Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids

We use the shear transformation zone (STZ) theory of dynamic plasticity to study the necking instability in a two-dimensional strip of amorphous solid. Our Eulerian description of large-scale deformation allows us to follow the instability far into the nonlinear regime. We find a strong rate dependence; the higher the applied strain rate, the further the strip extends before the onset of instability. The material hardens outside the necking region, but the description of plastic flow within the neck is distinctly different from that of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and added content, resubmitted to PR

A Herschel [C II] Galactic plane survey II: CO-dark H2 in clouds

ABRIDGED: Context: HI and CO large scale surveys of the Milky Way trace the diffuse atomic clouds and the dense shielded regions of molecular hydrogen clouds. However, until recently, we have not had spectrally resolved C+ surveys to characterize the photon dominated interstellar medium, including, the H2 gas without C, the CO-dark H2, in a large sample of clouds. Aims: To use a sparse Galactic plane survey of the 1.9 THz [C II] spectral line from the Herschel Open Time Key Programme, Galactic Observations of Terahertz C+ (GOT C+), to characterize the H2 gas without CO in a statistically significant sample of clouds. Methods: We identify individual clouds in the inner Galaxy by fitting [CII] and CO isotopologue spectra along each line of sight. We combine these with HI spectra, along with excitation models and cloud models of C+, to determine the column densities and fractional mass of CO-dark H2 clouds. Results: We identify 1804 narrow velocity [CII] interstellar cloud components in different categories. About 840 are diffuse molecular clouds with no CO, 510 are transition clouds containing [CII] and 12CO, but no 13CO, and the remainder are dense molecular clouds containing 13CO emission. The CO-dark H2 clouds are concentrated between Galactic radii 3.5 to 7.5 kpc and the column density of the CO-dark H2 layer varies significantly from cloud-to-cloud with an average 9X10^(20) cm-2. These clouds contain a significant fraction of CO-dark H2 mass, varying from ~75% for diffuse molecular clouds to ~20% for dense molecular clouds. Conclusions: We find a significant fraction of the warm molecular ISM gas is invisible in HI and CO, but is detected in [CII]. The fraction of CO-dark H2 is greatest in the diffuse clouds and decreases with increasing total column density, and is lowest in the massive clouds.Comment: 21 pages, 19 figures, accepted for publication in A&A (2014

New set of measures to analyze non-equilibrium structures

We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface deposition. Patterns growth in the Cahn-Hilliard Equation (used to model spinodal decomposition) are shown to exhibit three distinct stages. Two models of surface growth, namely the continuous Kardar-Parisi-Zhang (KPZ) model and the discrete Restricted-Solid-On-Solid (RSOS) model are shown to have different saturation exponents

Ionized gas at the edge of the Central Molecular Zone

To determine the properties of the ionized gas at the edge of the CMZ near Sgr E we observed a small portion of the edge of the CMZ near Sgr E with spectrally resolved [C II] 158 micron and [N II] 205 micron fine structure lines at six positions with the GREAT instrument on SOFIA and in [C II] using Herschel HIFI on-the-fly strip maps. We use the [N II] spectra along with a radiative transfer model to calculate the electron density of the gas and the [C II] maps to illuminate the morphology of the ionized gas and model the column density of CO-dark H2. We detect two [C II] and [N II] velocity components, one along the line of sight to a CO molecular cloud at -207 km/s associated with Sgr E and the other at -174 km/s outside the edge of another CO cloud. From the [N II] emission we find that the average electron density is in the range of about 5 to 25 cm{-3} for these features. This electron density is much higher than that of the warm ionized medium in the disk. The column density of the CO-dark H$_2$ layer in the -207 km/s cloud is about 1-2X10{21} cm{-2} in agreement with theoretical models. The CMZ extends further out in Galactic radius by 7 to 14 pc in ionized gas than it does in molecular gas traced by CO. The edge of the CMZ likely contains dense hot ionized gas surrounding the neutral molecular material. The high fractional abundance of N+ and high electron density require an intense EUV field with a photon flux of order 1e6 to 1e7 photons cm{-2} s{-1}, and/or efficient proton charge exchange with nitrogen, at temperatures of order 1e4 K, and/or a large flux of X-rays. Sgr E is a region of massive star formation which are a potential sources of the EUV radiation that can ionize the gas. In addition X-ray sources and the diffuse X-ray emission in the CMZ are candidates for ionizing nitrogen.Comment: 12 pages, 9 figure

Theoretical Black Hole Mass Distributions

We derive the theoretical distribution function of black hole masses by studying the formation processes of black holes. We use the results of recent 2D simulations of core-collapse to obtain the relation between remnant and progenitor masses and fold it with an initial mass function for the progenitors. We examine how the calculated black-hole mass distributions are modified by (i) strong wind mass loss at different evolutionary stages of the progenitors, and (ii) the presence of close binary companions to the black-hole progenitors. Thus, we are able to derive the binary black hole mass distribution. The compact remnant distribution is dominated by neutron stars in the mass range 1.2-1.6Msun and falls off exponentially at higher remnant masses. Our results are most sensitive to mass loss from winds which is even more important in close binaries. Wind mass-loss causes the black hole distribution to become flatter and limits the maximum possible black-hole mass (<10-15Msun). We also study the effects of the uncertainties in the explosion and unbinding energies for different progenitors. The distributions are continuous and extend over a broad range. We find no evidence for a gap at low values (3-5Msun) or for a peak at higher values (~7Msun) of black hole masses, but we argue that our black hole mass distribution for binaries is consistent with the current sample of measured black-hole masses in X-ray transients. We discuss possible biases against the detection or formation of X-ray transients with low-mass black holes. We also comment on the possibility of black-hole kicks and their effect on binaries.Comment: 22 pages, submitted to Ap

Comments on photonic shells

We investigate in detail the special case of an infinitely thin static cylindrical shell composed of counter-rotating photons on circular geodetical paths separating two distinct parts of Minkowski spacetimes--one inside and the other outside the shell--and compare it to a static disk shell formed by null particles counter-rotating on circular geodesics within the shell located between two sections of flat spacetime. One might ask whether the two cases are not, in fact, merely one

How Massive Single Stars End their Life

How massive stars die -- what sort of explosion and remnant each produces -- depends chiefly on the masses of their helium cores and hydrogen envelopes at death. For single stars, stellar winds are the only means of mass loss, and these are chiefly a function of the metallicity of the star. We discuss how metallicity, and a simplified prescription for its effect on mass loss, affects the evolution and final fate of massive stars. We map, as a function of mass and metallicity, where black holes and neutron stars are likely to form and where different types of supernovae are produced. Integrating over an initial mass function, we derive the relative populations as a function of metallicity. Provided single stars rotate rapidly enough at death, we speculate upon stellar populations that might produce gamma-ray bursts and jet-driven supernovae.Comment: 24 pages, 9 figues, submitted to Ap

Stability of a Nonequilibrium Interface in a Driven Phase Segregating System

We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the interface motion. A linear stability analysis of these equations results in a condition for the stability of a flat interface. We find that the stability properties of a flat interface depend on the structure of the driving term in the original equation.Comment: 14 pages Latex, 1 postscript-figur

Stiff knots

We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as the square of the bridge number; (ii) Braid localization is found to be a general feature of stiff strings entanglements, while angles and knot localization are forbidden. Moreover, we identify a family of knots for which the equilibrium shape is a circular braid. Two other equilibrium shapes are found from Monte Carlo simulations. These three shapes are confirmed by rudimentary experiments. Our approach is also extended to the problem of the minimization of the length of a knotted string with a maximum allowed curvature.Comment: Submitted to Phys. Rev.