Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto's method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto's original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto's original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2

On the Relation between Solar Activity and Clear-Sky Terrestrial Irradiance

The Mauna Loa Observatory record of direct-beam solar irradiance measurements for the years 1958-2010 is analysed to investigate the variation of clear-sky terrestrial insolation with solar activity over more than four solar cycles. The raw irradiance data exhibit a marked seasonal cycle, extended periods of lower irradiance due to emissions of volcanic aerosols, and a long-term decrease in atmospheric transmission independent of solar activity. After correcting for these effects, it is found that clear-sky terrestrial irradiance typically varies by about 0.2 +/- 0.1% over the course of the solar cycle, a change of the same order of magnitude as the variations of the total solar irradiance above the atmosphere. An investigation of changes in the clear-sky atmospheric transmission fails to find a significant trend with sunspot number. Hence there is no evidence for a yet unknown effect amplifying variations of clear-sky irradiance with solar activity.Comment: 16 pages, 7 figures, in press at Solar Physics; minor changes to the text to match final published versio

Existence and uniqueness for Legendre curves

We give a moving frame of a Legendre curve (or, a frontal) in the unite tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. The existence and uniqueness for Legendre curves are holded like as regular plane curves. It is quite useful to analyse the Legendre curves. As applications, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unite tangent bundle.

Subcritical and supercritical granular flow around an obstacle on a rough inclined plane

A blunt obstacle in the path of a rapid granular avalanche generates a bow shock (a jump in the avalanche thickness and velocity), a region of static grains upstream of the obstacle, and a grain-free region downstream. Here, it is shown that this interaction is qualitatively altered if the incline on which the avalanche is flowing is changed from smooth to rough. On a rough incline, the friction between the grains and the incline depends on the flow thickness and speed, which allows both rapid (supercritical) and slow (subcritical) steady uniform avalanches. For supercritical experimental flows, the material is diverted around a blunt obstacle by the formation of a bow shock and a static dead zone upstream of the obstacle. Downslope, a grain-free vacuum region forms, but, in contrast to flows on smooth beds, static levees form at the boundary between the vacuum region and the flow. In slower, subcritical, flows the flow is diverted smoothly around the dead zone and the obstacle without forming a bow shock. After the avalanche stops, signatures of the dead zone, levees and (in subcritical flows) a deeper region upslope of the obstacle are frozen into the deposit. To capture this behaviour, numerical simulations are performed with a depth-averaged avalanche model that includes frictional hysteresis and depth-averaged viscous terms, which are needed to accurately model the flowing and deposited regions. These results may be directly relevant to geophysical mass flows and snow avalanches, which flow over rough terrain and may impact barriers or other infrastructure

Depth-Resolved Composition and Electronic Structure of Buried Layers and Interfaces in a LaNiO3_3/SrTiO3_3 Superlattice from Soft- and Hard- X-ray Standing-Wave Angle-Resolved Photoemission

LaNiO$_3$ (LNO) is an intriguing member of the rare-earth nickelates in exhibiting a metal-insulator transition for a critical film thickness of about 4 unit cells [Son et al., Appl. Phys. Lett. 96, 062114 (2010)]; however, such thin films also show a transition to a metallic state in superlattices with SrTiO$_3$ (STO) [Son et al., Appl. Phys. Lett. 97, 202109 (2010)]. In order to better understand this transition, we have studied a strained LNO/STO superlattice with 10 repeats of [4 unit-cell LNO/3 unit-cell STO] grown on an (LaAlO$_3$)$_{0.3}$(Sr$_2$AlTaO$_6$)$_{0.7}$ substrate using soft x-ray standing-wave-excited angle-resolved photoemission (SWARPES), together with soft- and hard- x-ray photoemission measurements of core levels and densities-of-states valence spectra. The experimental results are compared with state-of-the-art density functional theory (DFT) calculations of band structures and densities of states. Using core-level rocking curves and x-ray optical modeling to assess the position of the standing wave, SWARPES measurements are carried out for various incidence angles and used to determine interface-specific changes in momentum-resolved electronic structure. We further show that the momentum-resolved behavior of the Ni 3d eg and t2g states near the Fermi level, as well as those at the bottom of the valence bands, is very similar to recently published SWARPES results for a related La$_{0.7}$Sr$_{0.3}$MnO$_3$/SrTiO$_3$ superlattice that was studied using the same technique (Gray et al., Europhysics Letters 104, 17004 (2013)), which further validates this experimental approach and our conclusions. Our conclusions are also supported in several ways by comparison to DFT calculations for the parent materials and the superlattice, including layer-resolved density-of-states results

Dynamics of the Tippe Top via Routhian Reduction

We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.Comment: 16 pages, 7 figures, added reference. Typos corrected and a forgotten term in de linearized system is adde

Backreacted T-folds and non-geometric regions in configuration space

We provide the backreaction of the T-fold doubly T-dual to a background with NSNS three-form flux on a three-torus. We extend the backreacted T-fold to include cases with a flux localized in one out of three directions. We analyze the resulting monodromy domain walls and vortices. In these backgrounds, we give an analysis of the action of T-duality on observables like charges and Wilson surfaces. We analyze arguments for the existence of regions in the configuration space of second quantized string theory that cannot be reduced to geometry. Finally, by allowing for space-dependent moduli, we find a supergravity solution which is a T-fold with hyperbolic monodromies.Comment: 25 pages, 4 figures; v2: minor changes, reference adde

Neutron scattering and molecular correlations in a supercooled liquid

We show that the intermediate scattering function $S_n(q,t)$ for neutron scattering (ns) can be expanded naturely with respect to a set of molecular correlation functions that give a complete description of the translational and orientational two-point correlations in the liquid. The general properties of this expansion are discussed with special focus on the $q$-dependence and hints for a (partial) determination of the molecular correlation functions from neutron scattering results are given. The resulting representation of the static structure factor $S_n(q)$ is studied in detail for a model system using data from a molecular dynamics simulation of a supercooled liquid of rigid diatomic molecules. The comparison between the exact result for $S_n(q)$ and different approximations that result from a truncation of the series representation demonstrates its good convergence for the given model system. On the other hand it shows explicitly that the coupling between translational (TDOF) and orientational degrees of freedom (ODOF) of each molecule and rotational motion of different molecules can not be neglected in the supercooled regime.Further we report the existence of a prepeak in the ns-static structure factor of the examined fragile glassformer, demonstrating that prepeaks can occur even in the most simple molecular liquids. Besides examining the dependence of the prepeak on the scattering length and the temperature we use the expansion of $S_n(q)$ into molecular correlation functions to point out intermediate range orientational order as its principle origin.Comment: 13 pages, 7 figure