759 research outputs found
Reconstructing Trees from Subtree Weights
The tree-metric theorem provides a necessary and sufficient condition for a
dissimilarity matrix to be a tree metric, and has served as the foundation for
numerous distance-based reconstruction methods in phylogenetics. Our main
result is an extension of the tree-metric theorem to more general dissimilarity
maps. In particular, we show that a tree with n leaves is reconstructible from
the weights of the m-leaf subtrees provided that n \geq 2m-1
Self-forced gravitational waveforms for Extreme and Intermediate mass ratio inspirals
We present the first orbit-integrated self force effects on the gravitational
waveform for an I(E)MRI source. We consider the quasi-circular motion of a
particle in the spacetime of a Schwarzschild black hole and study the
dependence of the dephasing of the corresponding gravitational waveforms due to
ignoring the conservative piece of the self force. We calculate the cumulative
dephasing of the waveforms and their overlap integral, and discuss the
importance of the conservative piece of the self force in detection and
parameter estimation. For long templates the inclusion of the conservative
piece is crucial for gravitational-wave astronomy, yet may be ignored for short
templates with little effect on detection rate. We then discuss the effect of
the mass ratio and the start point of the motion on the dephasing.Comment: 9 pages, 15 figures. Substantially expanded and revised. We added:
description of the orbits and analysis of the dependence of the dephasing
effect on the parameter space, specifically the mass ratio and starting point
of the motion. Also added a more thorough description of out metho
Energy in one dimensional linear waves in a string
We consider the energy density and energy transfer in small amplitude,
one-dimensional waves on a string, and find that the common expressions used in
textbooks for the introductory physics with calculus course give wrong results
for some cases, including standing waves. We discuss the origin of the problem,
and how it can be corrected in a way appropriate for the introductory calculus
based physics course.Comment: 5 page
Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation
Comparing the corrections to Kepler's law with orbital evolution under a self
force, we extract the finite, already regularized part of the latter in a
specific gauge. We apply this method to a quasi-circular orbit around a
Schwarzschild black hole of an extreme mass ratio binary, and determine the
first- and second-order conservative gravitational self force in a post
Newtonian expansion. We use these results in the construction of the
gravitational waveform, and revisit the question of the relative contribution
of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure
A Radiation Scalar for Numerical Relativity
This letter describes a scalar curvature invariant for general relativity
with a certain, distinctive feature. While many such invariants exist, this one
vanishes in regions of space-time which can be said unambiguously to contain no
gravitational radiation. In more general regions which incontrovertibly support
non-trivial radiation fields, it can be used to extract local,
coordinate-independent information partially characterizing that radiation.
While a clear, physical interpretation is possible only in such radiation
zones, a simple algorithm can be given to extend the definition smoothly to
generic regions of space-time.Comment: 4 pages, 1 EPS figur
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