Active Carbon and Oxygen Shell Burning Hydrodynamics

We have simulated 2.5$\times10^3$ s of the late evolution of a $23 \rm M_\odot$ star with full hydrodynamic behavior. We present the first simulations of a multiple-shell burning epoch, including the concurrent evolution and interaction of an oxygen and carbon burning shell. In addition, we have evolved a 3D model of the oxygen burning shell to sufficiently long times (300 s) to begin to assess the adequacy of the 2D approximation. We summarize striking new results: (1) strong interactions occur between active carbon and oxygen burning shells, (2) hydrodynamic wave motions in nonconvective regions, generated at the convective-radiative boundaries, are energetically important in both 2D and 3D with important consequences for compositional mixing, and (3) a spectrum of mixed p- and g-modes are unambiguously identified with corresponding adiabatic waves in these computational domains. We find that 2D convective motions are exaggerated relative to 3D because of vortex instability in 3D. We discuss the implications for supernova progenitor evolution and symmetry breaking in core collapse.Comment: 5 pages, 4 figures in emulateapj format. Accepted for publication in ApJ Letters. High resolution figure version available at http://spinach.as.arizona.ed

Steady-State Cracks in Viscoelastic Lattice Models II

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure

Langevin Equation for the Density of a System of Interacting Langevin Processes

We present a simple derivation of the stochastic equation obeyed by the density function for a system of Langevin processes interacting via a pairwise potential. The resulting equation is considerably different from the phenomenological equations usually used to describe the dynamics of non conserved (Model A) and conserved (Model B) particle systems. The major feature is that the spatial white noise for this system appears not additively but multiplicatively. This simply expresses the fact that the density cannot fluctuate in regions devoid of particles. The steady state for the density function may however still be recovered formally as a functional integral over the coursed grained free energy of the system as in Models A and B.Comment: 6 pages, latex, no figure

Steady-State Cracks in Viscoelastic Lattice Models

We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity $\eta$ allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement $\Delta$ and the number of transverse sites $N$. At any $N$, the continuum theory misses the lattice-trapping phenomenon; this is well-known, but the introduction of $\eta$ introduces some new twists. More importantly, for large $N$ even at large $\Delta$, the standard two-dimensional elastodynamics approach completely misses the $\eta$-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.Comment: 27 pages, 8 figure

Related progenitor models for long-duration gamma ray bursts and Type Ic superluminous supernovae

We model the late evolution and mass loss history of rapidly rotating Wolf-Rayet stars in the mass range $5\,\rm{M}_{\odot}\dots 100\,\rm{M}_{\odot}$. We find that quasi-chemically homogeneously evolving single stars computed with enhanced mixing retain very little or no helium and are compatible with Type\,Ic supernovae. The more efficient removal of core angular momentum and the expected smaller compact object mass in our lower mass models lead to core spins in the range suggested for magnetar driven superluminous supernovae. Our more massive models retain larger specific core angular momenta, expected for long-duration gamma-ray bursts in the collapsar scenario. Due to the absence of a significant He envelope, the rapidly increasing neutrino emission after core helium exhaustion leads to an accelerated contraction of the whole star, inducing a strong spin-up, and centrifugally driven mass loss at rates of up to $10^{-2}\,\rm{M}_{\odot}~\rm{yr^{-1}}$ in the last years to decades before core collapse. Since the angular momentum transport in our lower mass models enhances the envelope spin-up, they show the largest relative amounts of centrifugally enforced mass loss, i.e., up to 25\% of the expected ejecta mass. Our most massive models evolve into the pulsational pair-instability regime. We would thus expect signatures of interaction with a C/O-rich circumstellar medium for Type~Ic superluminous supernovae with ejecta masses below $\sim 10\,\rm{M}_{\odot}$ and for the most massive engine-driven explosions with ejecta masses above $\sim 30\,\rm{M}_{\odot}$. Signs of such interaction should be observable at early epochs of the supernova explosion, and may be related to bumps observed in the light curves of superluminous supernovae, or to the massive circumstellar CO-shell proposed for Type~Ic superluminous supernova Gaia16apd.Comment: 20 pages, 15 figures, 2 tables Accepted for publication in Ap

Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication

Phase-Field Model of Mode III Dynamic Fracture

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between ``broken'' and ``unbroken'' states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.Comment: submitted to PR

Does the continuum theory of dynamic fracture work?

We investigate the validity of the Linear Elastic Fracture Mechanics approach to dynamic fracture. We first test the predictions in a lattice simulation, using a formula of Eshelby for the time-dependent Stress Intensity Factor. Excellent agreement with the theory is found. We then use the same method to analyze the experiment of Sharon and Fineberg. The data here is not consistent with the theoretical expectation.Comment: 4 page

Nonlinear lattice model of viscoelastic Mode III fracture

We study the effect of general nonlinear force laws in viscoelastic lattice models of fracture, focusing on the existence and stability of steady-state Mode III cracks. We show that the hysteretic behavior at small driving is very sensitive to the smoothness of the force law. At large driving, we find a Hopf bifurcation to a straight crack whose velocity is periodic in time. The frequency of the unstable bifurcating mode depends on the smoothness of the potential, but is very close to an exact period-doubling instability. Slightly above the onset of the instability, the system settles into a exactly period-doubled state, presumably connected to the aforementioned bifurcation structure. We explicitly solve for this new state and map out its velocity-driving relation