The Statistical Physics of Athermal Materials

At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature, pressure, volume, and energy. In this review article, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune from the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials

Prolonging assembly through dissociation:A self assembly paradigm in microtubules

We study a one-dimensional model of microtubule assembly/disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that only consider a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative mechanism of recovery from shrinkage, and enhances fluctuations of filament lengths. Under conditions for which this alternative mechanism dominates, an increasing depolymerization rate leads to a decrease in dissociation rate and thus a net increase in assembly.Comment: accepted for publication in Physical Review

The prevalence and morphometric features of mastoid emissary vein on multidetector computed tomography

Background: The aim of the study was to evaluate the prevalence and morphometric features of mastoid emissary vein (MEV) on multidetector computed tomography (MDCT) scans, emphasize its clinical significance and review its surgical implications. Materials and methods: Cranial and temporal bone MDCTs of 248 patients (496 sides) were analysed by 2 radiologists. Mastoid foramen (MF) was defined on the 3 dimensional volume rendered (3DVR) images. The MF and mastoid emissary canal (MEC) were investigated in axial thin slices and the diameters of the largest MF and MEC were measured. Mean diameters of MF and MEC were determined. The number of the mastoid foramina was noted. Differences in MF prevalence by sex and side were evaluated. Results: The overall prevalence of MEC was 92.3%. It was observed in 91.5% of women and 93.3% of men. MEC was present on the right side in 84.7% and on the left side in 82.3% of temporal bones. The mean diameter of MF was 1.92 ± ± 1.02 mm on the right and 1.84 ± 0.98 mm on the left. In both sides the number of the MF’s changed from absent to triple. The mean diameter of MEC was 1.58 ± 0.86 mm on the right and 1.48 ± 0.79 mm on the left side. The mean diameter of MEC was significantly larger in men. No significant correlation was detected between age and the MEC diameter. Conclusions: The preoperative detection of mastoid emissary veins is necessary. The radiologists should be familiar with their clinical significance and variant appearances and report them accurately. Knowledge of their morphology and surgical implications by the surgeons will make them aware to avoid unexpected and fatal complications while operating in the suboccipital and mastoid area. MDCT is a reliable diagnostic tool for imaging the MEC and MF.

Rods are less fragile than spheres: Structural relaxation in dense liquids composed of anisotropic particles

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in 2D that interact via repulsive contact forces. We measure the structural relaxation times obtained from the long-time decay of the self-part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction \phi, temperature T, and aspect ratio \alpha. We are able to collapse the \phi and T-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of \alpha, onto a universal scaling function {\cal F}_{\pm}(|\phi-\phi_0|,T,\alpha), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in 3D. {\cal F_{\pm}} for both the translational and rotational DOF are characterized by the \alpha-dependent scaling exponents \mu and \delta and packing fraction \phi_0(\alpha) that signals the crossover in the scaling form {\cal F}_{\pm} from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility at \phi_0, m(\phi_0), decreases monotonically with increasing aspect ratio for both ellipses and dimers. Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic.Comment: 10 pages, 17 figures, and 1 tabl

A linear programming-based method for job shop scheduling

We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach

Hitomi Constraints on the 3.5 keV Line in the Perseus Galaxy Cluster

High-resolution X-ray spectroscopy with Hitomi was expected to resolve the origin of the faint unidentified E 3.5 ≈ keV emission line reported in several low-resolution studies of various massive systems, such as galaxies and clusters, including the Perseus cluster. We have analyzed the Hitomi first-light observation of the Perseus cluster. The emission line expected for Perseus based on the XMM-Newton signal from the large cluster sample under the dark matter decay scenario is too faint to be detectable in the Hitomi data. However, the previously reported 3.5 keV flux from Perseus was anomalously high compared to the sample-based prediction. We find no unidentified line at the reported high flux level. Taking into account the XMM measurement uncertainties for this region, the inconsistency with Hitomi is at a 99% significance for a broad dark matter line and at 99.7% for a narrow line from the gas. We do not find anomalously high fluxes of the nearby faint K line or the Ar satellite line that were proposed as explanations for the earlier 3.5 keV detections. We do find a hint of a broad excess near the energies of high-n transitions of S xvi E 3.44 ≃ keV rest-frame)—a possible signature of charge exchange in the molecular nebula and another proposed explanation for the unidentified line. While its energy is consistent with XMM pn detections, it is unlikely to explain the MOS signal. A confirmation of this interesting feature has to wait for a more sensitive observation with a future calorimeter experiment.United States. National Aeronautics and Space Administration. Science Mission DirectorateUnited States. Department of Energy (Lawrence Livermore National Laboratory. Contract DE-AC52- 07NA27344

A statistical mechanics framework for static granular matter

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram [1]. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble [2] which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by [3, 4].Comment: 21 pages, 15 figure

The Effect of Helium Sedimentation on Galaxy Cluster Masses and Scaling Relations

Recent theoretical studies predict that the inner regions of galaxy clusters may have an enhanced helium abundance due to sedimentation over the cluster lifetime. If sedimentation is not suppressed (e.g., by tangled magnetic fields), this may significantly affect the cluster mass estimates. We use Chandra X-ray observations of eight relaxed galaxy clusters to investigate the upper limits to the effect of helium sedimentation on the measurement of cluster masses and the best-fit slopes of the Y_X - M_500 and Y_X - M_2500 scaling relations. We calculated gas mass and total mass in two limiting cases: a uniform, un-enhanced abundance distribution and a radial distribution from numerical simulations of helium sedimentation on a timescale of 11 Gyrs. The assumed helium sedimentation model, on average, produces a negligible increase in the gas mass inferred within large radii (r < r500) (1.3 +/- 1.2 per cent) and a (10.2 +/- 5.5) per cent mean decrease in the total mass inferred within r < r500. Significantly stronger effects in the gas mass (10.5 +/- 0.8 per cent) and total mass (25.1 +/- 1.1 per cent) are seen at small radii owing to a larger variance in helium abundance in the inner region, r < 0.1 r500. We find that the slope of the Y_X -M_500 scaling relation is not significantly affected by helium sedimentation.Comment: 11 pages, accepted for publication in Astronomy and Astrophysic