mountains. Lithologic control on river profile form is reflected by convexities and knickpoints in a number of longitudinal profiles and by general trends of concavity as a function of lithology. Volcanic and sedimentary rocks are the principal rock types underlying the northern Oregon Coast Ranges (between 46°30′ and 45°N) where mixed bedrock–alluvial channels dominate. Average concavity, θ, is 0·57 in this region. In the alluviated central Oregon Coast Ranges (between 45° and 44°N) values of concavity are, on average, the highest (θ = 0·82). South of 44°N, however, bedrock channels are common and θ = 0·73. Mixed bedrock–alluvial channels characterize rivers in the Klamath Mountains (from 43°N south; θ = 0·64). Rock uplift rates of ≥0·5 mm a⁻¹, mixed bedrock–alluvial channels, and concavities of 0·53–0·70 occur within the northernmost Coast Ranges and Klamath Mountains. For rivers flowing over volcanic rocks θ = 0·53, and θ = 0·72 for reaches crossing sedimentary rocks. Whereas channel type and concavity generally co-vary with lithology along much of the range, rivers between 44·5° and 43°N do not follow these trends. Concavities are generally greater than 0·70, alluvial channels are common, and river profiles lack knickpoints between 44·5° and 44°N, despite the fact that lithology is arguably invariant. Moreover, rock uplift rates in this region vary from low, ≤0·5 mm a⁻¹, to subsidence (<0 mm a⁻¹). These observations are consistent with models of transient river response to a decrease in uplift rate. Conversely, the rivers between 44° and 43°N have similar concavities and flow on the same mapped bedrock unit as the central region, but have bedrock channels and irregular longitudinal profiles, suggesting the river profiles reflect a transient response to an increase in uplift rate. If changes in rock uplift rate explain the differences in river profile form and morphology, it is unlikely that rock uplift and erosion are in steady state in the Oregon coastal mountains. Copyright © 2006 John Wiley & Sons, Ltd.     

The community morphology of skilled migration: the changing role of voluntary and community organisations (VCOs) in the grounding of British migrant identities in Paris (France)

Research into skilled migrant communities tends to emphasize the grounding of identities through transnationalism and mobility. Less research has been conducted into how skilled migrants actually ground their identities within the city through everyday social networks. The paper addresses this imbalance by examining the changing significance of British voluntary and community organisations (VCOs) in Paris, France. Combining qualitative and quantitative data, findings show local migrant networks to be important focal points for the British even though migrants’ lives may increasingly be transnational in orientation. The research also shows that in situ social networks are evolving. Specifically, traditional forms of elite expatriate communality are not as omnipotent as they once were, with the popularity of some high-profile British VCOs in Paris declining over recent decades. The paper argues that the link between social dynamism and communal morphology helps explain this shift: as British middle-class lifestyles have fragmented, and as the British migrant population in Paris has grown in scale and scope, so the range of VCOs and associated informal networks has grown. Whilst some skilled migrants still embed within traditional expatriate organisations, Britishness is increasingly grounded elsewhere; both within the city through alternative social networks, and located beyond the city through transnational ties.