A new approach for calculating strain for particulate media

Discrete element modelling is a viable alternative to conventional continuum‐based analysis for analysing problems involving localized deformations of particulate media. However, to aid in the interpretation of the results, it is useful to express the results of discrete element analyses in terms of the continuum parameters of stress and strain. A number of homogenization methods have been proposed to calculate strain in discrete systems; however, two significant limitations of these methods remain. First, none of these methods incorporate particle rotation effects satisfactorily, although significant particle rotation occurs in shear bands in both physical tests and numerical simulations of granular materials. Additionally, observations of the particle displacement fields in shear bands in granular materials indicate that the displacements within the localizations are erratic. Consequently, existing linear, local interpolation approaches produce substantial variations in the strain values calculated in adjacent elements in the region of localization, hindering clear visualization of the strain localization as it evolves. A new method of domain discretization for calculating strain is proposed. This method is capable of capturing particle rotation and employs a non‐local meshfree interpolation procedure capable of smoothing the erratic displacements in strain localizations, which better defines their evolution. The proposed method is validated for problems involving both two and three dimensions. A number of methods are compared with the proposed method and pertinent insights are made. Copyright © 2003 John Wiley & Sons, Ltd.     

Contrasting stratified plutons exposed in tilt blocks, Eldorado Mountains, Colorado River Rift, NV, USA

Roof-to-floor exposures of mid-Miocene plutons in tilt blocks south of Las Vegas, NV, reveal distinct but strongly contrasting magma chamber statigraphy. The Searchlight and Aztec Wash plutons are well-exposed, stratified intrusions that show a similar broad range in composition from 45–75 wt.% SiO₂. Homogeneous granites that comprise about one-third of each intrusion are virtually identical in texture and elemental and isotopic chemistry. Mafic rocks that are present in both plutons document basaltic input into felsic magma chambers. Isotopic compositions suggest that mafic magmas were derived from enriched lithospheric mantle with minor crustal contamination, whereas more felsic rocks are hybrids that are either juvenile basaltic magma+crustal melt mixtures or products of anatexis of ancient crust+young (Mesozoic or Miocene?) mafic intraplate.

Despite general similarities, the two plutons differ markedly in dimensions and lithologic stratigraphy. The Searchlight pluton is much thicker (10 vs. 3 km) and has thick quartz monzonite zones at its roof and floor that are absent in the Aztec Wash pluton. Isotopic and elemental data from Searchlight pluton suggest that the upper and lower zones are cogenetic with the granite; we interpret the finer grained, slightly more felsic upper zone to represent a downward migrating solidification front and the lower zone to be cumulate. In contrast, the upper part of the Aztec Wash pluton is granite, and a heterogeneous, mafic-rich injection zone with distinct isotopic chemistry forms the lower two-thirds of the intrusion. Similar mafic rocks are relatively sparse in Searchlight pluton and do not appear to have played a central role in construction of the pluton. Large felsic and composite dikes that attest to repeated recharging and intrachamber magma transfer are common in the Aztec Wash pluton but absent in the Searchlight pluton. Thus, although both intrusions were filled by similar magmas and both developed internal stratification, the two intrusions evolved very differently. The distinctions may be attributable to scale and resulting longevity and/or to subtle differences in tectonic setting.     

Transnational elites in global cities: British expatriates in Singapore's financial district

Skilled international migration is as an important process of both contemporary globalization and the global city. The establishment of a transnational elite of expatriate labour in international finance plays a vital part in the accumulation of capital within international financial centres (IFCs). Expatriate labour has become a major determinant of the IFC, creating financial capital through complex social relations, knowledge networks, practices and discourses. The principal argument being made in this paper is that expatriates are major agents in the accumulation and transfer of financial knowledge in the IFC, and that such processes are undertaken through expatriate global–local knowledge networks and other social practices. The paper is divided into three major parts. Following a discussion of transnational elites as expatriates in global cities, which also conceptualises their contribution to the spatialization of financial knowledge networks, the empirical study investigates the working, social and cultural knowledge networks and practices of British expatriates in Singapore. Finally, the paper revisits the conceptual work on transnational elites and suggests that expatriates were deeply embedded in global–local relations in the workplace and the business/social sphere through interaction with local ‘western educated/experienced' Singaporeans, but were disembedded from the local in the home and other household social spaces due to the invisibility of the local population in their interactions. Both the theoretical and empirical analyses suggests that expatriates are flow in the Castellian spatial logic of the network society.     

Experimental constraints on major and trace element partitioning during partial melting of eclogite

Isobaric partial melting experiments were performed on an Fe-free synthetic composition to simulate partial melting of subducted oceanic crust. Nominally anhydrous experiments at 3.0 GPa yielded melts in equilibrium with garnet (13 to 16 mol.% grossular) and aluminous clinopyroxene (14 to 16 wt.% Al₂O₃). Melt compositions show decreasing Si and alkalis and increasing Ca, Mg, and Ti contents with increasing temperatures. Experiments at 1200 and 1300°C were rutile saturated, whereas experiments at 1400°C contained no residual rutile. We argue that during the initial stages of subduction, accessory rutile is likely to be stable in subsolidus eclogites of average midocean ridge basalt composition and that only large degrees of partial melting will eradicate rutile from an eclogitic source. At 3 GPa, any eclogites with a bulk TiO₂ content of ≥1.5 wt.% rutile will produce rutile-saturated partial melts, except at very high degrees of melting. At higher pressures, all bulk Ti may dissolve in clinopyroxene and garnet, leaving no accessory rutile.Trace element partition coefficients for 24 trace elements between clinopyroxene, garnet, and melt were determined by secondary-ion mass spectrometry analysis of experimental run products at 1400°C and 3 GPa. Partition coefficients for the rare earth elements agree well with previous studies and have been evaluated using the lattice strain model. Partitioning data for high-field strength elements indicate complementary D_Zr/D_Hf for clinopyroxene and garnet. Partial melting of an eclogitic component of different modal compositions may therefore explain both subchondritic and superchondritic Zr/Hf ratios. Superchondritic Zr/Hf has recently been observed in some ocean island basalts (OIB), and this may be taken as further evidence for components of recycled oceanic crust in OIB. The data also indicate slight Nb/Ta fractionation during partial melting of bimineralic eclogite, which is not, however, sufficient to explain some recently observed Nb/Ta fractionation in island arc rocks. Accessory rutile, however, can explain such fractionation.     

Os isotopes in mantle xenoliths from the Eifel volcanic field and the Vogelsberg (Germany): age constraints on the lithospheric mantle

The effects of mantle metasomatism on the sulfide phase in mantle xenoliths in general, and on the Os isotopic system in particular, have received increased attention in recent years. Here, we report on Os isotopic systematics of metasomatized mantle xenoliths from the late Quaternary Eifel (Dreiser Weiher and Meerfelder Maar) and neighboring Vogelsberg volcanic fields, which provide insight into the effects of melt extraction and metasomatism on Os isotopes and place constraints on the evolution of the lithospheric mantle component beneath central Europe. Sixteen harzburgite, lherzolite, and pyroxenite xenoliths from the Eifel and two lherzolite xenoliths from the Vogelsberg were analyzed for Os isotopes. Samples from the anhydrous peridotite suite (Ib) are highly variable in their Os isotopes, ranging from subchondritic values (¹⁸⁷Os/¹⁸⁸Os=0.1236) to suprachondritic values (¹⁸⁷Os/¹⁸⁸Os=0.1420), indicating that some of these samples have been overprinted by the addition of radiogenic Os and have lost the primary mantle Os that was presumably present. The suprachondritic values suggest a source for this Os in a reservoir with a time-integrated Re/Os ratio greater than that of the bulk Earth. Eifel samples with Os contents >1.5 ng/g from the hydrous suite (Ia) have relatively unradiogenic Os isotope compositions (¹⁸⁷Os/¹⁸⁸Os=0.1208-0.1237) and Al₂O₃-Os isotopic systematics consistent with ancient melt depletion and isolation from the convecting asthenospheric mantle for time periods similar to the age of the overlying crust (~1.5 Ga) as well with results from peridotite massifs in the European region. The LREE-metasomatism and the enrichment of Os (up to 6.47 ng/g) and As (sulfide metasomatism?) in the hydrous suite is strongly inversely correlated with the Os isotope ratios, demonstrating that mantle processes such as metasomatism can significantly modify the Os isotope chemistry of mantle xenoliths.     

Partitioning of fluorine and chlorine between biotite and granitic melt: experimental calibration at 200 MPa H2O

Experiments from 640 to 680?°C, 200 MPa H₂O at?f _O2?≈?NNO, employing a natural?F-rich?vitrophyric rhyolite from Spor Mountain, Utah, assessed the effect of variable Mg′ [100Mg/(Mg?+?Mn?+?Fe)] on the partitioning of fluorine and chlorine between biotite (Bt) and melt. Over this temperature interval, Bt (?±?fluorite, ?±?quartz) is the sole liquidus phase. Partition coefficients for fluorine between biotite and glass (D_F ^Bt/melt) show a strong dependence on the Mg′ of Bt.?D_F ^Bt/melt varies from???1.5 to 7.2 over the range of Mg′ from 21 to 76. A strong linear correlation between?D_F ^Bt/melt?and Mg′ has a slope of 9.4 and extrapolates through the origin (i.e., D_F ^Bt/melt?≈?0 at Mg′?=?0, an annite-siderophyllite solid solution in these experiments). D_Cl ^Bt/melt values (???1 to 6) in the same experiments vary inversely with Mg′. The Al-content of biotite does not vary with the aluminum saturation index (ASI?=?molar Al₂O₃/Σ alkali and alkaline earth oxides) of melt, but two exchange mechanisms involving Al appear to operate in these micas: (1) Al^vi?+?Al^iv?? Si^iv?+?Mg^iv, and Mg^iv?+?2Al^iv? 2Si^iv?+?□^iv. The effects of other components such as Li or other intensive parameters including f _O2 have yet to be evaluated?systematically. At comparable Mg′ of Bt, however, the Spor Mountain rhyolite yields higher D_F ^Bt/melt values than an Li-rich, strongly peraluminous melt previously investigated. The results indicate that the Mg′ of Bt exerts the principal control on halogen partitioning, with ASI and T as second-order variables. The experimental partition coefficients compare well with other experimental results but not with most volcanic rocks. Magmatic Bt from most rhyolites records higher D_F ^Bt/melt due to reequilibration with degassed (H₂O-depleted) magma and perhaps with F₂O_?1 exchange that may accompany oxidation ([Fe³⁺O] [Fe²⁺OH]_?1). This behavior is evident in magmatic biotite from a zoned peraluminous rhyolite complex near Morococala, Bolivia: Bt is sharply zoned with F-rich rims, but Bt(core)-melt inclusion pairs fall on our experimental curve for D_F ^Bt/melt. These experimental data can be used in part to assess the preservation of magmatic volatile contents in plutonic or volcanic silicic rocks. For plutonic rocks, the actual F-content of melt, not a relative activity ratio involving HF species, can be reasonably estimated if the mica has not undergone subsolidus reequilibration. This information is potentially useful for some shallow-level Ca-poor magmas that are thought to be rich in F (e.g., A- and S-type granites) but do not conserve F well as rocks.     

Trace-element and stable-isotope geochemistry of non-marine ostracod shells in Quaternary palaeoenvironmental reconstruction

Ostracods are small bivalved aquatic crustancean. They secrete shells of low-Mg calcite that are often preserved in lake sediments. Recent work has shown that the uptake of trace elements (especially Mg and Sr) into the shell may be a function of the salinity and temperature of the host water. Furthermore, ostracod shells are a source of carbonate for stable-isotope analysis. This paper reviews the application of ostracod shell chemistry to Quaternary palaeolimnology. Although such work has revealed the excellent potential of these techniques to provide quantitative palaeolimnological reconstructions, a number of problems have also emerged. These problems relate to (1) methods used for extraction of ostracod shells from sediment and their subsequent cleaning (2) post-mortem diagenesis and alteration of the shell (3) complications with the calcification mechanism (4) spatial and temporal variability in shell composition (5) the ecological tolerances of individual species and (6) the relationships between shell chemistry and palaeohydrology. To some extent, these problems are an inevitable outcome of the diversity of lacustrine systems: they may be overcome by developing a thorough understanding of the physiology, life-cycle and ecology of the species concerned, together with the modern limnology of the study site. Overall, these techniques have excellent potential in Quaternary palaeolimnology, especially when used with other palaeoenvironmental indicators.     

Intraplate uplift: new constraints on the Hoggar dome from the Illizi basin (Algeria)

Zones of anomalously high topography within continental interiors, distant from active plate boundaries, are interpreted as being either dynamically supported by viscous flow in the underlying mantle or influenced by plate tectonics. Constraining the models of their genesis requires accurate data on the timing and dimensions of such features. New apatite fission‐track and thermal maturity data from the Illizi Basin in Algeria quantify the magnitude and timing of kilometre–scale uplift and exhumation of the northern flank of the Hoggar swell in North Africa. The findings of this study, integrated with previously published thermochronological data, confirm that long‐wavelength regional uplift occurred during the Cenozoic extending over a distance in excess of 1500 km from north to south. The uplift, centred on the Hoggar Massif, significantly impacted the flanking Illizi and Tim Mersoï basins. The combination of thermal history modelling and regional stratigraphic observations indicates that the onset of exhumation of the Illizi Basin likely occurred during the Eocene, broadly coincident with magmatism on the Hoggar Massif to the south and the onset of tectonic shortening in the Atlasic belt to the north.     

Unbundling Stockholm: The networks, planning and social welfare nexus beyond the unitary city

This paper focuses on the extent to which recent infrastructure-oriented urban developments in Stockholm concord with various aspects of the ‘splintering urbanism’ thesis of Graham and Marvin. This contextualisation allows us to extend their work empirically and conceptually. In the first instance, we study a particular case of the decline of a unitary networked city (in an urban context largely absent from their book). In the second instance, we develop their notion of ‘unbundling’ to capture not just core changes in the organisation of infrastructure provision, but an overarching disjunction of the established nexus between networks, planning and social welfare in the city. This disjunction operates through interlinked transformations concerning, for example, privatisation and outsourcing in network services, separation of infrastructure planning from broader urban planning, contradictions between the environmental and social mandates of infrastructure, and a (prospective) curtailment of the redistributive, social role of essential network service provision. We conclude nonetheless that this ‘destructive’ moment of unbundling has not so far been pursued by more explicitly ‘creative’ urban fragmentation strategies, due largely to the vestiges of a socio-political consensus based around redistribution and equality. In this respect, the Stockholm case pleads for a conception of ‘splintering’ as a dynamic and multi-stage process which is not only always ongoing, unstable and incomplete, but also non-linear and open to resistance/regulation.