1,147 research outputs found
Scaling in a SU(2)/Z_3 model of cosmic superstring networks
Motivated by recent developments in superstring theory in the cosmological
context, we examine a field theory which contains string networks with 3-way
junctions. We perform numerical simulations of this model, identify the length
scales of the network that forms, and provide evidence that the length scales
tend towards a scaling regime, growing in proportion to time. We infer that the
presence of junctions does not in itself cause a superstring network to
dominate the energy density of the early Universe.Comment: 12pp, 3 fig
Charged Black Cosmic String
Global U(1) strings with cylindrical symmetry are studied in anti-de Sitter
spacetime. According as the magnitude of negative cosmological constant, they
form regular global cosmic strings, extremal black cosmic strings and charged
black cosmic strings, but no curvature singularity is involved. The
relationship between the topological charge of a neutral global string and the
black hole charge is clarified by duality transformation. Physical relevance as
straight string is briefly discussed.Comment: ll pages, LaTe
Defect formation and local gauge invariance
We propose a new mechanism for formation of topological defects in a U(1)
model with a local gauge symmetry. This mechanism leads to definite
predictions, which are qualitatively different from those of the Kibble-Zurek
mechanism of global theories. We confirm these predictions in numerical
simulations, and they can also be tested in superconductor experiments. We
believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and
the equations of motion added. To appear in PRL (http://prl.aps.org/
Transport of flexible chiral objects in a uniform shear flow
The transport of slightly deformable chiral objects in a uniform shear flow
is investigated. Depending on the equilibrium configuration one finds up to
four different asymptotic states that can be distinguished by a lateral drift
velocity of their center of mass, a rotational motion about the center of mass
and deformations of the object. These deformations influence the magnitudes of
the principal axes of the second moment tensor of the considered object and
also modify a scalar index characterizing its chirality. Moreover, the
deformations induced by the shear flow are essential for the phenomenon of
dynamical symmetry breaking: Objects that are achiral under equilibrium
conditions may dynamically acquire chirality and consequently experience a
drift in the lateral direction.Comment: 25 pages, 16 figure
Statistical Properties of Strings
We investigate numerically the configurational statistics of strings. The
algorithm models an ensemble of global cosmic strings, or equivalently
vortices in superfluid He. We use a new method which avoids the
specification of boundary conditions on the lattice. We therefore do not have
the artificial distinction between short and long string loops or a `second
phase' in the string network statistics associated with strings winding around
a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities
associated with the cubic lattices of previous work. We find that the
percentage of infinite string is somewhat lower than on cubic lattices, 63\%
instead of 80\%. We also investigate the Hagedorn transition, at which infinite
strings percolate, controlling the string density by rendering one of the
equilibrium states more probable. We measure the percolation threshold, the
critical exponent associated with the divergence of a suitably defined
susceptibility of the string loops, and that associated with the divergence of
the correlation length.Comment: 20 pages, 8 figures (uuencoded) appended, DAMTP-94-56, SUSX-TP-94-7
Numerical simulations of string networks in the Abelian-Higgs model
We present the results of a field theory simulation of networks of strings in
the Abelian Higgs model. Starting from a random initial configuration we show
that the resulting vortex tangle approaches a self-similar regime in which the
length density of lines of zeros of reduces as . We demonstrate
that the network loses energy directly into scalar and gauge radiation. These
results support a recent claim that particle production, and not gravitational
radiation, is the dominant energy loss mechanism for cosmic strings. This means
that cosmic strings in Grand Unified Theories are severely constrained by high
energy cosmic ray fluxes: either they are ruled out, or an implausibly small
fraction of their energy ends up in quarks and leptons.Comment: 4pp RevTeX, 3 eps figures, clarifications and new results included,
to be published in Phys. Rev. Let
Cosmic String Formation from Correlated Fields
We simulate the formation of cosmic strings at the zeros of a complex
Gaussian field with a power spectrum , specifically
addressing the issue of the fraction of length in infinite strings. We make two
improvements over previous simulations: we include a non-zero random background
field in our box to simulate the effect of long-wavelength modes, and we
examine the effects of smoothing the field on small scales. The inclusion of
the background field significantly reduces the fraction of length in infinite
strings for . Our results are consistent with the possibility that
infinite strings disappear at some in the range ,
although we cannot rule out , in which case infinite strings would
disappear only at the point where the mean string density goes to zero. We
present an analytic argument which suggests the latter case. Smoothing on small
scales eliminates closed loops on the order of the lattice cell size and leads
to a ``lattice-free" estimate of the infinite string fraction. As expected,
this fraction depends on the type of window function used for smoothing.Comment: 24 pages, latex, 10 figures, submitted to Phys Rev
Bifurcations and Chaos in the Six-Dimensional Turbulence Model of Gledzer
The cascade-shell model of turbulence with six real variables originated by
Gledzer is studied numerically using Mathematica 5.1. Periodic, doubly-periodic
and chaotic solutions and the routes to chaos via both frequency-locking and
period-doubling are found by the Poincar\'e plot of the first mode . The
circle map on the torus is well approximated by the summation of several
sinusoidal functions. The dependence of the rotation number on the viscosity
parameter is in accordance with that of the sine-circle map. The complicated
bifurcation structure and the revival of a stable periodic solution at the
smaller viscosity parameter in the present model indicates that the turbulent
state may be very sensitive to the Reynolds number.Comment: 19 pages, 12 figures submitted to JPS
Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling
The phenomenon of slow switching in populations of globally coupled
oscillators is discussed. This characteristic collective dynamics, which was
first discovered in a particular class of the phase oscillator model, is a
result of the formation of a heteroclinic loop connecting a pair of clustered
states of the population. We argue that the same behavior can arise in a wider
class of oscillator models with the amplitude degree of freedom. We also argue
how such heteroclinic loops arise inevitably and persist robustly in a
homogeneous population of globally coupled oscillators. Although the
heteroclinic loop might seem to arise only exceptionally, we find that it
appears rather easily by introducing the time-delay in the population which
would otherwise exhibit perfect phase synchrony. We argue that the appearance
of the heteroclinic loop induced by the delayed coupling is then characterized
by transcritical and saddle-node bifurcations. Slow switching arises when the
system with a heteroclinic loop is weakly perturbed. This will be demonstrated
with a vector model by applying weak noises. Other types of weak
symmetry-breaking perturbations can also cause slow switching.Comment: 10 pages, 14 figures, RevTex, twocolumn, to appear in Phys. Rev.
Gravitational Radiation by Cosmic Strings in a Junction
The formalism for computing the gravitational power radiation from
excitations on cosmic strings forming a junction is presented and applied to
the simple case of co-planar strings at a junction when the excitations are
generated along one string leg. The effects of polarization of the excitations
and of the back-reaction of the gravitational radiation on the small scale
structure of the strings are studied.Comment: minor changes added, the published version in JCA
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