Shear-transformation-zone theory of plastic deformation near the glass transition

The shear-transformation-zone (STZ) theory of plastic deformation in glass-forming materials is reformulated in light of recent progress in understanding the roles played the effective disorder temperature and entropy flow in nonequilibrium situations. A distinction between fast and slow internal state variables reduces the theory to just two coupled equations of motion, one describing the plastic response to applied stresses, and the other the dynamics of the effective temperature. The analysis leading to these equations contains, as a byproduct, a fundamental reinterpretation of the dynamic yield stress in amorphous materials. In order to put all these concepts together in a realistic context, the paper concludes with a reexamination of the experimentally observed rheological behavior of a bulk metallic glass. That reexamination serves as a test of the STZ dynamics, confirming that system parameters obtained from steady-state properties such as the viscosity can be used to predict transient behaviors.Comment: 15 pages, four figure

On the Collapsar Model of Long Gamma-Ray Bursts: Constraints from Cosmic Metallicity Evolution

We explore the consequences of new observational and theoretical evidence that long gamma-ray bursts prefer low metallicity environments. Using recently derived mass-metallicity correlations and the mass function from SDSS studies, and adopting an average cosmic metallicity evolution from \citet{kewley2005} and \citet{savaglio2005} we derive expressions for the the relative number of massive stars formed below a given fraction of solar metallicity, $\epsilon$, as function of redshift. We demonstrate that about 1/10th of all stars form with $\epsilon < 0.1$. Therefore, a picture where the majority of GRBs form with $\epsilon < 0.1$ is not inconsistent with an empirical global SN/GRB ratio of 1/1000. It implies that (1) GRB's peak at a significantly higher redshift than supernovae; (2) massive star evolution at low metallicity may be qualitatively different and; (3) the larger the low-metallicity bias of GRBs the less likely binary evolution channels can be significant GRB producers.Comment: 12 pages, 2 figures; accepted as ApJ Lette

Local Geometric Invariants of Integrable Evolution Equations

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.Comment: 15 pages, AMSTeX file (to appear in Journal of Mathematical Physics

Excitation Chains at the Glass Transition

The excitation-chain theory of the glass transition, proposed in an earlier publication, predicts diverging, super-Arrhenius relaxation times and, {\it via} a similarly diverging length scale, suggests a way of understanding the relations between dynamic and thermodynamic properties of glass-forming liquids. I argue here that critically large excitation chains play a role roughly analogous to that played by critical clusters in the droplet model of vapor condensation. The chains necessarily induce spatial heterogeneities in the equilibrium states of glassy systems; and these heterogeneities may be related to stretched-exponential relaxation. Unlike a first-order condensation point in a vapor, the glass transition is not a conventional phase transformation, and may not be a thermodynamic transition at all.Comment: 4 pages, no figure

Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization

A microscopic model for solidification

We present a novel picture of a non isothermal solidification process starting from a molecular level, where the microscopic origin of the basic mechanisms and of the instabilities characterizing the approach to equilibrium is rendered more apparent than in existing approaches based on coarse grained free energy functionals \`a la Landau. The system is composed by a lattice of Potts spins, which change their state according to the stochastic dynamics proposed some time ago by Creutz. Such a method is extended to include the presence of latent heat and thermal conduction. Not only the model agrees with previous continuum treatments, but it allows to introduce in a consistent fashion the microscopic stochastic fluctuations. These play an important role in nucleating the growing solid phase in the melt. The approach is also very satisfactory from the quantitative point of view since the relevant growth regimes are fully characterized in terms of scaling exponents.Comment: 7 pages Latex +3 figures.p

Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature

This investigation extends earlier studies of a shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. My main purpose here is to explore the possibility that the configurational degrees of freedom of such systems fall out of thermodynamic equilibrium with the heat bath during persistent mechanical deformation, and that the resulting state of configurational disorder may be characterized by an effective temperature. The further assumption that the population of STZ's equilibrates with the effective temperature allows the theory to be compared directly with experimentally measured properties of metallic glasses, including their calorimetric behavior. The coupling between the effective temperature and mechanical deformation suggests an explanation of shear-banding instabilities.Comment: 29 pages, 11 figure

Evolution, Explosion and Nucleosynthesis of Core Collapse Supernovae

We present a new set of presupernova evolutions and explosive yields of massive stars of initial solar composition (Y=0.285, Z=0.02) in the mass range 13-35 Msun. All the models have been computed with the latest version (4.97) of the FRANEC code that now includes a nuclear network extending from neutrons to Mo98. The explosive nucleosynthesis has been computed twice: a first one with an hydro code and a second one following the simpler radiation dominated shock approximation (RDA).Comment: 20 pages, 10 figures, 12 tables. Accepted for publication on Ap

The Supernova Channel of Super-AGB Stars

We study the late evolution of solar metallicity stars in the transition region between white dwarf formation and core collapse. This includes the super-asymptotic giant branch (super-AGB, SAGB) stars, which have massive enough cores to ignite carbon burning and form an oxygen-neon (ONe) core. The most massive SAGB stars have cores that may grow to the Chandrasekhar mass because of continued shell-burning. Their cores collapse, triggering a so called electron capture supernovae (ECSN). From stellar evolution models we find that the initial mass range for SAGB evolution is 7.5 ... 9.25\msun. We perform calculations with three different stellar evolution codes to investigate the sensitivity of this mass range to some of the uncertainties in current stellar models. The mass range significantly depends on the treatment of semiconvective mixing and convective overshooting. To consider the effect of a large number of thermal pulses, as expected in SAGB stars, we construct synthetic SAGB models that include a semi-analytical treatment of dredge-up, hot-bottom burning, and thermal pulse properties. This synthetic model enables us to compute the evolution of the main properties of SAGB stars from the onset of thermal pulses until the core reaches the Chandrasekhar mass or is uncovered by the stellar wind. Thereby, we determine the stellar initial mass ranges that produce ONe-white dwarfs and electron-capture supernovae. The latter is found to be 9.0 ... 9.25\msun for our fiducial model, implying that electron-capture supernovae would constitute about 4% of all supernovae in the local universe. Our synthetic approach allows us to explore the uncertainty of this number imposed by uncertainties in the third dredge-up efficiency and ABG mass loss rate. We find for ECSNe a upper limit of ~20% of all supernovae (abridged).Comment: 13 pages, 16 figures, submitted to ApJ, uses emulateap