819 research outputs found
The influence of Massive Black Hole Binaries on the Morphology of Merger Remnants
Massive black hole (MBH) binaries, formed as a result of galaxy mergers, are
expected to harden by dynamical friction and three-body stellar scatterings,
until emission of gravitational waves (GWs) leads to their final coalescence.
According to recent simulations, MBH binaries can efficiently harden via
stellar encounters only when the host geometry is triaxial, even if only
modestly, as angular momentum diffusion allows an efficient repopulation of the
binary loss cone. In this paper, we carry out a suite of N-body simulations of
equal-mass galaxy collisions, varying the initial orbits and density profiles
for the merging galaxies and running simulations both with and without central
MBHs. We find that the presence of an MBH binary in the remnant makes the
system nearly oblate, aligned with the galaxy merger plane, within a radius
enclosing 100 MBH masses. We never find binary hosts to be prolate on any
scale. The decaying MBHs slightly enhance the tangential anisotropy in the
centre of the remnant due to angular momentum injection and the slingshot
ejection of stars on nearly radial orbits. This latter effect results in about
1% of the remnant stars being expelled from the galactic nucleus. Finally, we
do not find any strong connection between the remnant morphology and the binary
hardening rate, which depends only on the inner density slope of the remnant
galaxy. Our results suggest that MBH binaries are able to coalesce within a few
Gyr, even if the binary is found to partially erase the merger-induced
triaxiality from the remnant.Comment: 16 pages, 13 figures, 4 tables; accepted for publication in MNRA
Dynamic movement primitives: volumetric obstacle avoidance
Dynamic Movement Primitives (DMPs) are a framework for learning a trajectory from a demonstration. The trajectory can be learned efficiently after only one demonstration, and it is immediate to adapt it to new goal positions and time duration. Moreover, the trajectory is also robust against perturbations. However, obstacle avoidance for DMPs is still an open problem. In this work, we propose an extension of DMPs to support volumetric obstacle avoidance based on the use of superquadric potentials. We show the advantages of this approach when obstacles have known shape, and we extend it to unknown objects using minimal enclosing ellipsoids. A simulation and experiments with a real robot validate the framework, and we make freely available our implementation
Optimal Collision Avoidance Trajectories for Unmanned/Remotely Piloted Aircraft
The post-911 environment has punctuated the force-multiplying capabilities that Remotely Piloted Aircraft (RPA) provides combatant commanders at all echelons on the battlefield. Not only have unmanned aircraft systems made near-revolutionary impacts on the battlefield, their utility and proliferation in law enforcement, homeland security, humanitarian operations, and commercial applications have likewise increased at a rapid rate. As such, under the Federal Aviation Administration (FAA) Modernization and Reform Act of 2012, the United States Congress tasked the FAA to provide for the safe integration of civil unmanned aircraft systems into the national airspace system (NAS) as soon as practicable, but not later than September 30, 2015. However, a necessary entrance criterion to operate RPAs in the NAS is the ability to Sense and Avoid (SAA) both cooperative and noncooperative air traffic to attain a target level of safety as a traditional manned aircraft platform. The goal of this research effort is twofold: First, develop techniques for calculating optimal avoidance trajectories, and second, develop techniques for estimating an intruder aircraft\u27s trajectory in a stochastic environment. This dissertation describes the optimal control problem associated with SAA and uses a direct orthogonal collocation method to solve this problem and then analyzes these results for different collision avoidance scenarios
The strongest gravitational lenses: I. The statistical impact of cluster mergers
For more than a decade now, it has been controversial whether or not the high
rate of giant gravitational arcs and the largest observed Einstein radii are
consistent with the standard cosmological model. Recent studies indicate that
mergers provide an efficient mechanism to substantially increase the
strong-lensing efficiency of individual clusters. Based on purely semi-analytic
methods, we investigated the statistical impact of cluster mergers on the
distribution of the largest Einstein radii and the optical depth for giant
gravitational arcs of selected cluster samples. Analysing representative
all-sky realizations of clusters at redshifts z < 1 and assuming a constant
source redshift of z_s = 2.0, we find that mergers increase the number of
Einstein radii above 10 arcsec (20 arcsec) by ~ 35 % (~ 55 %). Exploiting the
tight correlation between Einstein radii and lensing cross sections, we infer
that the optical depth for giant gravitational arcs with a length-to-width
ratio > 7.5 of those clusters with Einstein radii above 10 arcsec (20 arcsec)
increases by ~ 45 % (85 %). Our findings suggest that cluster mergers
significantly influence in particular the statistical lensing properties of the
strongest gravitational lenses. We conclude that semi-analytic studies must
inevitably take these events into account before questioning the standard
cosmological model on the basis of the largest observed Einstein radii and the
statistics of giant gravitational arcs.Comment: 23 pages, 18 figures; accepted for publication in Astronomy and
Astrophysics; v2: minor corrections (added clarifying comments; added Fig.
19) to match the accepted versio
A Branch-and-Bound Algorithm for Quadratically-Constrained Sparse Filter Design
This paper presents an exact algorithm for sparse filter design under a quadratic constraint on filter performance. The algorithm is based on branch-and-bound, a combinatorial optimization procedure that can either guarantee an optimal solution or produce a sparse solution with a bound on its deviation from optimality. To reduce the complexity of branch-and-bound, several methods are developed for bounding the optimal filter cost. Bounds based on infeasibility yield incrementally accumulating improvements with minimal computation, while two convex relaxations, referred to as linear and diagonal relaxations, are derived to provide stronger bounds. The approximation properties of the two relaxations are characterized analytically as well as numerically. Design examples involving wireless channel equalization and minimum-variance distortionless-response beamforming show that the complexity of obtaining certifiably optimal solutions can often be significantly reduced by incorporating diagonal relaxations, especially in more difficult instances. In the case of early termination due to computational constraints, diagonal relaxations strengthen the bound on the proximity of the final solution to the optimum.Texas Instruments Leadership University Consortium Progra
Fully Automatic Expression-Invariant Face Correspondence
We consider the problem of computing accurate point-to-point correspondences
among a set of human face scans with varying expressions. Our fully automatic
approach does not require any manually placed markers on the scan. Instead, the
approach learns the locations of a set of landmarks present in a database and
uses this knowledge to automatically predict the locations of these landmarks
on a newly available scan. The predicted landmarks are then used to compute
point-to-point correspondences between a template model and the newly available
scan. To accurately fit the expression of the template to the expression of the
scan, we use as template a blendshape model. Our algorithm was tested on a
database of human faces of different ethnic groups with strongly varying
expressions. Experimental results show that the obtained point-to-point
correspondence is both highly accurate and consistent for most of the tested 3D
face models
Locally optimal Delaunay-refinement and optimisation-based mesh generation
The field of mesh generation concerns the development of efficient algorithmic techniques to construct high-quality tessellations of complex geometrical objects. In this thesis, I investigate the problem of unstructured simplicial mesh generation for problems in two- and three-dimensional spaces, in which meshes consist of collections of triangular and tetrahedral elements. I focus on the development of efficient algorithms and computer programs to produce high-quality meshes for planar, surface and volumetric objects of arbitrary complexity. I develop and implement a number of new algorithms for mesh construction based on the Frontal-Delaunay paradigm - a hybridisation of conventional Delaunay-refinement and advancing-front techniques. I show that the proposed algorithms are a significant improvement on existing approaches, typically outperforming the Delaunay-refinement technique in terms of both element shape- and size-quality, while offering significantly improved theoretical robustness compared to advancing-front techniques. I verify experimentally that the proposed methods achieve the same element shape- and size-guarantees that are typically associated with conventional Delaunay-refinement techniques. In addition to mesh construction, methods for mesh improvement are also investigated. I develop and implement a family of techniques designed to improve the element shape quality of existing simplicial meshes, using a combination of optimisation-based vertex smoothing, local topological transformation and vertex insertion techniques. These operations are interleaved according to a new priority-based schedule, and I show that the resulting algorithms are competitive with existing state-of-the-art approaches in terms of mesh quality, while offering significant improvements in computational efficiency. Optimised C++ implementations for the proposed mesh generation and mesh optimisation algorithms are provided in the JIGSAW and JITTERBUG software libraries
- …