Non-equilibrium thermodynamics in sheared hard-sphere materials

We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards' statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume $V$ replaces the internal energy $U$ as a function of entropy $S$ in conventional statistical mechanics. In place of the effective temperature, the compactivity $X = \partial V / \partial S$ characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.Comment: 9 pages, 6 figure

Thermodynamic dislocation theory of high-temperature deformation in aluminum and steel

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperatures and smallest strain rates.Comment: 7 pages, 8 figure

Localized induction equation and pseudospherical surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A: Mathematical and Genera

Microstructural Shear Localization in Plastic Deformation of Amorphous Solids

The shear-transformation-zone (STZ) theory of plastic deformation predicts that sufficiently soft, non-crystalline solids are linearly unstable against forming periodic arrays of microstructural shear bands. A limited nonlinear analysis indicates that this instability may be the mechanism responsible for strain softening in both constant-stress and constant-strain-rate experiments. The analysis presented here pertains only to one-dimensional banding patterns in two-dimensional systems, and only to very low temperatures. It uses the rudimentary form of the STZ theory in which there is only a single kind of zone rather than a distribution of them with a range of transformation rates. Nevertheless, the results are in qualitative agreement with essential features of the available experimental data. The nonlinear theory also implies that harder materials, which do not undergo a microstructural instability, may form isolated shear bands in weak regions or, perhaps, at points of concentrated stress.Comment: 32 pages, 6 figure

Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume

Naturally-occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the peculiar phenomenon of auto-acoustic compaction -- non-monotonic variation of shear band volume with shear rate in angular particles -- recently observed in experiments. Our approach is based on the notion that the volume of a granular material is determined by an effective-disorder temperature known as the compactivity. Noise sources in a driven granular material couple its various degrees of freedom and the environment, causing the flow of entropy between them. The grain-scale dynamics is described by the shear-transformation-zone (STZ) theory of granular flow, which accounts for irreversible plastic deformation in terms of localized flow defects whose density is governed by the state of configurational disorder. To model the effects of grain shape and frictional characteristics, we propose an Ising-like internal variable to account for nearest-neighbor grain interlocking and geometric frustration, and interpret the effect of friction as an acoustic noise strength. We show quantitative agreement between experimental measurements and theoretical predictions, and propose additional experiments that provide stringent tests on the new theoretical elements.Comment: 12 pages, 3 figure

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

Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations

We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate-strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics, and thus produce useful information about a variety of granular phenomena including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.Comment: 12 pages, 8 figure

Constraining the mass transfer in massive binaries through progenitor evolution models of Wolf-Rayet+O binaries

Since close WR+O binaries are the result of a strong interaction of both stars in massive close binary systems, they can be used to constrain the highly uncertain mass and angular momentum budget during the major mass transfer phase. We explore the progenitor evolution of the three best suited WR+O binaries HD 90657, HD 186943 and HD 211853, which are characterized by a WR/O mass ratio of $\sim$0.5 and periods of 6..10 days. We are doing so at three different levels of approximation: predicting the massive binary evolution through simple mass loss and angular momentum loss estimates, through full binary evolution models with parametrized mass transfer efficiency, and through binary evolution models including rotation of both components and a physical model which allows to compute mass and angular momentum loss from the binary system as function of time during the mass transfer process. All three methods give consistently the same answers. Our results show that, if these systems formed through stable mass transfer, their initial periods were smaller than their current ones, which implies that mass transfer has started during the core hydrogen burning phase of the initially more massive star. Furthermore, the mass transfer in all three cases must have been highly non-conservative, with on average only $\sim$10% of the transferred mass being retained by the mass receiving star. This result gives support to our system mass and angular momentum loss model, which predicts that, in the considered systems, about 90% of the overflowing matter is expelled by the rapid rotation of the mass receiver close to the $\Omega$-limit, which is reached through the accretion of the remaining 10%.Comment: accepted A&A version of paper with better quality plots available at http://www.astro.uu.nl/~petrovi