U-Pb ages and Sr, Pb and Nd isotope data for gneisses near the Kolar Schist Belt: Evidence for the juxtaposition of discrete Archean terranes

Uranium-lead ages and Sr, Pb, and Nd isotopic data for gneisses near the Kolar Schist Belt and their interpretation as evidence for the juxtaposition of discrete Archean terranes were presented. The granodioritic Kambha gneiss east of the schist belt has a zircon age of 2532 + or - 3 Ma and mantle-like initial Sr, Pb, and Nd isotopic ratios. Therefore these gneisses are thought to represent new crust added to the craton in the latest Archean. By contrast, more mafic Dod gneisses and leucocratic Dosa gneisses west of the schist belt (2632 + or - 7 and 2610 + or - 10 Ma) show evidence for contamination of their magmatic precursors (LREE-enriched mantle-derived for the Dod gneisses) by older (greater than 3.2 Ga) continental crust. Fragments of this older crust may be present as granitic and tonalitic inclusions in the 2.6-Ga gneisses and in shear zones. The antiquity of these fragments is supported by their Nd, Sr, and Pb isotopic compositions and by 2.8 to greater than 3.2 Ga zircon cores

Tectonic setting of the Kolar Schist Belt, Karnataka, India

The tectonic setting of the Kolar Schist Belt and why the belt may represent a late Archean suture was discussed. The isotopic and chronological evidence that suggest diverse origins of the various packages of supracrustal rocks within the schist belt and the two gneiss terrains adjoining the belt were summarized. The eastern and western amphibolites were derived from sources at similar depths in the mantle (probably at similar ages, ca. 2.7 Ga), but these sources had distinct trace element compositions and histories. A distinctive feature of these differences was shown by the differences between the east and west amphibolites on a Ce vs. Nd diagram. In the gneisses the age and isotopic evidence suggest that the two terranes had distinct histories until after 2520 Ma and by 2420 Ma (Ar-40/Ar-39 age of muscovite in the sheared margin of the schist belt). Based on these data, the schist belt probably represents the site of accretion of diverse fragments (terrains) to the margin of the craton in the latest Archean, possibly as an Archean analog to the Phanerozoic North American Cordillera

The Kolar Schist Belt: A possible Archaean suture zone

The Kolar Schist Belt represents a N-S trending discontinuity in the structures, lithologies, and emplacement and metamorphic ages of late Archean gneisses. The suggestion of a much older basement on the west side of the belt is not seen on the east. Within the schist belt amphibolites from each side have distinctly different chemical characteristics, suggesting different sources at similar mantle depths. These amphibolites were probably not part of a single volcanic sequence, but may have formed about the same time in two completely different settings. Could the amphibolites with depleted light REE patterns represent Archean ocean floor volcanics which are derived from a mantle source with a long term depletion of the light REE? Why are the amphibolites giving an age which may be older than the exposed gneisses immediately on either side of the belt? These results suggest that it is necessary to seriously consider whether the Kolar Schist Belt may be a suture between two late Archean continental terranes

Canonical Formalism for a 2n-Dimensional Model with Topological Mass Generation

The four-dimensional model with topological mass generation that was found by Dvali, Jackiw and Pi has recently been generalized to any even number of dimensions (2n-dimensions) in a nontrivial manner in which a Stueckelberg-type mass term is introduced [S. Deguchi and S. Hayakawa, Phys. Rev. D 77, 045003 (2008), arXiv:0711.1446]. The present paper deals with a self-contained model, called here a modified hybrid model, proposed in this 2n-dimensional generalization and considers the canonical formalism for this model. For the sake of convenience, the canonical formalism itself is studied for a model equivalent to the modified hybrid model by following the recipe for treating constrained Hamiltonian systems. This formalism is applied to the canonical quantization of the equivalent model in order to clarify observable and unobservable particles in the model. The equivalent model (with a gauge-fixing term) is converted to the modified hybrid model (with a corresponding gauge-fixing term) in a Becchi-Rouet-Stora-Tyutin (BRST)-invariant manner. Thereby it is shown that the Chern-Pontryagin density behaves as an observable massive particle (or field). The topological mass generation is thus verified at the quantum-theoretical level.Comment: 29 pages, no figures, minor corrections, published versio

The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation does reproduce the generalized Frenet equation. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of $C_\beta$ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this $C_\beta$ framing relates intimately to the discrete Frenet framing. We also explain how inflection points can be located in the loops, and clarify their distinctive r\^ole in determining the loop structure of foldel proteins.Comment: 14 pages 12 figure

Invariant submanifold for series arrays of Josephson junctions

We study the nonlinear dynamics of series arrays of Josephson junctions in the large-N limit, where N is the number of junctions in the array. The junctions are assumed to be identical, overdamped, driven by a constant bias current and globally coupled through a common load. Previous simulations of such arrays revealed that their dynamics are remarkably simple, hinting at the presence of some hidden symmetry or other structure. These observations were later explained by the discovery of (N - 3) constants of motion, each choice of which confines the resulting flow in phase space to a low-dimensional invariant manifold. Here we show that the dimensionality can be reduced further by restricting attention to a special family of states recently identified by Ott and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an invariant submanifold of dimension one less than that found earlier. We derive and analyze the flow on this submanifold for two special cases: an array with purely resistive loading and another with resistive-inductive-capacitive loading. Our results recover (and in some instances improve) earlier findings based on linearization arguments.Comment: 10 pages, 6 figure

Soldered Bundle Background for the De Sitter Top

We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics and oriented matroid theory.Comment: 12 pages, Latex; some improvements introduced, reference added, typos correcte