4,195 research outputs found
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
Description and evaluation of the Acoustic Profiling of Ocean Currents (APOC) system used on R. V. Oceanus cruise 96 on 11-22 May 1981
The underway current profiling system which consists of a microprocessor controlled data logger that collects and formats data from a four beam Ametek-Straza 300 kHz acoustic Doppler current profiler, heading from the ship's gyrocompass, and navigation information from a Loran-C receiver and a satellite navigation unit is discussed. Data are recorded on magnetic tape and real time is calculated. Time averaging is required to remove effects of ship motion. An intercomparison is made with a moored vector measuring current meter (VMCM). The mean difference in hourly averaged APOC and VMCM currents over the four hour intercomparison is a few mm s minus including: two Gulf Stream crossings, a warm core ring survey, and shallow water in a frontal zone to the east of Nantucket Shoals
Hydrographic data from R/V endeavor cruise #90
The final cruise of the NSF sponsored Warm Core Rings Program studied a Warm Core Ring (WCR) in the Fall of 1982 as it formed from a large northward meander of the Gulf Stream. This ring, known as 82-H or the eighth ring identified in 1982, formed over the New England Seamounts near 39.5 deg N, 65 deg W. Surveys using Expendable Bathythermographs, Conductivity-Temperature-Depth-Oxygen stations and Doppler Current Profiling provide a look at the genesis of a WCR. These measurements reveal that WCR 82-H separated from the Gulf Stream sometime between October 2-5. This ring was a typical WCR with a diameter of about 200 km and speeds in the high velocity core of the 175 cm/sec. Satellite imagery of 82-H following the cruise showed that it drifted WSW in the Slope Water region at almost 9 km/day, had at least one interaction with the Gulf Stream and was last observed on February 8, 1983 at 39 deg N, 72 deg W
The geometry of the Barbour-Bertotti theories I. The reduction process
The dynamics of interacting particles is investigated in the
non-relativistic context of the Barbour-Bertotti theories. The reduction
process on this constrained system yields a Lagrangian in the form of a
Riemannian line element. The involved metric, degenerate in the flat
configuration space, is the first fundamental form of the space of orbits of
translations and rotations (the Leibniz group). The Riemann tensor and the
scalar curvature are computed by a generalized Gauss formula in terms of the
vorticity tensors of generators of the rotations. The curvature scalar is
further given in terms of the principal moments of inertia of the system. Line
configurations are singular for . A comparison with similar methods in
molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit
Poisson approximations for the Ising model
A -dimensional Ising model on a lattice torus is considered. As the size
of the lattice tends to infinity, a Poisson approximation is given for the
distribution of the number of copies in the lattice of any given local
configuration, provided the magnetic field tends to and the
pair potential remains fixed. Using the Stein-Chen method, a bound is given
for the total variation error in the ferromagnetic case.Comment: 25 pages, 1 figur
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
Quenched QCD at finite density
Simulations of quenched at relatively small but {\it nonzero} chemical
potential on lattices indicate that the nucleon
screening mass decreases linearly as increases predicting a critical
chemical potential of one third the nucleon mass, , by extrapolation.
The meson spectrum does not change as increases over the same range, from
zero to . Past studies of quenched lattice QCD have suggested that
there is phase transition at . We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for ranging from to
. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte
The Problem of Inertia in Friedmann Universes
In this paper we study the origin of inertia in a curved spacetime,
particularly the spatially flat, open and closed Friedmann universes. This is
done using Sciama's law of inertial induction, which is based on Mach's
principle, and expresses the analogy between the retarded far fields of
electrodynamics and those of gravitation. After obtaining covariant expressions
for electromagnetic fields due to an accelerating point charge in Friedmann
models, we adopt Sciama's law to obtain the inertial force on an accelerating
mass by integrating over the contributions from all the matter in the
universe. The resulting inertial force has the form , where
depends on the choice of the cosmological parameters such as ,
, and and is also red-shift dependent.Comment: 10 page
New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
I show how there is an ambiguity in how one treats auxiliary variables in
gauge theories including general relativity cast as 3 + 1 geometrodynamics.
Auxiliary variables may be treated pre-variationally as multiplier coordinates
or as the velocities corresponding to cyclic coordinates. The latter treatment
works through the physical meaninglessness of auxiliary variables' values
applying also to the end points (or end spatial hypersurfaces) of the
variation, so that these are free rather than fixed. [This is also known as
variation with natural boundary conditions.] Further principles of dynamics
workings such as Routhian reduction and the Dirac procedure are shown to have
parallel counterparts for this new formalism. One advantage of the new scheme
is that the corresponding actions are more manifestly relational. While the
electric potential is usually regarded as a multiplier coordinate and Arnowitt,
Deser and Misner have regarded the lapse and shift likewise, this paper's
scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose
corresponding velocities are, respectively, the abovementioned previously used
variables. This paper's way of thinking about gauge theory furthermore admits
interesting generalizations, which shall be provided in a second paper.Comment: 11 page
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
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