On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Seasonality of westerly moisture transport in the East Asian summer monsoon and its implications for interpreting precipitation δ18O

East Asian summer monsoon (EASM) rainfall impacts the world's most populous regions. Accurate EASM rainfall prediction necessitates robust paleoclimate reconstructions from proxy data and quantitative linkage to modern climatic conditions. Many precisely dated oxygen isotope records from Chinese stalagmites have been interpreted as directly reflecting past EASM rainfall amount variability, but recent research suggests that such records instead integrate multiple hydroclimatic processes. Using a Lagrangian precipitation moisture source diagnostic, we demonstrate that EASM rainfall is primarily derived from the Indian Ocean. Conversely, Pacific Ocean moisture export peaks during winter, and the moisture uptake area does not differ significantly between summer and winter and is thus a minor contributor to monsoonal precipitation. Our results are substantiated by an accurate reproduction of summer and winter spatial rainfall distributions across China. We also correlate modern EASM rainfall oxygen isotope ratios with instrumental rainfall amount and our moisture source data. This analysis reveals that the strength of the source effect is geographically variable, and differences in atmospheric moisture transport may significantly impact the isotopic signature of EASM rainfall at the Hulu, Dongge, and Wanxiang Cave sites. These results improve our ability to isolate the rainfall amount signal in paleomonsoon reconstructions and indicate that precipitation across central and eastern China will directly respond to variability in Indian Ocean moisture supply.

Re-examining the U.K.'s greatest tornado outbreak: forecasting the limited extent of tornadoes along a cold front

On 23 November 1981, a strong cold front swept across the U.K., producing tornadoes from the west to the east coasts. An extensive campaign to collect tornado reports by the Tornado and Storm Research Organisation (TORRO) resulted in 104 reports, the largest U.K. outbreak. The front was simulated with a convection-permitting numerical model down to 200-m horizontal grid spacing to better understand its evolution and meteorological environment. The event was typical of tornadoes in the U.K., with convective available potential energy (CAPE) less than 150 J kg-1, 0-1-km wind shear of 10-20 m s-1, and a narrow cold-frontal rainband forming precipitation cores and gaps. A line of cyclonic absolute vorticity existed along the front, with maxima as large as 0.04 s-1. Some hook-shaped misovortices bore kinematic similarity to supercells. The narrow swath along which the line was tornadic was bounded on the equatorward side by weak vorticity along the line and on the poleward side by zero CAPE, enclosing a region where the environment was otherwise favorable for tornadogenesis. To determine if the 104 tornado reports were plausible, first possible duplicate reports were eliminated, resulting in as few as 58 tornadoes to as many as 90. Second, the number of possible parent misovortices that may have spawned tornadoes is estimated from model output. The number of plausible tornado reports in the 200-m grid-spacing domain was 22 and as many as 44, whereas the model simulation was used to estimate 30 possible parent misovortices within this domain. These results suggest that 90 reports was plausible.

One, two or no record of late neoproterozoic glaciation in South-East Cameroon?

Severe climate changes culminating in at least three major glacial events have been recognized in the Neoproterozoic sedimentary record from many parts of the world Supportive to the global nature of these climatic shifts a considerable amount of data have been acquired from deposits exposed in Pan-African orogenic belts in southwestern and western Africa By comparison published data from the Pan-African belts in Central Africa are scarce We report here evidence of possibly two glacial events recorded in the Mintom Formation that is located on the margin of the Pan-African orogenic Yaounde belt in South-East Cameroon In the absence of reliable radiometric data only maximum and minimum age limits of 640 and 580 Ma respectively can at present be applied to the Mintom Formation The formation consists of two lithostratigraphic ensembles each subdivided in two members (i e in ascending stratigraphic order the Kol Metou Momibole and Atog Adjap Members) The basal ensemble exhibits a typical glacial to post-glacial succession It includes diamictites comprising cobbles and boulders in a massive argillaceous siltstone matrix and laminated siltstones followed by in sharp contact a 2 m-thick massive dolostone that yielded negative delta(13)C values (<-3 parts per thousand. V-PDB) similar to those reported for Marinoan cap carbonates elsewhere However uncertainty remains regarding the glacial influence on the siliciclastic facies because the diamictite is better explained as a mass-flow deposit and diagnostic features such as dropstones have not been seen in the overlying siltstones The Mintom Formation may thus provide an example of an unusual succession of non-glacial diamictite overlain by a truly glacial melt-related cap-carbonate We also report the recent discovery of ice-striated pavements on the structural surface cut in the Mintom Formation suggesting that glaciers developed after the latter had been deposited and deformed during the Pan-African orogeny Striations which consistently exhibit two principal orientations (N60 and N110) were identified in two different localities in the west of the study area on siltstones of the Kol Member and in the east on limestones of the Atog Adjap Member respectively N60-oriented striae indicate ice flow towards the WSW Assigning an age to these features remains problematical because they were not found associated with glaciogenic deposits Two hypotheses can equally be envisaged e either the striated surfaces are correlated (1) to the Gaskiers (or Neoproterozoic post-Gaskiers) glaciation and represent the youngest Ediacaran glacial event documented in the southern Yaounde belt or (2) to the Late Ordovician Hirnantian (Saharan) glaciation thereby providing new data about Hirnantian ice flows in Central Africa (C) 2010 Elsevier Ltd All rights reserved

GEOCHEMISTRY AND U-PB ZIRCON AGE OF THE INTERNAL OSSA-MORENA ZONE OPHIOLITE SEQUENCES: A REMNANT OF RHEIC OCEAN IN SW IBERIA

The Early Paleozoic geodynamic evolution in SW Iberia is believed to have been dominated by the opening of the Rheic Ocean. The Rheic Ocean is generally accepted to have resulted from the drift of peri-Gondwanan terranes such as Avalonia from the northern margin of Gondwana during Late Cambrian-Early Ordovician times. The closure of the Rheic Ocean was the final result of a continent-continent collision between Gondwana and Laurussia that produced the Variscan orogen. The Ossa-Morena Zone is a peri-Gondwana terrane, which preserves spread fragments of ophiolites - the Internal Ossa-Morena Zones Ophiolite Sequences (IOMZOS). The final patchwork of the IOMZOS shows a complete oceanic lithospheric sequence with geochemical characteristics similar to the ocean-floor basalts, without any orogenic fingerprint and/or crustal contamination. The IOMZOS were obducted and imbricated with high pressure lithologies. Based on structural, petrological and whole-rock geochemical data, the authors argue that the IOMZOS represent fragments of the oceanic lithosphere from the Rheic Ocean. Zircon SHRIMP U-Pb geochronological data on metagabbros point to an age of ca. 480 Ma for IOMZOS, providing evidence of a well-developed ocean in SW Iberia during this period, reinforcing the interpretation of the Rheic Ocean as a wide ocean among the peri-Gondwanan terranes during Early Ordovician times.

Geology and geochronology of the Betara region in south-southeastern Brazil: Evidence for possible Statherian (1.80-1.75 Ga) and Calymmian (1.50-1.45 Ga) extension events

The results of geological mapping, chemical analysis and radiometric dating of metabasic rocks of Betara Formation, and mapping and dating of those present in the Betara basement nucleus together with mylonitic granodiorite and syenogranite are reported here. U-Pb analysis of bulk zircon fractions from the metabasic rocks of the basement nucleus yielded a Statherian age of 1790 +/- 22 Ma, while the metabasic rocks from the upper part of the Betara Formation yielded a Calymmian age between 1500 and 1450 Ma. This age is a minimum for the deposition of the Betara Formation. The older metabasic rocks are associated with post-tectonic, possibly anorogenic syenogranite, while the younger ones are gabbro or very porphyritic ankaramite whose REE patterns are consistent with crystallization from an N-MORB parent magma. The observations and data point to the probable events associated with extensional processes of the end of Paleoproterozoic and early Mesoproterozoic. Similar registers of Statherian (1.80-1.75 Ga) and Calymmian (1.50-1.45 Ga) extensional events are recorded in other parts of the South American and African continents. The Neoproterozoic witnessed the formation and junction of the tectonic slices which formed the Apiai domain during the assemblage of western Gondwana. (C) 2010 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Integração de dados geofísicos e geológicos na avaliação ambiental e epidemiológica de radiações naturais (radônio) no escudo Sul-Riograndense (RS-Brasil)

Os efeitos provocados por radiações são conhecidos na literatura por meio dos estudos em usinas nucleares e em testes bélicos. Entretanto, os efeitos da radiação natural vêm despertando a atenção das autoridades da saúde, dentre as quais se destaca a Environmental Protection Agency (EPA) nos Estados Unidos e a National Radiological Protection Board (NRPB) no Reino Unido. Os efeitos epidemiológicos ocasionados por radiação de origem natural, mais especificamente a radiação emanada pelo gás radônio que fica acumulado em residências enclausuradas por muito tempo, tem sido alvo de intensas investigações. Nessa dissertação, foi realizada uma avaliação ambiental preliminar da radiação natural devida ao radônio como elemento epidemiológico no Escudo Sul-riograndense. Os dados utilizados para determinar o risco epidemiológico foram: neoplasias, radiação, geologia e população. O banco de dados dos casos de óbitos por neoplasias do estado foi obtido da Secretaria da Saúde, por meio do Núcleo de Informação em Saúde. A radiação natural devida ao radônio foi determinada a partir dos dados gamaespectrométricos obtidos de levantamento aerogeofísico da CPRM no Escudo Sul-riograndense, nos projetos Camaquã e Extremo Sudeste do Brasil realizados nos anos de 1973 e 1978, respectivamente. Os dados geológicos foram obtidos do Mapa Geológico do Estado de 1989. Os dados de população foram obtidos junto ao Instituto Brasileiro de Geografia e Estatística (IBGE). A integração de dados foi realizada usando a metodologia de matriz de sobreposição entre os dados de casos de óbitos por neoplasia e de gamaespectrometria. Os dados de população foram empregados para normalizar os dados de neoplasias, e o dado de geologia para correlacionar com a gamaespectrometria. Os resultados da integração são mapas classificados pelo grau de risco epidemiológico, nos quais é apresentada a relação entre os casos de neoplasias pela intensidade de radiação devida ao radônio. Nesse sentido, uma boa relação foi assinalada e são recomendados estudos adicionais sobre esse mesmo banco de dados.

Limites e evolução geodinâmica do Sistema Jaguaribeano, Província Borborema, Nordeste do Brasil

The studied area is geologically located in the Northern Domain of the Borborema Province (Northeast Brazil), limited to the south by the Patos shear zone. Terranes of the Jaguaribeano system are dominant, flanked by the Piranhas (E and S sides) and Central Ceará (NE side) terranes. Its basement comprises gneiss -migmatite terrains of Paleoproterozoic to Archean age (2.6 to 1.9 Ga old), overprinted by neoproterozoic to cambrian tectonotherma l events. Narrow supracrustal belts ( schist belts) display a 1.6 to 1.8 Ga age, as shown by whole - rock Rb-Sr and zircon U-Pb and Pb/Pb dates in acid metavolcanics which dominate in the lower section of these sequences, and in coeval metaplutonics (granitic augen gneisses). From the stratigraphic point of view, three Staterian belts are recognized: 1. Orós Belt - made up by the Orós Group, subdivided in the Santarém (predominantly pure to impure quartzites, micaschists and metacarbonates) and Campo Alegre (metandesites, metabasalts, metarhyolites and metarhyodacites, interlayered with metatuffs and metasediments) formations, and by the Serra do Deserto Magmatic Suite (granitic augen gneisses). 2. Jaguaribe Belt - its lithostratigrahic-lithodemic framework is similar to the one of the Orós Belt, however with a greater expression of the volcano -plutonic components (Campo Alegre Formation and Serra do Deserto Magmatic Suite). The Peixe Gordo Sequence, separately described, is also related to this belt and contain s metasedimentary, metavolcanic (with subordinated volcanoclastics) and metaplutonic units. The first one correlated to the Orós Group and the latter the Serra do Deserto Magmatic Suite. 3. Western Potiguar Belt - represented by the Serra de São José Gro up, subdivided in the Catolezinho (biotite -amphibole gneisses with intercalations of metacarbonates, calcsilicate rocks, amphibolites and quartzite beds to the top) and Minhuins (quartzites, micaschists, metaconglomerates, calcsilicate rocks, acid to the b asic metavolcanics and metatuffs) formations. Its late Paleoproterozoic (Staterian) age was established by a Pb/Pb date on zircons from a granitic orthogneiss of the Catolezinho Formation. The petrographic characteristics and sedimentary structures of the Santarém Formation of the Orós Group point to deltaic to shallow marine depositional systems, overlain by deep water deposits (turbidites). The geodynamic setting of this region encompassed a large depositional basin, probably extending to the east of the Portalegre shear zone and west of the Senador Pompeu shear zone, with possible equivalents in the Jucurutu Formation of the Seridó Belt and in the Ceará Group of central Ceará. The Arneiróz Belt, west Ceará, displays some stratigraphic features and granito ids geochemically akin to the ones of the Orós Belt. The evolutionary setting started with an extensional phase which was more active in the eastern part of this domain (Western Potiguar and part of the Jaguaribe belts), where the rudite and psamite sedime ntation relates to a fluviatile rift environment which evolved to a prograding deltaic system to the west (Orós Group). The basaltic andesitic and rhyolitic volcanics were associated to this extensional phase. During this magmatic event, acid magmas also crystallized at plutonic depths. The Orós Group illustrates the environmental conditions in the western part of this domain. Later on, after a large time gap (1.6 to 1.1 Ga), the region was subjected to an extensional deformational episode marked by 900 Ma old (Sm-Nd data) basic rocks, possibly in connection with the deposition of the Cachoeirinha Group south of the Patos shear zone. In the 800 to 500 Ma age interval, the region was affected by important deformational and metamorphic events coupled with in trusion of granitic rocks of variable size (dykes to batholiths), related to the Brasiliano/Pan -African geotectonic cycle. These events produced structural blocks which differentiate, one from the other, according to the importance of anatectic mobilizatio n, proportion of high-grade supracrustals and the amount of neoproterozoic -cambrian granitoid intrusions. On this basis, a large portion of the Jaguaretama Block/Terrane is relatively well preserved from this late overprint. The border belts of the Jagua retama Block (Western Potiguar and Arneiroz) display kyanite-bearing (medium pressure) mineral associations, while in the inner part of the block there is a north-south metamorphic zoning marked by staurolite or sillimanite peak metamorphic conditions. Regarding the deformations of the Staterian supracrustal rocks, second and third phases were the most important, diagnosed as having developed in a progressive tectonic process. In the general, more vigorous conditions of PT are related to the interval tardi - phase 2 early-phase 3, whose radiometric ages and regional structuring indicators places it in the Brasiliano/Pan-African Cycle. In the Staterian geodynamic setting of Brazilian Platform , these sequences are correlated to the lower Espinhaço Supergroup (p.ex., Rio dos Remédios and Paraguaçu groups, a paleproterozoic rift system in the São Francisco Craton), the Araí and Serra da Mesa groups (north of Goiás, in the so -called Goiás Central Massif), and the Uatumã Group (in the Amazonian Craton). Granitic ( augen gneisses) plutonics are also known from these areas, as for example the A-type granites intrusive in the Araí and Serra da Mesa groups, dated at 1.77 Ga. Gravimetric and geological data place the limits of the Jaguaribeano System (terranes) along the Senador Pompeu Shear Zone (western border) and the Portalegre- Farias Brito shear zone (eastern and southern). However, the same data area not conclusive as regards the interpretation of those structures as suture of the terrane docking process. The main features of those shear zones and of involved lothological associations, appear to favour an intracontinental transpressional -transcurrent regime, during Neoproterozoic-Cambrian times, marking discontinuities along which different crustal blocks were laterally dispersed. Inside of this orogenic system and according to the magnetic data (total field map), the most important terrane boundary appears to be the Jaguaribe shear zone. The geochronological data, on some tectonostratigraphic associations (partly represented by the Ceará and Jucurutu groups), still at a preliminary level, besides the lack of granitic zonation and other petrotectonic criteria, do not allow to propose tectonic terrane assembly diagrams for the studied area

The U-isotopes modeling in aquifers from Pocos de Caldas plateau, Brazil

U-modeled groundwater residence times were estimated by changes in U-234/U-238 activity ratio (AR) and U content of groundwaters from Pocos de Caldas city situated at the Pocos de Caldas alkaline massif, Brazil. The estimated ages are more realistic than others generated by the use of hydraulic conductivity data and available information about the weathering rate of rocks in the plateau. The U-234/U-238 AR and reciprocal of the dissolved U-content data also defined a ternary plot that allowed the calculation of the relative volume of three source waters for the mixed water. Such U-isotopes modeling for mixing calculations indicated that the dominant phase (68%) in the mixture is thermal.

PhotoLin: a program to identify and analyze linear structures in aerial photographs, satellite images and maps

A computer program, PhotoLin, written for an IBM-PC-compatible microcomputer is described which detects linear features in aerial photographs, satellite images and topographic maps. The program accepts images saved to PCX files as input and applies noise correction and smoothing filters and thinning routines. The output consists of a skeleton containing the median lines of linear features which can be represented on a map. The branches of the skeleton can be broken into sections of constant length for which the mean orientations are obtained for the preparation of rose diagrams. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Durango apatite fission-track dating using length-based age corrections and neutron fluence measurements by natural thorium thin films and natural U-doped glasses calibrated through natural uranium thin films

In this work, we present an approach for neutron fluence measurements based on natural thorium thin films and natural uranium-doped glasses calibrated through natural uranium thin films to be used for dating with the Fission-Track Method (FTM). This neutron dosimetry approach allows the employment of FTM even when dating is carried out using low neutron themalization facilities. Besides, it makes possible the determination of the Th/U ratio of the mineral to be dated. Durango apatite which is often employed in FTM as an age standard was analyzed. This apatite presented a fairly high Th/U ratio, 29.9 +/- 1.7. Th fissions were 18%, 12% and 10% of the total for irradiations where thermal to fast neutron flux ratios were 2.4, 4.4 and 5,2, respectively. These results show that Th fission must be considered for this apatite, when not well-thermalized irradiation facilities are used. The ratio between spontaneous and induced track length, L(S)/L(1), close to 0.89, indicates a certain amount of rejuvenation of the age of Durango apatite. Therefore, its apparent age should be corrected, the application of a technique based on track-length measurements produced a corrected age of 29.7 +/- 1.1 Ma, consistent with the independent reference age of this apatite (31.4 +/- 0.5 Ma). This result represents a support for viability of the neutron dosimetry approach studied in this work for FTM.(C) 2002 Elsevier B.V. B.V. All rights reserved.

Use of U-isotope disequilibrium to evaluate the weathering rate and fertilizer-derived uranium in São Paulo state, Brazil

The U-disequilibrium method was utilized to evaluate the velocity of alteration of rocks and fertilizer-derived uranium in the Corumbatai River basin, São Paulo state, Brazil. The Corumbatai River basin is affected by the continuous use of fertilizer-derived uranium utilized in sugar cane crops, increasing the dissolved uranium concentration in the Corumbatai River (Santa Terezinha station) in the wet period to 43%. The weathering rate in the Corumbatai River basin utilizing the U-isotope modeling was 0.0265 mm/year (corresponding to 38,000 years to weather 1 m of rock under actual climatic conditions). However, when the inputs of anthropogenic uranium were considered, then a weathering rate of 0.022 mm/year (corresponding to 45,500 years to weather 1 m of rock) was determined. The removed material in the Corumbatai River basin is mainly from two sub-basins (the Cabecas River and Passa Cinco River), where the sandstones weather easier than the siltstones and claystones in the basin.

U Pb and Sm Nd geochronologic studies of the eastern Borborema Province, Northeastern Brazil: initial conclusions

The Borborema Province of NE Brasil comprises the central part of a wide Pan-African-Brasiliano orogenetic belt that formed as a consequence of late Neoproterozoic convergence and collision of the São Luis-West Africa craton and the São Francisco-Congo-Kasai cratons. New Sm Nd and U Pb results from the eastern part of this province help to define the basic internal architecture and pre-collisional history of this province, with particular emphasis on delineating older cratonic terranes, their fragmentation during the Mesoproterozoic, and their assembly into West Gondwana during the Pan African-Brasiliano orogeny at ca. 600 Ma. The region can be divided into three major geotectonic domains: a) Rio Piranhas-Caldas Brandão massif, with overlying Paleoproterozoic to Neoproterozoic supracrustal rocks, north of the Patos Lineament; b) the Archean to Paleoproterozoic São Francisco craton (SFC) to the south; and c) a complex domain of Paleoproterozoic to Archean basement blocks with several intervening Mesoproterozoic to Neoproterozoic fold belts in the center (south of Patos Lineament and north of SFC). The northern and central domains comprise the Borborema Province. Archean basement gneiss and Transamazonian granulite of northern SFC are exposed in the southern part of the central domain, underlying southern parts of the Sergipano fold belt. Basement in the Rio Piranhas massif appears to consist mostly of Transamazonian (2.1 to 2.2 Ga) gneissic rocks; Nd model ages (TDM) of ca. 2.6 Ga for 2.15 Ga gneisses indicate a substantial Archean component in the protoliths to these gneisses. The Caldas Brandão massif to the east yields both Transamazonian and Archean U Pb zircon and Nd (TDM) ages, indicating a complex architecture. Metasedimentary rocks of the Jucurutu Formation yield detrital zircons with original crystallization ages as young as 1.8 Ga, indicating that these rocks may be late Paleoproterozoic and correlate with other ca. 1.8 Ga cratonic supracrustal rocks in Brazil such as the Roraima Group and Espinhaço Group. Most metavolcanic and pre-Brasiliano granitic units of the Sergipano (SDS), Pajeú-Paraíba (SPP), Riacho Pontal (SRP), and Piancó-Alto Brígida (SPAB) fold belts in the central domain formed ~ 1.0 ± 0.1 Ga, based on U Pb ages of zircons. Nd model ages (TDM) for these same rocks, as well as Brasiliano granites intruded into them and large parts of the Pernambuco-Alagoas massif, are commonly 1.3-1.7 Ga, indicating that rocks of the fold belts were not wholly derived from either older (> 2.1 Ga) or juvenile (ca. 1.0 Ga) crust, but include mixtures of both components. A simple interpretation of Brasiliano granite genesis and the Nd data implies that there is no Transamazonian or Archean basement underlying large parts of these fold belts or of the Pernambuco-Alagoas massif. An exception is a belt of syenitic Brasiliano plutons (Syenitoid Line) and host gneisses between SPAB and SPP that clearly has a Transamazonian (or older) source. In addition, there are several smaller blocks of Archean to Transamazonian gneiss that can be defined within and among these fold belts. These blocks do not appear to constitute a continuous basement complex, but appear to be isolated older crustal fragments. Our data support a model in which ca. 1.0 Ga rifting was an important tectonic and crust-forming event along the northern edge of the São Francisco craton. Our data also show that significant parts of the Borborema Province are not remobilized Transamazonian to Archean crust, but that Mesoproterozoic crust is a major feature of the Province. There are several small remnants of older crust within the area dominated by Mesoproterozoic crust, suggesting that the rifting event created several small continental fragments that were later incorporated into the Brasiliano collisional orogen. We cannot at present determine if the Rio Piranhas-Caldas Brandão massifs and the older crustal blocks of the central domain were originally part of the São Francisco craton or whether some (or all) of them came from more exotic parts of the Proterozoic Earth. Finally, our data have not yet revealed any juvenile terranes of either Transamazonian or Brasiliano age. © 1995.

Caracterização petrológica, geoquímica e geocronológica (U/Pb e Ar/Ar) do maciço sararé Nova Lacerda-MT

Pós-graduação em Geologia Regional - IGCE