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Chris Cannings: A Life in Games
Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career
Unambiguous determination of gravitational waveforms from binary black hole mergers
Gravitational radiation is properly defined only at future null infinity
(\scri), but in practice it is estimated from data calculated at a finite
radius. We have used characteristic extraction to calculate gravitational
radiation at \scri for the inspiral and merger of two equal mass non-spinning
black holes. Thus we have determined the first unambiguous merger waveforms for
this problem. The implementation is general purpose, and can be applied to
calculate the gravitational radiation, at \scri, given data at a finite
radius calculated in another computation.Comment: 4 pages, 3 figures, published versio
Strategies for the characteristic extraction of gravitational waveforms
We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component Psi4 to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the O(1/r) radiative part of Psi4 in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves
High-powered Gravitational News
We describe the computation of the Bondi news for gravitational radiation. We
have implemented a computer code for this problem. We discuss the theory behind
it as well as the results of validation tests. Our approach uses the
compactified null cone formalism, with the computational domain extending to
future null infinity and with a worldtube as inner boundary. We calculate the
appropriate full Einstein equations in computational eth form in (a) the
interior of the computational domain and (b) on the inner boundary. At future
null infinity, we transform the computed data into standard Bondi coordinates
and so are able to express the news in terms of its standard and
polarization components. The resulting code is stable and
second-order convergent. It runs successfully even in the highly nonlinear
case, and has been tested with the news as high as 400, which represents a
gravitational radiation power of about .Comment: 24 pages, 4 figures. To appear in Phys. Rev.
Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin- Models
We apply the microscopic coupled-cluster method (CCM) to the spin-
models on both the one-dimensional chain and the two-dimensional square
lattice. Based on a systematic approximation scheme of the CCM developed by us
previously, we carry out high-order {\it ab initio} calculations using
computer-algebraic techniques. The ground-state properties of the models are
obtained with high accuracy as functions of the anisotropy parameter.
Furthermore, our CCM analysis enables us to study their quantum critical
behavior in a systematic and unbiased manner.Comment: (to appear in PRL). 4 pages, ReVTeX, two figures available upon
request. UMIST Preprint MA-000-000
Ill-posedness in the Einstein equations
It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of
Mathematical Physics (to appear August 2000
Fin(d)ing Nemo? Partnerships in compliance and enforcement on the Great Barrier Reef.
complianceFin(d)ing Nemo? Partnerships in compliance and enforcement on the Great Barrier Reef
Cauchy boundaries in linearized gravitational theory
We investigate the numerical stability of Cauchy evolution of linearized
gravitational theory in a 3-dimensional bounded domain. Criteria of robust
stability are proposed, developed into a testbed and used to study various
evolution-boundary algorithms. We construct a standard explicit finite
difference code which solves the unconstrained linearized Einstein equations in
the 3+1 formulation and measure its stability properties under Dirichlet,
Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability
of a specific evolution-boundary algorithm under random constraint violating
initial data and random boundary data.Comment: 23 pages including 3 figures and 2 tables, revte
Gravitational waveforms with controlled accuracy
A partially first-order form of the characteristic formulation is introduced
to control the accuracy in the computation of gravitational waveforms produced
by highly distorted single black hole spacetimes. Our approach is to reduce the
system of equations to first-order differential form on the angular
derivatives, while retaining the proven radial and time integration schemes of
the standard characteristic formulation. This results in significantly improved
accuracy over the standard mixed-order approach in the extremely nonlinear
post-merger regime of binary black hole collisions.Comment: Revised version, published in Phys. Rev. D, RevTeX, 16 pages, 4
figure
Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms
We present numerical relativity simulations of nine-orbit equal-mass binary
neutron star covering the quasicircular late inspiral and merger. The extracted
gravitational waveforms are analyzed for convergence and accuracy. Second order
convergence is observed up to contact, i.e. about 3-4 cycles to merger; error
estimates can be made up to this point. The uncertainties on the phase and the
amplitude are dominated by truncation errors and can be minimized to 0.13 rad
and less then 1%, respectively, by using several simulations and extrapolating
in resolution. In the latter case finite-radius extraction uncertainties become
a source of error of the same order and have to be taken into account. The
waveforms are tested against accuracy standards for data analysis. The
uncertainties on the waveforms are such that accuracy standards are generically
not met for signal-to-noise ratios relevant for detection, except for some best
cases using extrapolation from several runs. A detailed analysis of the errors
is thus imperative for the use of numerical relativity waveforms from binary
neutron stars in quantitative studies. The waveforms are compared with the
post-Newtonian Taylor T4 approximants both for point-particle and including the
analytically known tidal corrections. The T4 approximants accumulate
significant phase differences of 2 rad at contact and 4 rad at merger,
underestimating the influence of finite size effects. Tidal signatures in the
waveforms are thus important at least during the last six orbits of the merger
process.Comment: Physical Review D (Vol.85, No.10) 201
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