305 research outputs found
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
Next to leading order eta production at hadron colliders
Inclusive eta production at hadron colliders is considered,based on
evaluation of eta fragmentation functions at next to leading order. Absolute
predictions at LHC and SSC are presented, including the ratio ,
together with the estimate of the theoretical uncertainty, as a possible
neutral background to the detection.Comment: 8 pages, latex, FNT/T-93/13,14 figures avilable upon reques
Magnetized cosmological perturbations
A large-scale cosmic magnetic field affects not only the growth of density
perturbations, but also rotational instabilities and anisotropic deformation in
the density distribution. We give a fully relativistic treatment of all these
effects, incorporating the magneto-curvature coupling that arises in a
relativistic approach. We show that this coupling produces a small enhancement
of the growing mode on superhorizon scales. The magnetic field generates new
nonadiabatic constant and decaying modes, as well as nonadiabatic corrections
to the standard growing and decaying modes. Magnetized isocurvature
perturbations are purely decaying on superhorizon scales. On subhorizon scales
before recombination, magnetized density perturbations propagate as
magneto-sonic waves, leading to a small decrease in the spacing of acoustic
peaks. Fluctuations in the field direction induce scale-dependent vorticity,
and generate precession in the rotational vector. On small scales, magnetized
density vortices propagate as Alfv\'{e}n waves during the radiation era. After
recombination, they decay slower than non-magnetized vortices. Magnetic
fluctuations are also an active source of anisotropic distortion in the density
distribution. We derive the evolution equations for this distortion, and find a
particular growing solution.Comment: Revised version, typos corrected, to appear in Phys. Rev.
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result
Euler-Poincar\'e approaches to nematodynamics
Nematodynamics is the orientation dynamics of flowless liquid-crystals. We
show how Euler-Poincar\'e reduction produces a unifying framework for various
theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen's micropolar
theory. In particular, we show that these theories are all compatible with each
other and some of them allow for more general configurations involving a non
vanishing discination density. All results are also extended to flowing liquid
crystals.Comment: 26 pages, no figure
Average luminosity distance in inhomogeneous universes
The paper studies the correction to the distance modulus induced by
inhomogeneities and averaged over all directions from a given observer. The
inhomogeneities are modeled as mass-compensated voids in random or regular
lattices within Swiss-cheese universes. Void radii below 300 Mpc are
considered, which are supported by current redshift surveys and limited by the
recently observed imprint such voids leave on CMB. The averaging over all
directions, performed by numerical ray tracing, is non-perturbative and
includes the supernovas inside the voids. Voids aligning along a certain
direction produce a cumulative gravitational lensing correction that increases
with their number. Such corrections are destroyed by the averaging over all
directions, even in non-randomized simple cubic void lattices. At low
redshifts, the average correction is not zero but decays with the peculiar
velocities and redshift. Its upper bound is provided by the maximal average
correction which assumes no random cancelations between different voids. It is
described well by a linear perturbation formula and, for the voids considered,
is 20% of the correction corresponding to the maximal peculiar velocity. The
average correction calculated in random and simple cubic void lattices is
severely damped below the predicted maximal one after a single void diameter.
That is traced to cancellations between the corrections from the fronts and
backs of different voids. All that implies that voids cannot imitate the effect
of dark energy unless they have radii and peculiar velocities much larger than
the currently observed. The results obtained allow one to readily predict the
redshift above which the direction-averaged fluctuation in the Hubble diagram
falls below a required precision and suggest a method to extract the background
Hubble constant from low redshift data without the need to correct for peculiar
velocities.Comment: 34 pages, 21 figures, matches the version accepted in JCA
Radiative Decay of a Long-Lived Particle and Big-Bang Nucleosynthesis
The effects of radiatively decaying, long-lived particles on big-bang
nucleosynthesis (BBN) are discussed. If high-energy photons are emitted after
BBN, they may change the abundances of the light elements through
photodissociation processes, which may result in a significant discrepancy
between the BBN theory and observation. We calculate the abundances of the
light elements, including the effects of photodissociation induced by a
radiatively decaying particle, but neglecting the hadronic branching ratio.
Using these calculated abundances, we derive a constraint on such particles by
comparing our theoretical results with observations. Taking into account the
recent controversies regarding the observations of the light-element
abundances, we derive constraints for various combinations of the measurements.
We also discuss several models which predict such radiatively decaying
particles, and we derive constraints on such models.Comment: Published version in Phys. Rev. D. Typos in figure captions correcte
Cosmic microwave background anisotropies in multi-connected flat spaces
This article investigates the signature of the seventeen multi-connected flat
spaces in cosmic microwave background (CMB) maps. For each such space it
recalls a fundamental domain and a set of generating matrices, and then goes on
to find an orthonormal basis for the set of eigenmodes of the Laplace operator
on that space. The basis eigenmodes are expressed as linear combinations of
eigenmodes of the simply connected Euclidean space. A preceding work, which
provides a general method for implementing multi-connected topologies in
standard CMB codes, is then applied to simulate CMB maps and angular power
spectra for each space. Unlike in the 3-torus, the results in most
multi-connected flat spaces depend on the location of the observer. This effect
is discussed in detail. In particular, it is shown that the correlated circles
on a CMB map are generically not back-to-back, so that negative search of
back-to-back circles in the WMAP data does not exclude a vast majority of flat
or nearly flat topologies.Comment: 33 pages, 19 figures, 1 table. Submitted to PR
Spinor Field in Bianchi type-I Universe: regular solutions
Self-consistent solutions to the nonlinear spinor field equations in General
Relativity has been studied for the case of Bianchi type-I (B-I) space-time. It
has been shown that, for some special type of nonliearity the model provides
regular solution, but this singularity-free solutions are attained at the cost
of broken dominant energy condition in Hawking-Penrose theorem. It has also
been shown that the introduction of -term in the Lagrangian generates
oscillations of the B-I model, which is not the case in absence of
term. Moreover, for the linear spinor field, the term provides
oscillatory solutions, those are regular everywhere, without violating dominant
energy condition.
Key words: Nonlinear spinor field (NLSF), Bianch type -I model (B-I),
term
PACS 98.80.C CosmologyComment: RevTex, 21 page
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