Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

We calculate the exact autocorrelation exponent lambda and persistence exponent theta, and also amplitudes, in the dilute limit of phase ordering for dimensions d >= 2. In the Lifshitz-Slyozov-Wagner limit of conserved order parameter dynamics we find theta = gamma_d*epsilon, a universal constant times the volume fraction. For autocorrelations, lambda = d at intermediate times, with a late time crossover to lambda >= d/2 + 2. We also derive lambda and theta for globally conserved dynamics and relate these to the q->infinity -state Potts model and soap froths, proposing new poisoning exponents.Comment: 4 pages, revtex. References added, abstract shortene

Time Variation of Fine Structure Constant and Proton-Electron Mass Ratio with Quintessence

Recent astrophysical observations of quasar absorption systems indicate that the fine structure constant $\alpha$ and the proton-electron mass ratio $\mu$ may have evolved through the history of the universe. Motivated by these observations, we consider the cosmological evolution of a quintessence-like scalar field $\phi$ coupled to gauge fields and matter which leads to effective modifications of the coupling constants and particle masses over time. We show that a class of models where the scalar field potential $V(\phi)$ and the couplings to matter $B(\phi)$ admit common extremum in $\phi$ naturally explains constraints on variations of both the fine structure constant and the proton-electron mass ratio.Comment: 9 pages, 4 figures, CosPA 2006 Proceeding. 9 pages, 4 figures, CosPA 2006 Proceeding will be published in the Mod. Phys. Lett.

A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal non-dissipative case is studied up to the equivalent of 2048^3 grid points for one of these flows. The temporal evolution of the logarithmic decrements, delta, of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.Comment: 8 pages, 4 figure