On the Distribution of Plasmoids In High-Lundquist-Number Magnetic Reconnection

The distribution function $f(\psi)$ of magnetic flux $\psi$ in plasmoids formed in high-Lundquist-number current sheets is studied by means of an analytic phenomenological model and direct numerical simulations. The distribution function is shown to follow a power law $f(\psi)\sim\psi^{-1}$, which differs from other recent theoretical predictions. Physical explanations are given for the discrepant predictions of other theoretical models.Comment: Accepted for publication in Phys. Rev. Let

B-L Cosmic strings and Baryogenesis

Cosmic strings arising from breaking of the $U(1)_{B-L}$ gauge symmetry that occurs in a wide variety of unified models can carry zero modes of heavy Majorana neutrinos. Decaying and/or repeatedly self-interacting closed loops of these ``$B-L$'' cosmic strings can be a non-thermal source of heavy right-handed Majorana neutrinos whose decay can contribute to the observed baryon asymmetry of the Universe (BAU) via the leptogenesis route. The $B-L$ cosmic strings are expected in GUT models such as SO(10), where they can be formed at an intermediate stage of symmetry breaking well below the GUT scale $\sim 10^{16}$ GeV; such light strings are not excluded by the CMB anisotropy data and may well exist. We estimate the contribution of $B-L$ cosmic string loops to the baryon-to-photon ratio of the Universe in the light of current knowledge on neutrino masses and mixings implied by atmospheric and solar neutrino measurements. We find that $B-L$ cosmic string loops can contribute significantly to the BAU for $U(1)_{B-L}$ symmetry breaking scale \eta_{B-L}\gsim 1.7\times 10^{11}\gev. At the same time, in order for the contribution of decaying $B-L$ cosmic string loops not to exceed the observed baryon-to-photon ratio inferred from the recent WMAP results, the lightest heavy right-handed Majorana neutrino mass $M_1$ must satisfy the constraint M_1 \leq 2.4 \times 10^{12}(\eta_{B-L}/10^{13}\gev)^{1/2}\gev. This may have interesting implications for the associated Yukawa couplings in the heavy neutrino sector and consequently for the light neutrino masses generated through see-saw mechanism.Comment: match with the published versio

Dynamics of unbinding of polymers in a random medium

We have studied the aging effect on the dynamics of unbinding of a double stranded directed polymer in a random medium. By using the Monte Carlo dynamics of a lattice model in two dimensions, for which disorder is known to be relevant, the unbinding dynamics is studied by allowing the bound polymer to relax in the random medium for a waiting time and then allowing the two strands to unbind. The subsequent dynamics is formulated in terms of the overlap of the two strands and also the overlap of each polymer with the configuration at the start of the unbinding process. The interrelations between the two and the nature of the dependence on the waiting time are studied.Comment: 7 pages, latex, 3 figures, To appear in J. Chem. Phy

A Constrained Tectonics Model for Coronal Heating

An analytical and numerical treatment is given of a constrained version of the tectonics model developed by Priest, Heyvaerts, & Title [2002]. We begin with an initial uniform magnetic field ${\bf B} = B_0 \hat{\bf z}$ that is line-tied at the surfaces $z = 0$ and $z = L$. This initial configuration is twisted by photospheric footpoint motion that is assumed to depend on only one coordinate ($x$) transverse to the initial magnetic field. The geometric constraints imposed by our assumption precludes the occurrence of reconnection and secondary instabilities, but enables us to follow for long times the dissipation of energy due to the effects of resistivity and viscosity. In this limit, we demonstrate that when the coherence time of random photospheric footpoint motion is much smaller by several orders of magnitude compared with the resistive diffusion time, the heating due to Ohmic and viscous dissipation becomes independent of the resistivity of the plasma. Furthermore, we obtain scaling relations that suggest that even if reconnection and/or secondary instabilities were to limit the build-up of magnetic energy in such a model, the overall heating rate will still be independent of the resistivity