A technique for 3-D robot vision for space applications

An extension of the MIAG algorithm for recognition and motion parameter determination of general 3-D polyhedral objects based on model matching techniques and using Moment Invariants as features of object representation is discussed. Results of tests conducted on the algorithm under conditions simulating space conditions are presented

PRS-Net: planar reflective symmetry detection net for 3D models

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces

Discrete isometry groups of symmetric spaces

This survey is based on a series of lectures that we gave at MSRI in Spring 2015 and on a series of papers, mostly written jointly with Joan Porti. Our goal here is to: 1. Describe a class of discrete subgroups $\Gamma<G$ of higher rank semisimple Lie groups, which exhibit some "rank 1 behavior". 2. Give different characterizations of the subclass of Anosov subgroups, which generalize convex-cocompact subgroups of rank 1 Lie groups, in terms of various equivalent dynamical and geometric properties (such as asymptotically embedded, RCA, Morse, URU). 3. Discuss the topological dynamics of discrete subgroups $\Gamma$ on flag manifolds associated to $G$ and Finsler compactifications of associated symmetric spaces $X=G/K$. Find domains of proper discontinuity and use them to construct natural bordifications and compactifications of the locally symmetric spaces $X/\Gamma$.Comment: 77 page

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Spacetime approach to force-free magnetospheres

Force-Free Electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone. Such plasma is thought to play a key role in the physics of pulsars and active black holes. Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time. In this article we systematically develop the theory of force-free magnetospheres taking a spacetime perspective. Using a suite of spacetime tools and techniques (notably exterior calculus) we cover 1) the basics of the theory, 2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), 3) the behavior of current sheets, 4) the general theory of stationary, axisymmetric magnetospheres and 5) general properties of pulsar and black hole magnetospheres. We thereby synthesize, clarify and generalize known aspects of the physics of force-free magnetospheres, while also introducing several new results.Comment: v2: numerous improvements; v3: further improvements, matches published versio

Generic guide concepts for the European Spallation Source

The construction of the European Spallation Source (ESS) faces many challenges from the neutron beam transport point of view: The spallation source is specified as being driven by a 5 MW beam of protons, each with 2 GeV energy, and yet the requirements in instrument background suppression relative to measured signal vary between 10$^{-6}$ and 10$^{-8}$. The energetic particles, particularly above 20 MeV, which are expected to be produced in abundance in the target, have to be filtered in order to make the beamlines safe, operational and provide good quality measurements with low background. We present generic neutron guides of short and medium length instruments which are optimized for good performance at minimal cost. Direct line of sight to the source is avoided twice, with either the first point out of line of sight or both being inside the bunker (20\,m) to minimize shielding costs. These guide geometries are regarded as a baseline to define standards for instruments to be constructed at ESS. They are used to find commonalities and develop principles and solutions for common problems. Lastly, we report the impact of employing the over-illumination concept to mitigate losses from random misalignment passively, and that over-illumination should be used sparingly in key locations to be effective. For more widespread alignment issues, a more direct, active approach is likely to be needed

Self-force with (3+1) codes: a primer for numerical relativists

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $< 1$. We also demonstrate consistency between $t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.Comment: 23 pages, 13 figure

The last gasps of VY CMa: Aperture synthesis and adaptive optics imagery

We present new observations of the red supergiant VY CMa at 1.25 micron, 1.65 micron, 2.26 micron, 3.08 micron and 4.8 micron. Two complementary observational techniques were utilized: non-redundant aperture masking on the 10-m Keck-I telescope yielding images of the innermost regions at unprecedented resolution, and adaptive optics imaging on the ESO 3.6-m telescope at La Silla attaining extremely high (~10^5) peak-to-noise dynamic range over a wide field. For the first time the inner dust shell has been resolved in the near-infrared to reveal a one-sided extension of circumstellar emission within 0.1" (~15 R_star) of the star. The line-of-sight optical depths of the circumstellar dust shell at 1.65 micron, 2.26 micron, and 3.08 micron have been estimated to be 1.86 +/- 0.42, 0.85 +/- 0.20, and 0.44 +/- 0.11. These new results allow the bolometric luminosity of VY~CMa to be estimated independent of the dust shell geometry, yielding L_star ~ 2x10^5 L_sun. A variety of dust condensations, including a large scattering plume and a bow-shaped dust feature, were observed in the faint, extended nebula up to 4" from the central source. While the origin of the nebulous plume remains uncertain, a geometrical model is developed assuming the plume is produced by radially-driven dust grains forming at a rotating flow insertion point with a rotational period between 1200-4200 years, which is perhaps the stellar rotational period or the orbital period of an unseen companion.Comment: 25 pages total with 1 table and 5 figures. Accepted by Astrophysical Journal (to appear in February 1999

Recent mathematical developments in the Skyrme model

In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of the model. Then we review the instanton method which yields an analytical approximation to the minimum energy configuration in any sector of fixed baryon number, as well as an approximation to the surfaces which join together all the low energy critical points. We present some explicit results for B=2. We then describe the work done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theory. Next we turn to recent work on the dynamics of Skyrmions. We focus exclusively on the low energy interaction, specifically the gradient flow method put forward by Manton. We illustrate the method with some expository toy models. We end this review with a presentation of our own work on the semi-classical quantization of nucleon states and low energy nucleon-nucleon scattering.Comment: 129 pages, about 30 figures, original manuscript of published Physics Report