1,600 research outputs found
Rifts in Spreading Wax Layers
We report experimental results on the rift formation between two freezing wax
plates. The plates were pulled apart with constant velocity, while floating on
the melt, in a way akin to the tectonic plates of the earth's crust. At slow
spreading rates, a rift, initially perpendicular to the spreading direction,
was found to be stable, while above a critical spreading rate a "spiky" rift
with fracture zones almost parallel to the spreading direction developed. At
yet higher spreading rates a second transition from the spiky rift to a zig-zag
pattern occurred. In this regime the rift can be characterized by a single
angle which was found to be dependent on the spreading rate. We show that the
oblique spreading angles agree with a simple geometrical model. The coarsening
of the zig-zag pattern over time and the three-dimensional structure of the
solidified crust are also discussed.Comment: 4 pages, Postscript fil
Cosmological Surrealism: More than ``Eternal Reality" is Needed
Inflationary Cosmology makes the universe ``eternal" and provides for
recurrent universe creation, ad infinitum -- making it also plausible to assume
that ``our" Big Bang was also preceeded by others, etc.. However, GR tells us
that in the ``parent" universe's reference frame, the newborn universe's
expansion will never start. Our picture of ``reality" in spacetime has to be
enlarged.Comment: 7 pages, TAUP N23
Robust Inference of Trees
This paper is concerned with the reliable inference of optimal
tree-approximations to the dependency structure of an unknown distribution
generating data. The traditional approach to the problem measures the
dependency strength between random variables by the index called mutual
information. In this paper reliability is achieved by Walley's imprecise
Dirichlet model, which generalizes Bayesian learning with Dirichlet priors.
Adopting the imprecise Dirichlet model results in posterior interval
expectation for mutual information, and in a set of plausible trees consistent
with the data. Reliable inference about the actual tree is achieved by focusing
on the substructure common to all the plausible trees. We develop an exact
algorithm that infers the substructure in time O(m^4), m being the number of
random variables. The new algorithm is applied to a set of data sampled from a
known distribution. The method is shown to reliably infer edges of the actual
tree even when the data are very scarce, unlike the traditional approach.
Finally, we provide lower and upper credibility limits for mutual information
under the imprecise Dirichlet model. These enable the previous developments to
be extended to a full inferential method for trees.Comment: 26 pages, 7 figure
Negaton and Positon Solutions of the KDV Equation
We give a systematic classification and a detailed discussion of the
structure, motion and scattering of the recently discovered negaton and positon
solutions of the Korteweg-de Vries equation. There are two distinct types of
negaton solutions which we label and , where is the
order of the Wronskian used in the derivation. For negatons, the number of
singularities and zeros is finite and they show very interesting time
dependence. The general motion is in the positive direction, except for
certain negatons which exhibit one oscillation around the origin. In contrast,
there is just one type of positon solution, which we label . For
positons, one gets a finite number of singularities for odd, but an
infinite number for even values of . The general motion of positons is in
the negative direction with periodic oscillations. Negatons and positons
retain their identities in a scattering process and their phase shifts are
discussed. We obtain a simple explanation of all phase shifts by generalizing
the notions of ``mass" and ``center of mass" to singular solutions. Finally, it
is shown that negaton and positon solutions of the KdV equation can be used to
obtain corresponding new solutions of the modified KdV equation.Comment: 20 pages plus 12 figures(available from authors on request),Latex
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Nucleating Black Holes via Non-Orientable Instantons
We extend the analysis of black hole pair creation to include non- orientable
instantons. We classify these instantons in terms of their fundamental
symmetries and orientations. Many of these instantons admit the pin structure
which corresponds to the fermions actually observed in nature, and so the
natural objection that these manifolds do not admit spin structure may not be
relevant. Furthermore, we analyse the thermodynamical properties of
non-orientable black holes and find that in the non-extreme case, there are
interesting modifications of the usual formulae for temperature and entropy.Comment: 27 pages LaTeX, minor typos are correcte
Balancing Minimum Spanning and Shortest Path Trees
This paper give a simple linear-time algorithm that, given a weighted
digraph, finds a spanning tree that simultaneously approximates a shortest-path
tree and a minimum spanning tree. The algorithm provides a continuous
trade-off: given the two trees and epsilon > 0, the algorithm returns a
spanning tree in which the distance between any vertex and the root of the
shortest-path tree is at most 1+epsilon times the shortest-path distance, and
yet the total weight of the tree is at most 1+2/epsilon times the weight of a
minimum spanning tree. This is the best tradeoff possible. The paper also
describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993
On the formation of black holes in non-symmetric gravity
It has been recently suggested that the Non-symmetric Gravitational Theory
(NGT) is free of black holes. Here, we study the linear version of NGT. We find
that even with spherical symmetry the skew part of the metric is generally
non-static. In addition, if the skew field is initially regular, it will remain
regular everywhere and, in particular, at the horizon. Therefore, in the
fully-nonlinear theory, if the initial skew-field is sufficiently small, the
formation of a black hole is to be anticipated.Comment: 9 pages, ordinary LaTex
The physical meaning of the "boost-rotation symmetric" solutions within the general interpretation of Einstein's theory of gravitation
The answer to the question, what physical meaning should be attributed to the
so-called boost-rotation symmetric exact solutions to the field equations of
general relativity, is provided within the general interpretation scheme for
the ``theories of relativity'', based on group theoretical arguments, and set
forth by Erich Kretschmann already in the year 1917.Comment: 9 pages, 1 figure; text to appear in General Relativity and
Gravitatio
Non-integrability of the mixmaster universe
We comment on an analysis by Contopoulos et al. which demonstrates that the
governing six-dimensional Einstein equations for the mixmaster space-time
metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case
irrespective of the value, , of the generating Hamiltonian which is a
constant of motion. For we find numerous closed orbits with two
unstable eigenvalues strongly indicating that there cannot exist two additional
first integrals apart from the Hamiltonian and thus that the system, at least
for this case, is very likely not integrable. In addition, we present numerical
evidence that the average Lyapunov exponent nevertheless vanishes. The model is
thus a very interesting example of a Hamiltonian dynamical system, which is
likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures
compressed and uuencoded with uufiles. Revised version to appear in J Phys.
Black Holes in Modified Gravity (MOG)
The field equations for Scalar-Tensor-Vector-Gravity (STVG) or modified
gravity (MOG) have a static, spherically symmetric black hole solution
determined by the mass with two horizons. The strength of the gravitational
constant is where is a parameter. A regular
singularity-free MOG solution is derived using a nonlinear field dynamics for
the repulsive gravitational field component and a reasonable physical
energy-momentum tensor. The Kruskal-Szekeres completion of the MOG black hole
solution is obtained. The Kerr-MOG black hole solution is determined by the
mass , the parameter and the spin angular momentum . The
equations of motion and the stability condition of a test particle orbiting the
MOG black hole are derived, and the radius of the black hole photosphere and
the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are
calculated. A traversable wormhole solution is constructed with a throat
stabilized by the repulsive component of the gravitational field.Comment: 14 pages, 3 figures. Upgraded version of paper to match published
version in European Physics Journal
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