The Anisotropy of MHD Alfv\'{e}nic Turbulence

We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-{\it independent}. We discuss why this is {\it not} the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along {\it local} magnetic field lines. The results are consistent with the scaling law $\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here $\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.Comment: 13 pages (11 NEW figures), ApJ, in press (Aug 10, 2000?

Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli

Let -1\leq B<A\leq 1. Condition on \beta, is determined so that 1+\beta zp'(z)/p^k(z)\prec(1+Az)/(1+Bz)\;(-1<k\leq3) implies p(z)\prec \sqrt{1+z}. Similarly, condition on \beta is determined so that 1+\beta zp'(z)/p^n(z) or p(z)+\beta zp'(z)/p^n(z)\prec\sqrt{1+z}\;(n=0, 1, 2) implies p(z)\prec(1+Az)/(1+Bz) or \sqrt{1+z}. In addition to that condition on \beta is derived so that p(z)\prec(1+Az)/(1+Bz) when p(z)+\beta zp'(z)/p(z)\prec\sqrt{1+z}. Few more problems of the similar flavor are also considered

Baryon Masses in Partially Quenched Heavy Hadron Chiral Perturbation Theory

The masses of baryons containing a heavy quark are calculated to next-to-leading order in partially quenched heavy hadron chiral perturbation theory. Calculations are performed for three light flavors in the isospin limit and additionally for two light non-degenerate flavors. The results presented are necessary for extrapolating lattice QCD and partially quenched lattice QCD calculations of the heavy hadron masses.Comment: 20 pages, 2 figures, RevTex

Compressible Sub-Alfvenic MHD turbulence in Low-beta Plasmas

We present a model for compressible sub-Alfvenic isothermal magnetohydrodynamic (MHD) turbulence in low-beta plasmas and numerically test it. We separate MHD fluctuations into 3 distinct families - Alfven, slow, and fast modes. We find that, production of slow and fast modes by Alfvenic turbulence is suppressed. As a result, Alfven modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfven modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.Comment: 4 pages, 8 figures, Phys. Rev. Lett., in pres

Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition

The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the flow of the marginal couplings is studied. Our results indicate that higher-derivative terms of the color-unit-vector $\mathbf{n}$ field are necessary for the description of topologically stable knotlike solitons which have been conjectured to be the large-distance degrees of freedom.Comment: 15 pages, no figures, v2: minor improvements, one reference added, version to appear in PR