46,108 research outputs found
An alternative formulation of classical electromagnetic duality
By introducing a doublet of electromagnetic four dimensional vector
potentials, we set up a manifestly Lorentz covariant and SO(2) duality
invariant classical field theory of electric and magnetic charges. In our
formulation one does not need to introduce the concept of Dirac string.Comment: 14 pages, no figures, Latex, minor corrections, references and
acknowledgements adde
Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions
A diffusion-limited aggregation process, in which clusters coalesce by means
of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a
heuristic argument that predicts logarithmic corrections to the mean-field
asymptotic behavior for the concentration of clusters of mass at time ,
, for . The total
concentration of clusters, , decays as at . We also investigate the problem with a localized steady source of
monomers and find that the steady-state concentration scales as
, , and , respectively,
for the spatial dimension equal to 1, 2, and 3. The total number of
clusters, , grows with time as , , and
for = 1, 2, and 3. Furthermore, in three dimensions we
obtain an asymptotic solution for the steady state cluster-mass distribution:
, with the scaling function
and the scaling variable .Comment: 12 pages, plain Te
Quantum Hall Ferromagnetism in a Two-Dimensional Electron System
Experiments on a nearly spin degenerate two-dimensional electron system
reveals unusual hysteretic and relaxational transport in the fractional quantum
Hall effect regime. The transition between the spin-polarized (with fill
fraction ) and spin-unpolarized () states is accompanied
by a complicated series of hysteresis loops reminiscent of a classical
ferromagnet. In correlation with the hysteresis, magnetoresistance can either
grow or decay logarithmically in time with remarkable persistence and does not
saturate. In contrast to the established models of relaxation, the relaxation
rate exhibits an anomalous divergence as temperature is reduced. These results
indicate the presence of novel two-dimensional ferromagnetism with a
complicated magnetic domain dynamic.Comment: 15 pages, 5 figure
Asymptotic behavior of A + B --> inert for particles with a drift
We consider the asymptotic behavior of the (one dimensional) two-species
annihilation reaction A + B --> 0, where both species have a uniform drift in
the same direction and like species have a hard core exclusion. Extensive
numerical simulations show that starting with an initially random distribution
of A's and B's at equal concentration the density decays like t^{-1/3} for long
times. This process is thus in a different universality class from the cases
without drift or with drift in different directions for the different species.Comment: LaTeX, 6pp including 3 figures in LaTeX picture mod
Granular gases under extreme driving
We study inelastic gases in two dimensions using event-driven molecular
dynamics simulations. Our focus is the nature of the stationary state attained
by rare injection of large amounts of energy to balance the dissipation due to
collisions. We find that under such extreme driving, with the injection rate
much smaller than the collision rate, the velocity distribution has a power-law
high energy tail. The numerically measured exponent characterizing this tail is
in excellent agreement with predictions of kinetic theory over a wide range of
system parameters. We conclude that driving by rare but powerful energy
injection leads to a well-mixed gas and constitutes an alternative mechanism
for agitating granular matter. In this distinct nonequilibrium steady-state,
energy cascades from large to small scales. Our simulations also show that when
the injection rate is comparable with the collision rate, the velocity
distribution has a stretched exponential tail.Comment: 6 pages, 7 figures; new version contains 2 new figures and text
describing cascade
Cosmic-ray acceleration in supernova remnants: non-linear theory revised
A rapidly growing amount of evidences, mostly coming from the recent
gamma-ray observations of Galactic supernova remnants (SNRs), is seriously
challenging our understanding of how particles are accelerated at fast shocks.
The cosmic-ray (CR) spectra required to account for the observed phenomenology
are in fact as steep as , i.e., steeper than the
test-particle prediction of first-order Fermi acceleration, and significantly
steeper than what expected in a more refined non-linear theory of diffusive
shock acceleration. By accounting for the dynamical back-reaction of the
non-thermal particles, such a theory in fact predicts that the more efficient
the particle acceleration, the flatter the CR spectrum. In this work we put
forward a self-consistent scenario in which the account for the magnetic field
amplification induced by CR streaming produces the conditions for reversing
such a trend, allowing --- at the same time --- for rather steep spectra and CR
acceleration efficiencies (about 20%) consistent with the hypothesis that SNRs
are the sources of Galactic CRs. In particular, we quantitatively work out the
details of instantaneous and cumulative CR spectra during the evolution of a
typical SNR, also stressing the implications of the observed levels of
magnetization on both the expected maximum energy and the predicted CR
acceleration efficiency. The latter naturally turns out to saturate around
10-30%, almost independently of the fraction of particles injected into the
acceleration process as long as this fraction is larger than about .Comment: 24 pages, 5 figures, accepted for publication in JCA
Spatial Organization in the Reaction A + B --> inert for Particles with a Drift
We describe the spatial structure of particles in the (one dimensional)
two-species annihilation reaction A + B --> 0, where both species have a
uniform drift in the same direction and like species have a hard core
exclusion. For the case of equal initial concentration, at long times, there
are three relevant length scales: the typical distance between similar
(neighboring) particles, the typical distance between dissimilar (neighboring)
particles, and the typical size of a cluster of one type of particles. These
length scales are found to be generically different than that found for
particles without a drift.Comment: 10 pp of gzipped uuencoded postscrip
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