Understanding singularities in Cartan's and NSF geometric structures

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.Comment: 22 pages, 2 figure

Fuzzy spectral and spatial feature integration for classification of nonferrous materials in hyperspectral data

Hyperspectral data allows the construction of more elaborate models to sample the properties of the nonferrous materials than the standard RGB color representation. In this paper, the nonferrous waste materials are studied as they cannot be sorted by classical procedures due to their color, weight and shape similarities. The experimental results presented in this paper reveal that factors such as the various levels of oxidization of the waste materials and the slight differences in their chemical composition preclude the use of the spectral features in a simplistic manner for robust material classification. To address these problems, the proposed FUSSER (fuzzy spectral and spatial classifier) algorithm detailed in this paper merges the spectral and spatial features to obtain a combined feature vector that is able to better sample the properties of the nonferrous materials than the single pixel spectral features when applied to the construction of multivariate Gaussian distributions. This approach allows the implementation of statistical region merging techniques in order to increase the performance of the classification process. To achieve an efficient implementation, the dimensionality of the hyperspectral data is reduced by constructing bio-inspired spectral fuzzy sets that minimize the amount of redundant information contained in adjacent hyperspectral bands. The experimental results indicate that the proposed algorithm increased the overall classification rate from 44% using RGB data up to 98% when the spectral-spatial features are used for nonferrous material classification

Integrating Singular Functions on the Sphere

We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of residues through a limiting procedure.Comment: 15 pages, revte

Null Surfaces and the Bach Equations

It is shown that the integrability conditions that arise in the Null Surface Formulation (NSF) of general relativity (GR) impose a field equation on the local null surfaces which is equivalent to the vanishing of the Bach tensor. This field equation is written explicitly to second order in a perturbation expansion. The field equation is further simplified if asymptotic flatness is imposed on the underlying space-time. The resulting equation determines the global null surfaces of asymptotically flat, radiative space-times. It is also shown that the source term of this equation is constructed from the free Bondi data at future null infinity. Possible generalizations of this field equation are analyzed. In particular we include other field equations for surfaces that have already appeared in the literature which coincide with ours at a linear level. We find that the other equations do not yield null surfaces for GR

Null surfaces formulation in 3D

The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One method makes explicit use of the conformal factor while the other only uses conformal information. The resulting set of equations contain the same geometrical meaning as the 4-D formulation without the technical complexities of the higher dimensional analog. A canonical family of null surfaces in this formulation, the light cone cuts of null infinity, are constructed on asymptotically flat space times and some of their kinematical aspects discussed. A particular example, which nevertheless contains most of the generic features is explicitly constructed and analyzed, revealing the behavior predicted in the full theory

Schwarzschild Tests of the Wahlquist-Estabrook-Buchman-Bardeen Tetrad Formulation for Numerical Relativity

A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit spherical symmetry and tested for accuracy and stability in the evolution of spherically symmetric black holes (the Schwarzschild geometry). The lapse and shift which specify the evolution of the coordinates relative to the tetrad congruence are reset at frequent time intervals to keep the constant-time hypersurfaces nearly orthogonal to the tetrad congruence and the spatial coordinate satisfying a kind of minimal rate of strain condition. By arranging through initial conditions that the constant-time hypersurfaces are asymptotically hyperbolic, we simplify the boundary value problem and improve stability of the evolution. Results are obtained for both tetrad gauges (``Nester'' and ``Lorentz'') of the WEBB formalism using finite difference numerical methods. We are able to obtain stable unconstrained evolution with the Nester gauge for certain initial conditions, but not with the Lorentz gauge.Comment: (accepted by Phys. Rev. D) minor changes; typos correcte

Electromagnetic Springback Reshaping

Electromagnetic forming is an impulse-based forming technique where high dynamic pressure is distributed to conductive materials by pure electromagnetic interaction. The aim of this paper is to present how springback can be controlled when the EMF technique is used as a second corrective step; bringing formed parts to the desired final shape by means of magnetic impulses in critical areas of the formed components. This analysis is based on the results of two experimental studies. In the first, the selected preformed specimen shape is the L-shape bent part of HSS DP600, in 0.8 and 1.95 mm thickness, and Aluminium Alloy 5754, in 1 and 2 mm thickness. The second geometries are two rocket nozzle panels made of a thick but soft copper alloy. While the geometry and the material are the similar, the first approach of this work was developed using smaller panels (about 30 cm long) and the full size (about 1 m long), in order to study the behaviour of the material and the approximate energy levels required to scale up the full size panels. Overall this study shows EM forming can have a potent effect in controlling springback

Connectivity, neutral theories and the assessment of species vulnerability to global change in temperate estuaries

One of the main adaptation strategies to global change scenarios, aiming to preserve ecosystem functioning and biodiversity, is to maximise ecosystem resilience. The resilience of a species metapopulation can be improved by facilitating connectivity between local populations, which will prevent demographic stochasticity and inbreeding. The objective of this investigation is to estimate the degree of connectivity among estuarine species along the north-eastern Iberian coast, in order to assess community vulnerability to global change scenarios. To address this objective, two connectivity proxy types have been used based upon genetic and ecological drift processes: 1) DNA markers for the bivalve cockle (Cerastoderma edule) and seagrass Zostera noltei, and 2) the decrease in the number of species shared between two sites with geographic distance; neutral biodiversity theory predicts that dispersal limitation modulates this decrease, and this has been explored in estuarine plants and macroinvertebrates. Results indicate dispersal limitation for both saltmarsh plants and seagrass beds community and Z. noltei populations; this suggests they are especially vulnerable to expected climate changes on their habitats. In contrast, unstructured spatial pattern found in macroinvertebrate communities and in C. edule genetic populations in the area suggests that estuarine soft-bottom macroinvertebrates with planktonic larval dispersal strategies may have a high resilience capacity to moderate changes within their habitats. Our findings can help environmental managers to prioritise the most vulnerable species and habitats to be restored

Biologically-inspired data decorrelation for hyperspectral imaging

Hyper-spectral data allows the construction of more robust statistical models to sample the material properties than the standard tri-chromatic color representation. However, because of the large dimensionality and complexity of the hyper-spectral data, the extraction of robust features (image descriptors) is not a trivial issue. Thus, to facilitate efficient feature extraction, decorrelation techniques are commonly applied to reduce the dimensionality of the hyper-spectral data with the aim of generating compact and highly discriminative image descriptors. Current methodologies for data decorrelation such as principal component analysis (PCA), linear discriminant analysis (LDA), wavelet decomposition (WD), or band selection methods require complex and subjective training procedures and in addition the compressed spectral information is not directly related to the physical (spectral) characteristics associated with the analyzed materials. The major objective of this article is to introduce and evaluate a new data decorrelation methodology using an approach that closely emulates the human vision. The proposed data decorrelation scheme has been employed to optimally minimize the amount of redundant information contained in the highly correlated hyper-spectral bands and has been comprehensively evaluated in the context of non-ferrous material classificatio