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 $m$ at time $t$, $c(m,t)~m^{-1/2}(log(t)/t)^{3/4}$, for $1 << m << \sqrt{t/log(t)}$. The total concentration of clusters, $c(t)$, decays as $c(t)~\sqrt{log(t)/t}$ at $t --> \infty$. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration $c(r)$ scales as $r^{-1}(log(r))^{1/2}$, $r^{-1}$, and $r^{-1}(log(r))^{-1/2}$, respectively, for the spatial dimension $d$ equal to 1, 2, and 3. The total number of clusters, $N(t)$, grows with time as $(log(t))^{3/2}$, $t^{1/2}$, and $t(log(t))^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady state cluster-mass distribution: $c(m,r) \sim r^{-1}(log(r))^{-1}\Phi(z)$, with the scaling function $\Phi(z)=z^{-1/2}\exp(-z)$ and the scaling variable $z ~ m/\sqrt{log(r)}$.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 $\nu = 1/3$) and spin-unpolarized ($\nu = 2/5$) 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 $E^{-2.2}--E^{-2.4}$, 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 $10^{-4}$.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