Successful Supersymmetric Inflation

We reconsider the problems of cosmological inflation in effective supergravity theories. A singlet field in a hidden sector is demonstrated to yield an acceptable inflationary potential, without fine tuning. In the simplest such model, the requirement of generating the microwave background anisotropy measured by COBE fixes the inflationary scale to be about $10^{14}$ GeV, implying a reheat temperature of order $10^{5}$ GeV. This is low enough to solve the gravitino problem but high enough to allow baryogenesis after inflation. Such consistency requires that the generation of gravitational waves be negligible and that the spectrum of scalar density perturbations depart significantly from scale-invariance, thus improving the fit to large-scale structure in an universe dominated by cold dark matter. We also consider the problems associated with gravitino production through inflaton decay and with other weakly coupled fields such as the moduli encountered in (compactified) string theories.Comment: 27 pages (LaTeX) including 1 embedded (PostScript) figure. Revised to include a fuller discussion of initial conditions (leading to "eternal" inflation) and the role of moduli; some reordering of sections for greater clarity. Accepted for publication in Nuclear Physics

Abelian-Higgs-Navier-Stokes Hydrodynamics for Nematic Films with Defects

A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects is developed. A gauge field incorporating screening is introduced, resulting in the static elastic free energy having the form of a two-dimensional Abelian-Higgs model. Hydrodynamic equations are derived via the standard methods of de~Groot and Mazur. By working in the vicinity of the Bogomol'nyi equations consequences for defect centre motion are outlined.Comment: 12 page

Phase Diagram of the Extended Hubbard Model with Pair Hopping Interaction

A one-dimensional model of interacting electrons with on-site $U$, nearest-neighbor $V$, and pair-hopping interaction $W$ is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large $U$ and $V$, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for $W<0$, $|U-2V|<|2W|$, and to a staggered magnetization located on bonds between sites for $W>0$, $|U-2V|<W$. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the $\eta_{\pi}$-superconducting phase at $|U-2V| \ll 2t \leq W$ is briefly discussed.Comment: 6 pages in revtex format, 2 fig files in ep

Circumstellar dust shells of hot post-AGB stars

Using a radiative transfer code (DUSTY) parameters of the circumstellar dust shells of 15 hot post-AGB stars have been derived. Combining the optical, near and far-infrared (ISO, IRAS) data of the stars, we have reconstructed their spectral energy distributions (SEDs) and estimated the dust temperatures, mass loss rates, angular radii of the inner boundary of the dust envelopes and the distances to these stars. The mass loss rates (10$^{-6}-10^{-5}$M$_{\odot}$yr$^{-1}$) are intermediate between stars at the tip of the AGB and the PN phase. We have also studied the ISO spectra of 7 of these stars. Amorphous and crystalline silicate features were observed in IRAS14331-6435 (Hen3-1013), IRAS18062+2410 (SAO85766) and IRAS22023+5249 (LSIII +5224) indicating oxygen-rich circumstellar dust shells. The presence of unidentified infrared (UIR) band at 7.7$\mu$, SiC emission at 11.5$\mu$ and the "26$\mu$" and "main 30$\mu$" features in the ISO spectrum of IRAS17311-4924 (Hen3-1428) suggest that the central star may be carbon-rich. The ISO spectrum of IRAS17423-1755 (Hen3-1475) shows a broad absorption feature at 3.1$\mu$ due to C$_{2}$H$_{2}$ and/or HCN which is usually detected in the circumstellar shells of carbon-rich stars.Comment: 18 pages, accepted for publication in A&

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model

Second-order closure models for supersonic turbulent flows

Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging