Métodos espectrais aplicados à relatividade numérica: determinação dos dados iniciais

Neste trabalho aplicamos métodos espectrais para a determinação da configuração inicial de três espaços-tempos contendo buracos negros. Para isto apresentamos primeiro a foliação do espaço-tempo em hipersuperfícies tridimensionais espaciais parametrizadas pela função temporal t. Este processo é chamado de decomposição 3+1 [2] [5]. O resultado deste processo são dois conjuntos de equações classificadas em equações de vínculo e evolução [4]. As equações de vínculo podem ser divididas em vínculos Hamiltoniano e dos momentos. Para a obtenção dos dados iniciais dos problemas estudados aqui, apenas a equação de vínculo Hamiltoniano será resolvida numericamente, pois as equações de vínculo dos momentos possuem solução analítica nestes casos. Uma pequena descrição dos métodos espectrais é apresentada, destacando-se os método de Galerkin, método pseudoespectral ou de colocação e método de Tau, que são empregados na resolução das equações de vínculo Hamiltoniano dos problemas estudados. Verificamos que os resultados obtidos neste trabalho superam aqueles produzidos por Kidder e Finn [15], devido a uma escolha diferente das funções de base, que aqui satisfazem uma das condições de contorno.

Tectônica de emplacement dos diques toleíticos do Arco de Ponta Grossa, entre Curitiba e Paranaguá (PR)

Apesar da grande quantidade de estudos geoquímicos e geocronológicos que têm sido executados no enxame de diques de Ponta Grossa (EDPG), pouco se sabe a respeito da tectônica associada ao seu sin e pós emplacement. O objetivo desse estudo é identificar nos diques possíveis indicadores cinemáticos a fim de compreender essa dinâmica, além de caracterizar a tectônica rúptil Meso-cenozóica associada à área, afetando todas as rochas. A área de estudo está situada no entorno da Baía de Paranaguá, estado do Paraná, onde os diques do EDPG afloram intrudindo domínios pré-cambrianos, compostos por gnaisses, sequências metassedimentares e suítes graníticas pertencentes ao Terreno Paranaguá e uma pequena parte às Microplacas Curitiba e Luís Alves, ambos em contato através de Zonas de cisalhamento (SIGA JR, 1995). Essas rochas possuem direção de foliação marcante NE-SW. Os diques estudados foram divididos em dois grupos com base em estudos petrográficos, com forte predomínio dos básicos toleíticos e subordinadamente, os básicos alcalinos. Alguns diques compostos também foram encontrados, o que demonstra ao menos dois pulsos magmáticos possivelmente associados ao mesmo evento. São diques verticais a subverticais e possuem direção principal NW-SE. Com frequência apresentam fraturamento interno de direção NE-SW, provavelmente associados ao seu processo de resfriamento. Possuem formato tabular, porém não é raro que ocorram irregulares. As principais feições indicativas de movimentação oblíqua na intrusão desses diques são as estruturas de borda em degraus, tocos e zigue-zague, que demonstram em geral uma componente distensional destral de deslocamento. Agregando dados dos demais enxames de diques toleíticos principais, chegou-se a um valor médio de N80E para o tensor σ3 da abertura do Atlântico Sul, coerente com o esperado também para EDPG, visto que foram intrudidos em um ambiente transtensivo (CORREA GOMES, 1996). Falhas e fraturas são observadas cortando tanto as rochas encaixantes quanto os diques, caracterizando uma tectônica posterior à intrusão. As principais famílias de fraturas são N20-30E, N30-40W, N80W e N60-70E, formando zonas preferenciais de erosão no cruzamento entre elas. As falhas podem apresentar plano de falha bem definido com estrias e ressaltos, ocorrendo preenchidas ou não, tendo sido observados preenchimento de sílica e material carbonático. Predomina nas falhas observadas, cinemática sinistral demonstrando mudança no campo de esforços com relação ao emplacement dos diques. O estudo da tectônica rúptil assim como do emplacement dos diques da área vem a contribuir para o melhor entendimento dos processos de abertura do Oceano Atlântico Sul, além de abranger a região emersa do que constitui o embasamento da bacia de Santos, foco de extensivos estudos atualmente, podendo-se inferir que os mesmos processos tenham afetado a região offshore.

Uso de espinores na investigação do limite de Karlhede para ondas pp

Neste trabalho foi feito um estudo do limite de Karlhede para ondas pp. Para este fim, uma revisão rigorosa de Geometria Diferencial foi apresentada numa abordagem independente de sistemas de coordenadas. Além da abordagem usual, a curvatura de uma variedade riemanniana foi reescrita usando os formalismos de referenciais, formas diferenciais e espinores do grupo de Lorentz. O problema de equivalência para geometrias riemannianas foi formulado e as peculiaridades de sua aplicação é a Relatividade Geral são delineadas. O limite teórico de Karlhede para espaços-tempo de vácuo de tipo Petrov N foi apresentado. Esse limite é estudado na prática usando técnicas espinores e as condições para sua existência são resolvidas sem a introdução de sistemas de coordenadas.

A new distance for scale-invariant 3D shape recognition and registration

This paper presents a method for vote-based 3D shape recognition and registration, in particular using mean shift on 3D pose votes in the space of direct similarity transforms for the first time. We introduce a new distance between poses in this spacethe SRT distance. It is left-invariant, unlike Euclidean distance, and has a unique, closed-form mean, in contrast to Riemannian distance, so is fast to compute. We demonstrate improved performance over the state of the art in both recognition and registration on a real and challenging dataset, by comparing our distance with others in a mean shift framework, as well as with the commonly used Hough voting approach. © 2011 IEEE.

Scale-invariant vote-based 3D recognition and registration from point clouds

This chapter presents a method for vote-based 3D shape recognition and registration, in particular using mean shift on 3D pose votes in the space of direct similarity transformations for the first time. We introduce a new distance between poses in this spacethe SRT distance. It is left-invariant, unlike Euclidean distance, and has a unique, closed-form mean, in contrast to Riemannian distance, so is fast to compute. We demonstrate improved performance over the state of the art in both recognition and registration on a (real and) challenging dataset, by comparing our distance with others in a mean shift framework, as well as with the commonly used Hough voting approach. © 2013 Springer-Verlag Berlin Heidelberg.

A Grassman-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with recently proposed Newton algorithms on Riemannian manifolds.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Optimal data fitting on lie groups: A coset approach

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in n to data which can be solved using principal component analysis. We show how the fitting problem can be reduced for biinvariant distances to a generalized mean calculation on an homogeneous space. For biinvariant Riemannian distances we provide an algorithm based on the Karcher mean gradient algorithm. We illustrate our approach by some examples on SO(n). © 2010 Springer -Verlag Berlin Heidelberg.

Anisotropy preserving DTI processing

Statistical analysis of diffusion tensor imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of diffusion tensors). Building upon earlier studies exploiting a Riemannian framework to address these challenges, the present paper proposes a novel metric and an accompanying computational framework for DTI data processing. The proposed approach grounds the signal processing operations in interpolating curves. Well-chosen interpolating curves are shown to provide a computational framework that is at the same time tractable and information relevant for DTI processing. In addition, and in contrast to earlier methods, it provides an interpolation method which preserves anisotropy, a central information carried by diffusion tensor data. © 2013 Springer Science+Business Media New York.

Manopt, a matlab toolbox for optimization on manifolds

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design effcient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. By dealing internally with most of the differential geometry, the package aims particularly at lowering the entrance barrier. © 2014 Nicolas Boumal.

Incremental pairwise discriminant analysis based visual tracking

The distinguishment between the object appearance and the background is the useful cues available for visual tracking in which the discriminant analysis is widely applied However due to the diversity of the background observation there are not adequate negative samples from the background which usually lead the discriminant method to tracking failure Thus a natural solution is to construct an object-background pair constrained by the spatial structure which could not only reduce the neg-sample number but also make full use of the background information surrounding the object However this Idea is threatened by the variant of both the object appearance and the spatial-constrained background observation especially when the background shifts as the moving of the object Thus an Incremental pairwise discriminant subspace is constructed in this paper to delineate the variant of the distinguishment In order to maintain the correct the ability of correctly describing the subspace we enforce two novel constraints for the optimal adaptation (1) pairwise data discriminant constraint and (2) subspace smoothness The experimental results demonstrate that the proposed approach can alleviate adaptation drift and achieve better visual tracking results for a large variety of nonstationary scenes (C) 2010 Elsevier B V All rights reserved

山东莒南地区韧性剪切带的变形特征与形成演化

Ju Nan of Shandong province is located at southwest of Sulu UHP (ultrahigh-pressure) metamorphic terrane. It is composed of gneiss, paragneiss, eclogites, ultramafic rocks, marble and quartzite. A large ductile shear zone extends east-west has been found at the Zhubian, The south of Junan county. The Zhubian ductile shear zone is composed of high srain rock and mylonites. The mylonites fall into 3 types: Initial gneiss mylonite, mylonite and altramylonit.obvious lineation of penetration,foliation,S-Cfabrics,porphyroclasts,folds,irregularundulatory,extinction,subgrain boundary, dynamic recrystallization microstructure, core-mantle structure and are common in the ductile shear zone. Based on field work and microstructural analyse, a conclution is arrived: The ductile shear zone is an approximately SE trending faults. The Zhubian ductile shear zone formed at Ep ―Hb facies conditions which could be proved by deformaed and metamorphosed mineral aggregates, Deformation behavior, Ternary-feldspar geothermometry and so on. Zircon MC―ICP―MS U-Pb analysis is performed on the mylonite and have an average age ―835.9±13.9Ma, it’s the primary rocks formed age. The Zhubian ductile shear zone maybe formed at 224-242Ma.

陇西盆地晚第三纪风尘沉积的地层学研究

In Asia, the significant environment changes in Cenozoic include: uplift of Himalayas and Tibetan Plateau, formation Asian monsoon system, Aridification in Central Asia. One of major advances in recent studies of eolian deposit on the Loess Plateau is the verification of the eolian origin for the Late Tertiary Hipparion Red-Earth (also called red-Clay) underlying the Quaternary loess. Thus, the Late Tertiary eolian deposit, which has been proven a nearly continuous terrestrial record and sensitive to climate change, provides us an important archive to understand these above Cenozoic environment events. The deposit in eastern Loess Plateau has been extensively studied, while the property and age of deposit underlying the Quaternary loess in western plateau remains unclear. In this paper, detail investigations were made on the Sedimentology, geochemistry of Longxi section, a typical section in western Loess Plateau, to address its origin, and on micromammalian fossils and magnetostratigraphy to address its age. The main conclusions are presented as following: 1. The sedimentological and geochemical properties in Longxi section are highly similar to typical Quaternary eolian deposit in Loess Plateau. Nearly 100 paleosols are recognized in the field, and the grain size are very fine with the median grain size centered at 4～7μm. There is a good agreement of both major and trace element compositions between Longxi deposit and the Quaternary Loess. The REE distribution patterns of Longxi deposit and the Quaternary loess are remarkably similar in shape, with enrichment LREE and fairly flat HREE profiles and clear negative Eu anomaly. The mangnetic minerals in Longxi deposit are mainly magnetite, hematite and maghematite, which are similar to those of the Hipparion Red-Earth and Quaternary Loess. The major difference among them is that the samples from Longxi section contain more hematite. The characteristics of anisotropy of magnetic susceptibility (AMS) in Longxi deposit is highly consistent with that of Quaternary loess, while values of the major AMS parameters, e.g. anisotropy degree, magnetic foliation and lineation, are significantly lower than those of fluvial and lake deposits. These evidences indicate an eolian origin for the sediment. 2. An investigation of micromammalian fossils was firstly carried out for determining the approximate age of the sequence because of lack of materials for accurate isotope dating. Three fossil assemblages were obtained which indicate a chronological range from the Middle Miocene to Late Miocene. The magnetostratigraphical study suggests that it is a near continuous terrestrial record for the period from 13.23 to 6.23 MaB.P. The obtained chronology is highly consistent with fossils assemblages. This section is the oldest eolian deposit presently known in Loess Plateau. 3. The magnetic susceptibly value is high in paleosols than in surrounded weak-weathered layers, which suggests that it may be a climate index on orbital time scale. While it cannot be used as a proxy to address the long-term, change of climate on tectonic time scale, as content of the magnetic minerals is highly variable in different parts of the section. 4. The appearance of Middle Miocene eolian deposit in the Loess Plateau marks the strengthening of aridification of Central Asia. The high degree of similarity between the geochemical properties of Longxi eolian deposit, Hipparion Red-Earth and Quaternary loess a suggests that a rather similar source provenance. The dust accumulation rate (DAR) of Longxi section, which is widely used as a proxy to document the aridity in source areas in marine and terrestrial record studies, recorded the aridity condition in northwestern China over a period from Middle Miocene to Late Miocene. The DAR of the section shows that the continent aridity remains moderate and relative stable over that period.

中国黄土的磁组构特征及其古风向指示意义

The transportation and deposition of eolian materials of Chinese loess is correlated and effected by the monsoon from the mid-high latitude. Therefore study of the winter monsoon evolution can help us to understand the dynamic mechanism to climate changes in the east-Asian areas. The anisotropy of magnetic susceptibility (AMS) measurements have been carried out on the samples from the last 250ka wind -blown loess-paleosol sequences at Baicaoyuan and Luochuan. And the main conclusions are following:The magnetic foliation is almost horizontal of the two sections. AMS canthus be represented by an oblate ellipsoid with average K3 perpendicular to thebedding plane and Ki within the bedding plane. It has also shown that the ^-factor isless than 0.5 of the majority of samples. So the two sections are normal magneticfabric for sediments.The degree of anisotropy always shows a strong correlation with the foliationrather than with lineation, therefore the anisotropy is controlled by the foliation.Furthermore the foliation is nearly less than 1.02 and shows the typical wind-blownsediments anisotropy.The intensity of winter monsoon, grain size of the eolian inputs, the foliationand the degree of anisotropy are somewhat inter-related. Generally, the higherintensity of the winter monsoon will carry coarser-grained eolian material, therebyresulting in a larger foliation during deposition. Also the post-depositional compactioncontributes to the anisotropy.The AMS features between loess and paleosol are somewhat different. Wefound that the F, P values of paleosol are lower than that of its parent loess respectively. Moreover, the difference does also exists between the two sections. The anisotropy of Baicaoyuan is more significant than Luochuan section, which maybe related with the location and the intensity of the post-deposition reworks.5. We note that the declination of the long axis is NWW in Baicaoyuan section and the observed NWW direction of the winter monsoon winds based on AMS is consistent with the view that the winter monsoons prevail along the NW-SE direction. But at the Luochuan section, because of the strong affection of the post-deposition reworks, the direction of the long axis is nearly random in the foliation and hardly recognizes the paleowind direction since the last two interglacials.Correlation between the two loess-paleosol sequences implies that it is available in arid or semi-arid areas to take AMS to recognize the paleowind directions on the Loess Plateau.

Caratterizzazione geo-petrografica, petrologica e geochimica di rocce anatettiche del nord Sardegna

The High Grade Metamorphic Complex (HGMC) of Variscan basement of north Sardinia is characterized by the widespread of migmatites. This study is focused on two localities of NE Sardinia (Porto Ottiolu and Punta Sirenella) where ortho- and para-derivates migmatites outcrop. A geological and structural survey was carried out, leading to the realization of a geological schematic map of Punta Sirenella area. Several samples of different rocks were collected for petrographic, micro-structural minero-chemical and geochemical analyses. In the Porto Ottiolu area three main deformation phases have been identified; D1, characterized by tight folds with sub-horizontal axes, rarely preserved in paragneisses; D2, that produce a pervasive foliation oriented N100° 45°SW marked by biotite and sillimanite blastesis and locally transposed by shear zone oriented N170°; D3, late deformation phase caused symmetric folds with sub-horizontal axes with no axial plane schistosity. Leucosomes form pods and layers along S2 schistosity but also leucosomes along shear zones have been observed. In the Punta Sirenella area, three main deformation phases have been identified; D1, is manifested by the transposition of centimeter-sized leucosomes and is rarely observed in paragneisses were produce open folds with sub-vertical axes; D2, NW-SE oriented on whose XY plane three mineralogical lineation (quartz+plagioclase, fibrolite+quarz and muscovite) lie; D3, a ductile-brittle deformation phase that produce a mylonitc S3 foliation that locally become the most evident schistosity in the field oriented N140° steeply dipping toward NE. In both areas, leucosomes of sedimentary-derived migmatites are generally trondhjemitic pointing out for a H2O fluxed melting reaction, but also granitic leucosomes have been found, produced by muscovite dehydration melting. Leucosomes of migmatitic orthogneiss instead, have granitic compositions. Migmatization started early, during the compressional and crustal thickening (sin-D1, pre-D2) and was still active during exhumation stage. For each studied outcrop of migmatite pseudosections for the average mesosome composition have been calculated; these pseudosections have been used to model the P-T conditions of anatexis on the basis of the melt volume (%) of melt, Si/Al and Na/K molar ratios, modal content of garnet and Si content in metamorphic white mica. Further pseudosections have been calculated for the average composition of leucosomes in order to define the P-T conditions of the end of the crystallization through intersection of solidus curve and isopleths of Si content in white mica and/or XMg ratio in biotite. Thermodynamic modeling on ortho- and sedimentary-derived migmatites of Punta Sirenella yield P-T conditions of 1.1-1.3 GPa - 670-740°C for migmatitic event and 0.75-0.90 GPa - 660-730°C for the end of crystallization. These conditions are fit well with previous studies on adjacent rocks. Modeling of Porto Ottiolu ortho- and sedimentary-derived migmatites yield P-T conditions of 0.85-1.05 GPa - 690-730°C for migmatitic event and 0.35-0.55 GPa - 630-690°C strongly affected by re-equilibration during exhumation, expecially for crystallization conditions. Geochemical analyses of samples belonging to Porto Ottiolu and Punta Sirenella orthogneisses show a strong link with those of other orthogneisses outcropping in NE Sardinia (for instance, Lode-Mamone and Golfo Aranci) that are considered the intrusive counterparts of middle-Ordovician metavolcanics rocks outcropping in the Nappe Zone. Thus, the studied ortogneiss bodies, even lacking radiometric data, can be considered as belonging to the same magmatic cycle.