942 research outputs found
Foundations of Relational Particle Dynamics
Relational particle dynamics include the dynamics of pure shape and cases in
which absolute scale or absolute rotation are additionally meaningful. These
are interesting as regards the absolute versus relative motion debate as well
as discussion of conceptual issues connected with the problem of time in
quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces
of shapes are n-spheres and complex projective spaces, from which knowledge I
construct natural mechanics on these spaces. I also show that these coincide
with Barbour's indirectly-constructed relational dynamics by performing a full
reduction on the latter. Then the identification of the configuration spaces as
n-spheres and complex projective spaces, for which spaces much mathematics is
available, significantly advances the understanding of Barbour's relational
theory in spatial dimensions 1 and 2. I also provide the parallel study of a
new theory for which positon and scale are purely relative but orientation is
absolute. The configuration space for this is an n-sphere regardless of the
spatial dimension, which renders this theory a more tractable arena for
investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update
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
Gravitomagnetism and the Clock Effect
The main theoretical aspects of gravitomagnetism are reviewed. It is shown
that the gravitomagnetic precession of a gyroscope is intimately connected with
the special temporal structure around a rotating mass that is revealed by the
gravitomagnetic clock effect. This remarkable effect, which involves the
difference in the proper periods of a standard clock in prograde and retrograde
circular geodesic orbits around a rotating mass, is discussed in detail. The
implications of this effect for the notion of ``inertial dragging'' in the
general theory of relativity are presented. The theory of the clock effect is
developed within the PPN framework and the possibility of measuring it via
spaceborne clocks is examined.Comment: 27 pages, LaTeX, submitted to Proc. Bad Honnef Meeting on: GYROS,
CLOCKS, AND INTERFEROMETERS: TESTING GENERAL RELATIVITY IN SPACE (22 - 27
August 1999; Bad Honnef, Germany
Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations
Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux–Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita–Itoh–Bogoyavlensky, Toda, and Adler–Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new
High-temperature ferromagnetism of electrons in narrow impurity bands: Application to CaB
Ferromagnetism with high Curie temperature , well above room
temperature, and very small saturation moment has been reported in various
carbon and boron systems. It is argued that the magnetization must be very
inhomogeneous with only a small fraction of the sample ferromagnetically
ordered. It is shown that a possible source of high within the
ferromagnetic regions is itinerant electrons occupying a narrow impurity band.
Correlation effects do not reduce the effective interaction which enters the
Stoner criterion in the same way as in a bulk band. It is also shown how, in
the impurity band case, spin wave excitations may not be effective in lowering
below its value given by Stoner theory. These ideas are applied to
CaB and a thorough review of the experimental situation in this material is
given. It is suggested that the intrinsic magnetism of the B and O
dimers might be exploited in suitable structures containing these elements.Comment: 26 pages, 2 figure
The relativistic Sagnac Effect: two derivations
The phase shift due to the Sagnac Effect, for relativistic matter and
electromagnetic beams, counter-propagating in a rotating interferometer, is
deduced using two different approaches. From one hand, we show that the
relativistic law of velocity addition leads to the well known Sagnac time
difference, which is the same independently of the physical nature of the
interfering beams, evidencing in this way the universality of the effect.
Another derivation is based on a formal analogy with the phase shift induced by
the magnetic potential for charged particles travelling in a region where a
constant vector potential is present: this is the so called Aharonov-Bohm
effect. Both derivations are carried out in a fully relativistic context, using
a suitable 1+3 splitting that allows us to recognize and define the space where
electromagnetic and matter waves propagate: this is an extended 3-space, which
we call "relative space". It is recognized as the only space having an actual
physical meaning from an operational point of view, and it is identified as the
'physical space of the rotating platform': the geometry of this space turns out
to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor
corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and
M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also
http://digilander.libero.it/solciclo
Classification of non-Riemannian doubled-yet-gauged spacetime
Assuming covariant fields as the `fundamental' variables,
Double Field Theory can accommodate novel geometries where a Riemannian metric
cannot be defined, even locally. Here we present a complete classification of
such non-Riemannian spacetimes in terms of two non-negative integers,
, . Upon these backgrounds, strings become
chiral and anti-chiral over and directions respectively, while
particles and strings are frozen over the directions. In
particular, we identify as Riemannian manifolds, as
non-relativistic spacetime, as Gomis-Ooguri non-relativistic string,
as ultra-relativistic Carroll geometry, and as Siegel's
chiral string. Combined with a covariant Kaluza-Klein ansatz which we further
spell, leads to Newton-Cartan gravity. Alternative to the conventional
string compactifications on small manifolds, non-Riemannian spacetime such as
, may open a new scheme of the dimensional reduction from ten to
four.Comment: 1+41 pages; v2) Refs added; v3) Published version; v4) Sign error in
(2.51) correcte
On the gravitodynamics of moving bodies
In the present work we propose a generalization of Newton's gravitational
theory from the original works of Heaviside and Sciama, that takes into account
both approaches, and accomplishes the same result in a simpler way than the
standard cosmological approach. The established formulation describes the local
gravitational field related to the observables and effectively implements the
Mach's principle in a quantitative form that retakes Dirac's large number
hypothesis. As a consequence of the equivalence principle and the application
of this formulation to the observable universe, we obtain, as an immediate
result, a value of Omega = 2. We construct a dynamic model for a galaxy without
dark matter, which fits well with recent observational data, in terms of a
variable effective inertial mass that reflects the present dynamic state of the
universe and that replicates from first principles, the phenomenology proposed
in MOND. The remarkable aspect of these results is the connection of the effect
dubbed dark matter with the dark energy field, which makes it possible for us
to interpret it as longitudinal gravitational waves.Comment: 18 pages, 4 figures. Final version: almost identical to the reference
journal; Cent. Eur. J. Phys. 201
Soft systems methodology: a context within a 50-year retrospective of OR/MS
Soft systems methodology (SSM) has been used in the practice of operations research and management science OR/MS) since the early 1970s. In the 1990s, it emerged as a viable academic discipline. Unfortunately, its proponents consider SSM and traditional systems thinking to be mutually exclusive. Despite the differences claimed by SSM proponents between the two, they have been complementary. An extensive sampling of the OR/MS literature over its entire lifetime demonstrates the richness with which the non-SSM literature has been addressing the very same issues as does SSM
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