2,203 research outputs found
The MaxwellâVlasov equations in EulerâPoincarĂ© form
Low's well-known action principle for the MaxwellâVlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By imposing suitable constraints on the variations and analyzing invariance properties of the Lagrangian, as one does for the Euler equations for the rigid body and ideal fluids, we first transform this action principle into purely Eulerian variables. Hamilton's principle for the Eulerian description of Low's action principle then casts the MaxwellâVlasov equations into EulerâPoincarĂ© form for right invariant motion on the diffeomorphism group of position-velocity phase space, [openface R]6. Legendre transforming the Eulerian form of Low's action principle produces the Hamiltonian formulation of these equations in the Eulerian description. Since it arises from EulerâPoincarĂ© equations, this Hamiltonian formulation can be written in terms of a Poisson structure that contains the LieâPoisson bracket on the dual of a semidirect product Lie algebra. Because of degeneracies in the Lagrangian, the Legendre transform is dealt with using the Dirac theory of constraints. Another MaxwellâVlasov Poisson structure is known, whose ingredients are the LieâPoisson bracket on the dual of the Lie algebra of symplectomorphisms of phase space and the BornâInfeld brackets for the Maxwell field. We discuss the relationship between these two Hamiltonian formulations. We also discuss the general KelvinâNoether theorem for EulerâPoincarĂ© equations and its meaning in the plasma context
A Century of Cosmology
In the century since Einstein's anno mirabilis of 1905, our concept of the
Universe has expanded from Kapteyn's flattened disk of stars only 10 kpc across
to an observed horizon about 30 Gpc across that is only a tiny fraction of an
immensely large inflated bubble. The expansion of our knowledge about the
Universe, both in the types of data and the sheer quantity of data, has been
just as dramatic. This talk will summarize this century of progress and our
current understanding of the cosmos.Comment: Talk presented at the "Relativistic Astrophysics and Cosmology -
Einstein's Legacy" meeting in Munich, Nov 2005. Proceedings will be published
in the Springer-Verlag "ESO Astrophysics Symposia" series. 10 pages Latex
with 2 figure
On the stability of self-gravitating accreting flows
Analytic methods show stability of the stationary accretion of test fluids
but they are inconclusive in the case of self-gravitating stationary flows. We
investigate numerically stability of those stationary flows onto compact
objects that are transonic and rich in gas. In all studied examples solutions
appear stable. Numerical investigation suggests also that the analogy between
sonic and event horizons holds for small perturbations of compact support but
fails in the case of finite perturbations.Comment: 10 pages, accepted for publication in PR
APOLLO: the Apache Point Observatory Lunar Laser-ranging Operation: Instrument Description and First Detections
A next-generation lunar laser ranging apparatus using the 3.5 m telescope at
the Apache Point Observatory in southern New Mexico has begun science
operation. APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation)
has achieved one-millimeter range precision to the moon which should lead to
approximately one-order-of-magnitude improvements in the precision of several
tests of fundamental properties of gravity. We briefly motivate the scientific
goals, and then give a detailed discussion of the APOLLO instrumentation.Comment: 37 pages; 10 figures; 1 table: accepted for publication in PAS
Modeling Repulsive Gravity with Creation
There is a growing interest in the cosmologists for theories with negative
energy scalar fields and creation, in order to model a repulsive gravity. The
classical steady state cosmology proposed by Bondi, Gold and Hoyle in 1948, was
the first such theory which used a negative kinetic energy creation field to
invoke creation of matter. We emphasize that creation plays very crucial role
in cosmology and provides a natural explanation to the various explosive
phenomena occurring in local (z<0.1) and extra galactic universe. We exemplify
this point of view by considering the resurrected version of this theory - the
quasi-steady state theory, which tries to relate creation events directly to
the large scale dynamics of the universe and supplies more natural explanations
of the observed phenomena. Although the theory predicts a decelerating universe
at the present era, it explains successfully the recent SNe Ia observations
(which require an accelerating universe in the standard cosmology), as we show
in this paper by performing a Bayesian analysis of the data.Comment: The paper uses an old SNeIa dataset. With the new improved data, for
example the updated gold sample (Riess et al, astro-ph/0611572), the fit
improves considerably (\chi^2/DoF=197/180 and a probability of
goodness-of-fit=18%
Non-singular radiation cosmological models
In this paper we analyse the possibility of constructing singularity-free
inhomogeneous cosmological models with a pure radiation field as matter
content. It is shown that the conditions for regularity are very easy to
implement and therefore there is a huge number of such spacetimes.Comment: 13 pages, LaTex, ws-mpla, to appear in Modern Physics Letters
An absolute calibration system for millimeter-accuracy APOLLO measurements
Lunar laser ranging provides a number of leading experimental tests of
gravitation -- important in our quest to unify General Relativity and the
Standard Model of physics. The Apache Point Observatory Lunar Laser-ranging
Operation (APOLLO) has for years achieved median range precision at the ~2 mm
level. Yet residuals in model-measurement comparisons are an order-of-magnitude
larger, raising the question of whether the ranging data are not nearly as
accurate as they are precise, or if the models are incomplete or
ill-conditioned. This paper describes a new absolute calibration system (ACS)
intended both as a tool for exposing and eliminating sources of systematic
error, and also as a means to directly calibrate ranging data in-situ. The
system consists of a high-repetition-rate (80 MHz) laser emitting short (< 10
ps) pulses that are locked to a cesium clock. In essence, the ACS delivers
photons to the APOLLO detector at exquisitely well-defined time intervals as a
"truth" input against which APOLLO's timing performance may be judged and
corrected. Preliminary analysis indicates no inaccuracies in APOLLO data beyond
the ~3 mm level, suggesting that historical APOLLO data are of high quality and
motivating continued work on model capabilities. The ACS provides the means to
deliver APOLLO data both accurate and precise below the 2 mm level.Comment: 21 pages, 10 figures, submitted to Classical and Quantum Gravit
The Triple-Alpha Process and the Anthropically Allowed Values of the Weak Scale
In multiple-universe models, the constants of nature may have different
values in different universes. Agrawal, Barr, Donoghue and Seckel have pointed
out that the Higgs mass parameter, as the only dimensionful parameter of the
standard model, is of particular interest. By considering a range of values of
this parameter, they showed that the Higgs vacuum expectation value must have a
magnitude less than 5.0 times its observed value, in order for complex
elements, and thus life, to form. In this report, we look at the effects of the
Higgs mass parameter on the triple-alpha process in stars. This process, which
is greatly enhanced by a resonance in Carbon-12, is responsible for virtually
all of the carbon production in the universe. We find that the Higgs vacuum
expectation value must have a magnitude greater than 0.90 times its observed
value in order for an appreciable amount of carbon to form, thus significantly
narrowing the allowed region of Agrawal et al.Comment: 9 pages, 1 figur
Thiol-yne \u27Click\u27 Chemistry As a Route to Functional Lipid Mimetics
Thiol-alkyne \u27click\u27 chemistry is a modular, efficient mechanism to synthesize complex A2B 3-arm star polymers. This general motif is similar to a phospholipid where the A blocks correspond to lypophilic chains and the B block represents the polar head group. In this communication we employ thiol-yne chemistry to produce polypeptide-based A2B lipid mimetics. The utility of the thiol-yne reaction is demonstrated by using a divergent and a convergent approach in the synthesis. These polymers self-assemble in aqueous solution into spherical vesicles with a relatively narrow size distribution independent of block composition over the range studied. Using the thiol-yne convergent synthesis, we envision a modular approach to functionalize proteins or oligopeptides with lipophilic chains that can imbed seamlessly into a cell membrane
Two-Dimensional Topology of the 2dF Galaxy Redshift Survey
We study the topology of the publicly available data released by the 2dFGRS.
The 2dFGRS data contains over 100,000 galaxy redshifts with a magnitude limit
of b_J=19.45 and is the largest such survey to date. The data lie over a wide
range of right ascension (75 degree strips) but only within a narrow range of
declination (10 degree and 15 degree strips). This allows measurements of the
two-dimensional genus to be made.
The NGP displays a slight meatball shift topology, whereas the SGP displays a
bubble like topology. The current SGP data also have a slightly higher genus
amplitude. In both cases, a slight excess of overdense regions are found over
underdense regions. We assess the significance of these features using mock
catalogs drawn from the Virgo Consortium's Hubble Volume LCDM z=0 simulation.
We find that differences between the NGP and SGP genus curves are only
significant at the 1 sigma level. The average genus curve of the 2dFGRS agrees
well with that extracted from the LCDM mock catalogs.
We compare the amplitude of the 2dFGRS genus curve to the amplitude of a
Gaussian random field with the same power spectrum as the 2dFGRS and find,
contradictory to results for the 3D genus of other samples, that the amplitude
of the GRF genus curve is slightly lower than that of the 2dFGRS. This could be
due to a a feature in the current data set or the 2D genus may not be as
sensitive as the 3D genus to non-linear clustering due to the averaging over
the thickness of the slice in 2D. (Abridged)Comment: Submitted to ApJ A version with Figure 1 in higher resolution can be
obtained from http://www.physics.drexel.edu/~hoyle
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