95 research outputs found
Numerical calculations near spatial infinity
After describing in short some problems and methods regarding the smoothness
of null infinity for isolated systems, I present numerical calculations in
which both spatial and null infinity can be studied. The reduced conformal
field equations based on the conformal Gauss gauge allow us in spherical
symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in
a smooth way including spacelike, null and timelike infinity and the domain
close to the singularity.Comment: 10 pages, 2 postscript figures, uses psfrag; to appear in the
Proceedings of the Spanish Relativity Meeting (ERE 2006), Palma de Mallorca,
Spain, 4-8 September 200
Swarm-Based Optimization with Random Descent
We extend our study of the swarm-based gradient descent method for non-convex
optimization, [Lu, Tadmor & Zenginoglu, arXiv:2211.17157], to allow random
descent directions. We recall that the swarm-based approach consists of a swarm
of agents, each identified with a position, , and mass, . The
key is the transfer of mass from high ground to low(-est) ground. The mass of
an agent dictates its step size: lighter agents take larger steps. In this
paper, the essential new feature is the choice of direction: rather than
restricting the swarm to march in the steepest gradient descent, we let agents
proceed in randomly chosen directions centered around -- but otherwise
different from -- the gradient direction. The random search secures the descent
property while at the same time, enabling greater exploration of ambient space.
Convergence analysis and benchmark optimizations demonstrate the effectiveness
of the swarm-based random descent method as a multi-dimensional global
optimizer
A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
We present a new approach to solve the 2+1 Teukolsky equation for
gravitational perturbations of a Kerr black hole. Our approach relies on a new
horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial
compactification. In particular, we present a framework for waveform generation
from point-particle perturbations. Extensive tests of a time domain
implementation in the code {\it Teukode} are presented. The code can
efficiently deliver waveforms at future null infinity. As a first application
of the method, we compute the gravitational waveforms from inspiraling and
coalescing black-hole binaries in the large-mass-ratio limit. The smaller mass
black hole is modeled as a point particle whose dynamics is driven by an
effective-one-body-resummed analytical radiation reaction force. We compare the
analytical angular momentum loss to the gravitational wave angular momentum
flux. We find that higher-order post-Newtonian corrections are needed to
improve the consistency for rapidly spinning binaries. Close to merger, the
subdominant multipolar amplitudes (notably the ones) are enhanced for
retrograde orbits with respect to prograde ones. We argue that this effect
mirrors nonnegligible deviations from circularity of the dynamics during the
late-plunge and merger phase. We compute the gravitational wave energy flux
flowing into the black hole during the inspiral using a time-domain formalism
proposed by Poisson. Finally, a self-consistent, iterative method to compute
the gravitational wave fluxes at leading-order in the mass of the particle is
presented. For a specific case study with =0.9, a simulation that uses
the consistent flux differs from one that uses the analytical flux by
gravitational wave cycles over a total of about cycles. In this case the
horizon absorption accounts for about gravitational wave cycles
Hyperboloidal data and evolution
We discuss the hyperboloidal evolution problem in general relativity from a
numerical perspective, and present some new results. Families of initial data
which are the hyperboloidal analogue of Brill waves are constructed
numerically, and a systematic search for apparent horizons is performed.
Schwarzschild-Kruskal spacetime is discussed as a first application of
Friedrich's general conformal field equations in spherical symmetry, and the
Maxwell equations are discussed on a nontrivial background as a toy model for
continuum instabilities.Comment: 11 pages, 9 figures. To appear in the Proceedings of the Spanish
Relativity Meeting (ERE 2005), Oviedo, Spain, 6-10 Sept 200
Self-force via Green functions and worldline integration
A compact object moving in curved spacetime interacts with its own
gravitational field. This leads to both dissipative and conservative
corrections to the motion, which can be interpreted as a self-force acting on
the object. The original formalism describing this self-force relied heavily on
the Green function of the linear differential operator that governs
gravitational perturbations. However, because the global calculation of Green
functions in non-trivial black hole spacetimes has been an open problem until
recently, alternative methods were established to calculate self-force effects
using sophisticated regularization techniques that avoid the computation of the
global Green function. We present a method for calculating the self-force that
employs the global Green function and is therefore closely modeled after the
original self-force expressions. Our quantitative method involves two stages:
(i) numerical approximation of the retarded Green function in the background
spacetime; (ii) evaluation of convolution integrals along the worldline of the
object. This novel approach can be used along arbitrary worldlines, including
those currently inaccessible to more established computational techniques.
Furthermore, it yields geometrical insight into the contributions to
self-interaction from curved geometry (back-scattering) and trapping of null
geodesics. We demonstrate the method on the motion of a scalar charge in
Schwarzschild spacetime. This toy model retains the physical history-dependence
of the self-force but avoids gauge issues and allows us to focus on basic
principles. We compute the self-field and self-force for many worldlines
including accelerated circular orbits, eccentric orbits at the separatrix, and
radial infall. This method, closely modeled after the original formalism,
provides a promising complementary approach to the self-force problem.Comment: 18 pages, 9 figure
Towards an organizational theory of hubris: symptoms, behaviours and social fields within finance and banking
Hubris has become a popular explanation for all kinds of business failure. It is often reduced to the one-dimensional notion of âover-confidenceâ, particularly on the part of CEOs. There is a need to clarify the extent to which other attitudes and behaviours constitute hubris, and how they are affected by such organisational dynamics as the struggle for power, status and material rewards between actors. This article explores these issues within the finance and banking sectors. It uses the Critical Incident Technique to identify behaviours associated with hubris and probes the interaction between them and the organisational contexts in which they occur. Five categories of behaviour based on an analysis of 101 incidents are described, as are a series of âinflection dynamicsâ that reinforce the behaviours in question and constitute a social field conducive to hubris. I challenge the reductionist views that hubris is primarily a psychological state consisting mainly of âover-confidenceâ. This article seeks to complexify the term hubris and to develop an organisational rather than purely psychology theory of its emergence and institutionalisation within finance and banking
A Random Forest Assisted Evolutionary Algorithm for Data-Driven Constrained Multi-Objective Combinatorial Optimization of Trauma Systems for publication
Many real-world optimization problems can be
solved by using the data-driven approach only, simply because no
analytic objective functions are available for evaluating candidate
solutions. In this work, we address a class of expensive datadriven
constrained multi-objective combinatorial optimization
problems, where the objectives and constraints can be calculated
only on the basis of large amount of data. To solve this class
of problems, we propose to use random forests and radial basis
function networks as surrogates to approximate both objective
and constraint functions. In addition, logistic regression models
are introduced to rectify the surrogate-assisted fitness evaluations
and a stochastic ranking selection is adopted to further reduce
the influences of the approximated constraint functions. Three
variants of the proposed algorithm are empirically evaluated on
multi-objective knapsack benchmark problems and two realworld
trauma system design problems. Experimental results
demonstrate that the variant using random forest models as
the surrogates are effective and efficient in solving data-driven
constrained multi-objective combinatorial optimization problems
Binary black-hole simulation SXS:BBH:0054
Simulation of a black-hole binary system evolved by the SpEC code
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