Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

ELA-ICP-MS U-Pb zircon geochronology of regional volcanism hosting the Bajo de la Alumbrera Cu-Au deposit: implications for porphyry-related mineralization

ELA-ICP-MS U-Pb zircon geochronology has been used to show that the porphyritic intrusions related to the formation of the Bajo de la Alumbrera porphyry Cu-Au deposit, NW Argentina, are cogenetic with stratigraphically well-constrained volcanic and volcaniclastic rocks of the Late Miocene Farallon Negro Volcanic Complex. Zircon geochronology for intrusions in this deposit and the host volcanic sequence show that multiple mineralized porphyries were emplaced in a volcanic complex that developed over 1.5 million years. Volcanism occurred in a multivent volcanic complex in a siliciclastic intermontane basin. The complex evolved from early mafic-intermediate effusive phases to a later silicic explosive phase associated with mafic intrusions. Zircons from the basal mafic-intermediate lavas have ages that range from 8.46 +/- 0.14 to 7.94 +/- 0.27 Ma. Regionally extensive silicic explosive volcanism occurred at similar to8.0 Ma (8.05 +/- 0.13 and 7.96 +/- 0.11 Ma), which is co-temporal with intrusion of the earliest mineralized porphyries at Bajo de la Alumbrera (8.02 +/- 0.14 and 7.98 +/- 0.14 Ma). Regional uplift and erosion followed during which the magmatic-hydrothermal system was probably unroofed. Shortly thereafter, dacitic lava domes were extruded (7.95 +/- 0.17 Ma) and rhyolitic diatremes (7.79 +/- 0.13 Ma) deposited thick tuff blankets, across the region. Emplacement of large intermediate composition stocks occurred at 7.37 +/- 0.22 Ma, shortly before renewed magmatism occurred at Bajo de la Alumbrera (7.10 +/- 0.07 Ma). The latest porphyry intrusive event is temporally associated with new ore-bearing magmatic-hydrothermal fluids. Other dacitic intrusions are associated with subeconomic deposits that formed synchronously with the mineralized porphyries at Bajo de la Alumbrera. However, their emplacement continued (from 7.10 +/- 0.06 to 6.93 +/- 0.07 Ma) after the final intrusion at Bajo de al Alumbrera. Regional volcanism had ceased by 6.8 Ma (6.92 +/- 0.07 Ma). The brief history of the volcanic complex hosting the Bajo de la Alumbrera Cu-Au deposit differs from that of other Andean provinces hosting porphyry deposits. For example, at the El Salvador porphyry copper district in Chile, magmatism related to Cu mineralization was episodic in regional igneous activity that occurred over tens of millions of years. Bajo de la Alumbrera resulted from the superposition of multiple porphyry-related hydrothermal systems, temporally separated by a million years. It appears that the metal budget in porphyry ore deposits is not simply a function of their longevity and/or the superposition of multiple porphyry systems. Nor is it a function of the duration of the associated cycle of magmatism. Instead, the timing of processes operating in the parental magma body is the controlling factor in the formation of a fertile porphyry-related ore system.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Geogenic sources and sinks of trace metals in the Larsemann Hills, East Antarctica: Natural processes and human impact

To evaluate the extent of human impact on a pristine Antarctic environment, natural baseline levels of trace metals have been established in the basement rocks of the Larsemann Hills, East Antarctica. From a mineralogical and geochemical point of view the Larsemann Hills basement is relatively homogeneous, and contains high levels of Pb, Th and U. These may become soluble during the relatively mild Antarctic summer and be transported to lake waters by surface and subsurface melt water. Melt waters may also be locally enriched in V, Cr, Co, Ni, Zn and Sri derived from weathering of metabasite pods. With a few notable exceptions, the trace metal concentrations measured in the Larsemann Hills lake waters can be entirely accounted for by natural processes such as sea spray and surface melt water input. Thus, the amount of trace metals released by weathering of basement lithologies and dispersed into the Larsemann Hills environment, and presumably in similar Antarctic environments, is, in general, not negligible, and may locally be substantial. The Larsemann Hills sediments are coarse-grained and contain minute amounts of clay-size particles, although human activities have contributed to the generation of fine-grained material at the most impacted sites. Irrespective of their origin, these small amounts of fine-grained clastic sediments have a relatively small surface area and charge, and are not as effective metal sinks as the abundant, thick cyanobacterial algal mats that cover the lake floors. Thus, the concentration of trace metals in the Larsemann Hills lake waters is regulated by biological activity and thawing-freezing cycles, rather than by the type and amount of clastic sediment supply. (c) 2005 Elsevier Ltd. All rights reserved.

Dating paleochannel iron ore by (U-Th)/He analysis of supergene goethite, Hamersley province, Australia

(U-Th)/He dating of late-stage authigenic goethite, combined with corrections for diffusive loss of He-4 by the He-4/He-3 methodology, reveals strong correlation between a sample's age and its depth in ferruginized channel sediments from the Yandicoogina deposit, Western Australia. Corrected ages, ranging from ca. 18 Ma near the surface to ca. 5 Ma at the bottom of the profile, indicate that ferruginization of the aggraded channels becomes progressively younger with depth. This trend is consistent with goethite precipitation at the groundwater-atmosphere interface during water table drawdown driven by the aridification of Western Australia during the Neogene. The results demonstrate that the (U-Th)/He system is ideal for dating goethite if diffusive loss corrections are applied. The approach is suitable for dating weathering reactions on Earth and should also be suitable for dating Fe oxyhydroxides in the Martian regolith.