The effect of a finite mass reservoir on the collapse of spherical isothermal clouds and the evolution of protostellar accretion
Motivated by recent observations that detect an outer boundary for starless cores, and evidence for time-dependent mass accretion in the Class 0 and Class I protostellar phases, we re-examine the case of spherical isothermal collapse in the case of a finite mass reservoir. The presence of a core boundary, implemented through a constant-volume approximation in our simulation, results in the generation of an inward-propagating rarefaction wave. This steepens the gas density profile from r -2 (self-similar value) to r -3 or steeper. After a protostar forms, the mass accretion rate M evolves through three distinct phases: (1) an early phase of decline in M, which is a non-self-similar effect due to rapid and spatially non-uniform infall in the pre-stellar phase; (2) for large cores, an intermediate phase of near-constant M from the infall of the outer part of the self-similar density profile, which has low (subsonic) infall speed in the pre-stellar phase; and (3) a late phase of rapid decline in M when accretion occurs from the region affected by the inward-propagating rarefaction wave. Our model clouds of small to intermediate size make a direct transition from phase (1) to phase (3) above. Both the first and second phase (if the latter is indeed present) are characterized by a temporally increasing bolometric luminosity L bol , while L bol is decreasing in the third (final) phase. We identify the period of temporally increasing L bol with the Class 0 phase, and the later period of terminal accretion and decreasing L bol with the Class I phase. The peak in L bol corresponds to the evolutionary time when 50 ± 15 per cent of the cloud mass has been accreted by the protostar. This is in agreement with the classification scheme proposed in the early 1990s by Andre et al.; our model adds a physical context to their interpretation. We show how our results can be used to explain tracks of envelope mass M env versus L bol for protostars in Taurus and Ophiuchus. We also develop an analytic formalism that successfully reproduces the protostellar accretion rate from profiles of density and infall speed in the pre-stellar phase. It shows that the spatial gradient of infall speed that develops in the pre-stellar phase is a primary cause of the temporal decline in M during the early phase of protostellar accretion.

title: Magnetically-regulated fragmentation induced by nonlinear flows and ambipolar diffusion
abstract: We present a parameter study of simulations of fragmentation regulated by gravity, magnetic fields, ambipolar diffusion, and nonlinear flows. The thin-sheet approximation is employed with periodic lateral boundary conditions, and the nonlinear flow field (“turbulence”) is allowed to freely decay. In agreement with previous results in the literature, our results show that the onset of runaway collapse (formation of the first star) in subcritical clouds is significantly accelerated by nonlinear flows in which a large-scale wave mode dominates the power spectrum. In addition, we find that a power spectrum with equal energy on all scales also accelerates collapse, but by a

title: 2D solar modeling
abstract: Understanding the reasons of the cyclic variation of the total solar irradiance is one of the most challenging targets of modern astrophysics. These studies prove to be essential also for a more climatologic issue, associated to the global warming. Any attempt to determine the solar components of this phenomenon must include the effects of the magnetic field, whose strength and shape in the solar interior are far from being completely known. Modeling the presence and the effects of a magnetic field requires a 2D approach, since the assumption of radial symmetry is too limiting for this topic. We present the structure of a 2D evolution code that was purposely designed for this scope; rotation, magnetic field and turbulence can be taken into account. Some preliminary results are presented and commented.

title: Effect of harmonic confinement on correlation studies of a spin-polarized s-wave superconductor
abstract: We study different correlation functions for a spin imbalanced and harmonically trapped Fermi gas in two dimensions described by an attractive Hubbard model. Eigensolutions obtained via numerically solving Bogoliubov de Gennes equations are used to compute the local pairing amplitudes which show significantly different behaviour for the trapped case where the profile is radially modulated in contrast with a spatial modulation extending throughout the lattice geometry when trap effects are switched off. Further, different experimentally accessible quantities, such as pair–pair, density–density correlations and local density fluctuations show characteristic fluctuations for the spin polarized phase, which however wash away as the trapping effects are turned on. A contrasting scenario is presented corresponding to the case when the spin polarization effects are turned off.

title: THE INTERPLAY OF TURBULENCE AND MAGNETIC FIELDS IN STAR-FORMING REGIONS: SIMULATIONS AND OBSERVATIONS
abstract: We analyze a suite of thin-sheet magnetohydrodynamical simulations based on the formulation of Basu, Ciolek, Dapp, and Wurster. These simulations allow us to examine the observational consequences to a star-forming region of varying the input level of turbulence (between thermal and a Mach number of 4) and the initial magnetic field strength corresponding to a range of mass to flux ratios between subcritical ({mu}{sub 0} = 0.5) and supercritical ({mu}{sub 0} = 10). The input turbulence is allowed to decay over the duration of the simulation. We compare the measured observable quantities with those found from surveying the Perseus molecular cloud. We find that only the most turbulent of simulations (high Mach number and weak magnetic field) have sufficient large-scale velocity dispersion (at {approx}1 pc) to match that observed across extinction regions in Perseus. Generally, the simulated core ({approx}0.02 pc) and line-of-sight velocity dispersions provide a decent match to observations. The motion between the simulated core and its local environment, however, is far too large in simulations with high large-scale velocity dispersion.

title: The Intrinsic Shapes of Molecular Cloud Fragments over a Range of Length Scales
abstract: We decipher intrinsic three-dimensional shape distributions of molecular clouds, cloud cores, Bok globules, and condensations using recently compiled catalogs of observed axis ratios for these objects mapped in carbon monoxide, in ammonia, through optical selection, or in continuum dust emission. We apply statistical techniques to compare assumed intrinsic axis ratio distributions with observed projected axis ratio distributions. Intrinsically triaxial shapes produce projected distributions that agree with observations. Molecular clouds mapped in 12CO are intrinsically triaxial but more nearly prolate than oblate, while the smaller cloud cores, Bok globules, and condensations are also intrinsically triaxial but more nearly oblate than prolate.

title: NONLINEAR QUANTUM MECHANICS IMPLIES POLYNOMIAL-TIME SOLUTION FOR NP-COMPLETE AND P PROBLEMS
abstract: If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demonstrated using the Weinberg model of nonlinear quantum mechanics.