Numerical Toy-Model Calculation of the Nucleon Spin Autocorrelation Function in a Supernova Core

We develop a simple model for the evolution of a nucleon spin in a hot and dense nuclear medium. A given nucleon is limited to one-dimensional motion in a distribution of external, spin-dependent scattering potentials. We calculate the nucleon spin autocorrelation function numerically for a variety of potential densities and distributions which are meant to bracket realistic conditions in a supernova core. For all plausible configurations the width of the spin-density structure function is found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates the width and thus suggests a large suppression of the neutrino opacities by nucleon spin fluctuations. Our results suggest that it may be justified to neglect the collisional broadening of the spin-density structure function for the purpose of estimating the neutrino opacities in the deep inner core of a supernova. On the other hand, we find no indication that processes such as axion or neutrino pair emission, which depend on nucleon spin fluctuations, are substantially suppressed beyond the multiple-scattering effect already discussed in the literature. Aside from these practical conclusions, our model reveals a number of interesting and unexpected insights. For example, the spin-relaxation rate saturates with increasing potential strength only if bound states are not allowed to form by including a repulsive core. There is no saturation with increasing density of scattering potentials until localized eigenstates of energy begin to form.Comment: 14 latex pages in two-column format, 15 postscript figures included, uses revtex.sty and epsf.sty. Submitted to Physical Review

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented

On some singularities of the correlation functions that determine neutrino opacities

Certain perturbation graphs in the calculation of the effects of the medium on neutrino scattering in supernova matter have a nonintegrable singularity in a physical region. A number of papers have addressed the apparent pathology through an ansatz that invokes higher order (rescattering) effects. Taking the Gamow-Teller terms as an example, we display an expression for the spin-spin correlation function that determines the cross-sections. It is clear from the form that there are no pathologies in the order by order perturbation expansion. Explicit formulae are given for a simple case, leading to an answer that is very different from one given by other authors.Comment: 8 page

Kaon Condensation in a Nambu--Jona-Lasinio (NJL) Model at High Density

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed colour-flavour locked state (CFLK0) within the context of a mean-field NJL model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the CFLK0 state to the parity even CFL state, and to determine locations of the metal/insulator transition to a phase with gapless fermionic excitations in the presence of a non-zero hypercharge chemical potential and a non-zero strange quark mass. The transition points are compared with results derived previously via effective theories and with partially self-consistent NJL calculations. We find that the qualitative physics does not change, but that the transitions are slightly lower.Comment: 21 pages, ReVTeX4. Clarified discussion and minor change

On the ground state of gapless two flavor color superconductors

This paper is devoted to the study of some aspects of the instability of two flavor color superconductive quark matter. We find that, beside color condensates, the Goldstone boson related to the breaking of $U(1)_A$ suffers of a velocity instability. We relate this wrong sign problem, which implies the existence of a Goldstone current in the ground state or of gluonic condensation, to the negative squared Meissner mass of the $8^{th}$ gluon in the g2SC phase. Moreover we investigate the Meissner masses of the gluons and the squared velocity of the Goldstone in the multiple plane wave LOFF states, arguing that in such phases both the chromo-magnetic instability and the velocity instability are most probably removed. We also do not expect Higgs instability in such multiple plane wave LOFF. The true vacuum of gapless two flavor superconductors is thus expected to be a multiple plane wave LOFF state.Comment: 16 pages, RevTe3X4 styl

Evaluating the Gapless Color-Flavor Locked Phase

In neutral cold quark matter that is sufficiently dense that the strange quark mass M_s is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We recently argued that the next phase down in density (as a function of decreasing quark chemical potential mu or increasing strange quark mass M_s) is the new ``gapless CFL'' (``gCFL'') phase in which only seven quasiparticles have a gap, while there are gapless quasiparticles described by two dispersion relations at three momenta. There is a continuous quantum phase transition from CFL to gCFL quark matter at M_s^2/mu approximately equal to 2*Delta, with Delta the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination "Q-tilde" of electric and color charges, but it is a Q-tilde-conductor with gapless Q-tilde-charged quasiparticles and a nonzero electron density. In this paper, we evaluate the gapless CFL phase, in several senses. We present the details underlying our earlier work which showed how this phase arises. We display all nine quasiparticle dispersion relations in full detail. Using a general pairing ansatz that only neglects effects that are known to be small, we perform a comparison of the free energies of the gCFL, CFL, 2SC, gapless 2SC, and 2SCus phases. We conclude that as density drops, making the CFL phase less favored, the gCFL phase is the next spatially uniform quark matter phase to occur. A mixed phase made of colored components would have lower free energy if color were a global symmetry, but in QCD such a mixed phase is penalized severely.Comment: 18 pages, RevTeX; Version to appear in Phys Rev D. Minor rewording, references adde

Consistent boundary conditions for Reduced Navier-Stokes (RNS) scheme applied to 3-dimensional internal viscous flows

A consistent and efficient set of boundary conditions is developed for the multi-sweep space-marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for 3-D internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. These solutions are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions for internal flows with strong interaction, as would be encountered in ducts and turbomachinery geometries

Electron acoustic solitons in the Earth's magnetotail

International audienceSmall amplitude electron - acoustic solitons are studied in a magnetized plasma consisting of two types of electrons, namely cold electron beam and background plasma electrons and two temperature ion plasma. The analysis predicts rarefactive solitons. The model may provide a possible explanation for the perpendicular polarization of the low-frequency component of the broadband electrostatic noise observed in the Earth's magnetotail