7,415 research outputs found
The random phase approximation applied to ice
Standard density functionals without van der Waals interactions yield an
unsatisfactory description of ice phases, specifically, high density phases
occurring under pressure are too unstable compared to the common low density
phase I observed at ambient conditions. Although the description is
improved by using functionals that include van der Waals interactions, the
errors in relative volumes remain sizable. Here we assess the random phase
approximation (RPA) for the correlation energy and compare our results to
experimental data as well as diffusion Monte Carlo data for ice. The RPA yields
a very balanced description for all considered phases, approaching the accuracy
of diffusion Monte Carlo in relative energies and volumes. This opens a route
towards a concise description of molecular water phases on surfaces and in
cavities
Limit curve theorems in Lorentzian geometry
The subject of limit curve theorems in Lorentzian geometry is reviewed. A
general limit curve theorem is formulated which includes the case of converging
curves with endpoints and the case in which the limit points assigned since the
beginning are one, two or at most denumerable. Some applications are
considered. It is proved that in chronological spacetimes, strong causality is
either everywhere verified or everywhere violated on maximizing lightlike
segments with open domain. As a consequence, if in a chronological spacetime
two distinct lightlike lines intersect each other then strong causality holds
at their points. Finally, it is proved that two distinct components of the
chronology violating set have disjoint closures or there is a lightlike line
passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio
The Geometry of Warped Product Singularities
In this article the degenerate warped products of singular semi-Riemannian
manifolds are studied. They were used recently by the author to handle
singularities occurring in General Relativity, in black holes and at the
big-bang. One main result presented here is that a degenerate warped product of
semi-regular semi-Riemannian manifolds with the warping function satisfying a
certain condition is a semi-regular semi-Riemannian manifold. The connection
and the Riemann curvature of the warped product are expressed in terms of those
of the factor manifolds. Examples of singular semi-Riemannian manifolds which
are semi-regular are constructed as warped products. Applications include
cosmological models and black holes solutions with semi-regular singularities.
Such singularities are compatible with a certain reformulation of the Einstein
equation, which in addition holds at semi-regular singularities too.Comment: 14 page
Effects of Corner Geometry and Adiabatic Extensions on Heat Transfer through a Differentially Heated Square Cavity
This study is concerned with heat transfer by natural convection in a differentially heated square cavity. The purpose is to explore numerically the effects of the corner geometry and adiabatic extensions on heat transfer through the sidewalls. Two sets of simulations have been carried out in this study. The first set is concerned with steady-state calculations with different corner shapes, and the second set considers both steady-state and transient heat transfer with adiabatic extensions of various dimensions. The numerical results are presented in this paper
Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms
We give a spinorial characterization of isometrically immersed surfaces of
arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For
Lorentzian surfaces, this generalizes a recent work of the first author in
to other Lorentzian space forms. We also characterize
immersions of Riemannian surfaces in these spaces. From this we can deduce
analogous results for timelike immersions of Lorentzian surfaces in space forms
of corresponding signature, as well as for spacelike and timelike immersions of
surfaces of signature (0,2), hence achieving a complete spinorial description
for this class of pseudo-Riemannian immersions.Comment: 9 page
Titanium solubility in olivine in the system TiO2–MgO–SiO2: no evidence for an ultra-deep origin of Ti-bearing olivine
Painleve-Gullstrand Coordinates for the Kerr Solution
We construct a coordinate system for the Kerr solution, based on the zero
angular momentum observers dropped from infinity, which generalizes the
Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr
metric can then be interpreted as describing space flowing on a (curved)
Riemannian 3-manifold. The stationary limit arises as the set of points on this
manifold where the speed of the flow equals the speed of light, and the
horizons as the set of points where the radial speed equals the speed of light.
A deeper analysis of what is meant by the flow of space reveals that the
acceleration of free-falling objects is generally not in the direction of this
flow. Finally, we compare the new coordinate system with the closely related
Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign
error in the expression of the function delta correcte
Synchrotron radiation study of the relation between structure and strain in polyurethane elastomers
This paper describes a system for the study of the relation between structure and applied strain in thermoplastic polyurethane elastomers using the Australian National Beamline Facility at the Photon Factory, KEK, Tsukuba, Japan. The system uses the sagittal focusing monochromator at beamline 20B to provide a high-intensity focused beam which then falls on the specimen mounted in a miniature tensometer mounted in the unique vacuum diffractometer (BIGDIFF). Imaging plates were used to record simultaneously SAXS and WAXS patterns from the specimen at a particular strain. The change in SAXS and WAXS patterns with loading and unloading was recorded using a ten-plate imaging-plate changer
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