1,492 research outputs found
A Visualization of Null Geodesics for the Bonnor Massive Dipole
In this work we simulate null geodesics for the Bonnor massive dipole metric
by implementing a symbolic-numerical algorithm in Sage and Python. This program
is also capable of visualizing in 3D, in principle, the geodesics for any given
metric. Geodesics are launched from a common point, collectively forming a cone
of light beams, simulating a solid-angle section of a point source in front of
a massive object with a magnetic field. Parallel light beams also were
considered, and their bending due to the curvature of the space-time was
simulated.Comment: 9 pages, 5 figures, Presented at XIX Simposio Internacional de
M\'etodos Matem\'aticos Aplicados a las Ciencias (19th International
Symposium of Mathematical Methods Applied to Sciences, XIX-SIMMAC
Uncertainty in phylogenetic tree estimates
Estimating phylogenetic trees is an important problem in evolutionary
biology, environmental policy and medicine. Although trees are estimated, their
uncertainties are discarded by mathematicians working in tree space. Here we
explicitly model the multivariate uncertainty of tree estimates. We consider
both the cases where uncertainty information arises extrinsically (through
covariate information) and intrinsically (through the tree estimates
themselves). The importance of accounting for tree uncertainty in tree space is
demonstrated in two case studies. In the first instance, differences between
gene trees are small relative to their uncertainties, while in the second, the
differences are relatively large. Our main goal is visualization of tree
uncertainty, and we demonstrate advantages of our method with respect to
reproducibility, speed and preservation of topological differences compared to
visualization based on multidimensional scaling. The proposal highlights that
phylogenetic trees are estimated in an extremely high-dimensional space,
resulting in uncertainty information that cannot be discarded. Most
importantly, it is a method that allows biologists to diagnose whether
differences between gene trees are biologically meaningful, or due to
uncertainty in estimation.Comment: Final version accepted to Journal of Computational and Graphical
Statistic
Godel spacetime: elliptic-like geodesics and gyroscope precession
We study elliptic-like geodesic motion on hyperplanes orthogonal to the
cylindrical symmetry axes of the Godel spacetime by using an
eccentricity-semi-latus rectum parametrization which is familiar from the
Newtonian description of a two-body system. We compute several quantities which
summarize the main features of the motion, namely the coordinate time and
proper time periods of the radial motion, the frequency of the azimuthal
motion, the full variation of the azimuthal angle over a period, etc. Exact as
well as approximate (i.e., Taylor-expanded in the limit of small eccentricity)
analytic expressions of all these quantities are obtained. Finally, we consider
their application to the gyroscope precession frequency along these orbits,
generalizing the existing results for the circular case.Comment: 14 pages, 7 figures; revtex macro
Spacetime Embedding Diagrams for Black Holes
We show that the 1+1 dimensional reduction (i.e., the radial plane) of the
Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how
features of this spacetime can be seen from the embedding diagram. The purpose
of this work is educational: The associated embedding diagrams may be useful
for explaining aspects of black holes to students who are familiar with special
relativity, but not general relativity.Comment: 22 pages, 21 figures, RevTex. To be submitted to the American Journal
of Physics. Experts will wish only to skim appendix A and to look at the
pictures. Suggested Maple code is now compatible with MapleV4r
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