13,198 research outputs found
Geometrical optics for scalar, electromagnetic and gravitational waves in curved spacetime
The geometrical-optics expansion reduces the problem of solving wave
equations to one of solving transport equations along rays. Here we consider
scalar, electromagnetic and gravitational waves propagating on a curved
spacetime in general relativity. We show that each is governed by a wave
equation with the same principal part. It follows that: each wave propagates at
the speed of light along rays (null generators of hypersurfaces of constant
phase); the square of the wave amplitude varies in inverse proportion to the
cross section of the beam; and the polarization is parallel-propagated along
the ray (the Skrotskii/Rytov effect). We show that the optical scalars for a
beam, and various Newman-Penrose scalars describing a parallel-propagated null
tetrad, can be found by solving transport equations in a second-order
formulation. Unlike the Sachs equations, this formulation makes it
straightforward to find such scalars beyond the first conjugate point of a
congruence, where neighbouring rays cross, and the scalars diverge. We discuss
differential precession across the beam which leads to a modified phase in the
geometrical-optics expansion.Comment: 17 pages, 1 figure. Proceedings for IV Amazonian Symposium on
Physics, Belem, Brazil at UFPA on 18-22 Sep 201
Recommended from our members
Tantilla oolitica
Number of Pages: 1Integrative BiologyGeological Science
Recommended from our members
Neoseps and N. reynoldsi
Number of Pages: 2Integrative BiologyGeological Science
Autonomous and Financial Mortgage Prepayment
Using individual data from Freddie Mac's portfolio of conventional mortgages, this paper estimates prepayment probabilities as a function of characteristics pertaining to the borrower, the loan, regional, and economic variables. Distinction is made between induced and autonomous prepayments. Based on the curvature of the underlying termination pattern, nonparametric methods are derived to estimate the prepayment probabilities and to predict a mortgage life under various scenarios. The findings point to a response asymmetry with respect to the level and trend of interest rates. Non-interest effects reveal the significance of the borrower's characteristics, property age, and regional mobility rates on mortgage termination.
Chemical accuracy from quantum Monte Carlo for the Benzene Dimer
We report an accurate study of interactions between Benzene molecules using
variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC)
methods. We compare these results with density functional theory (DFT) using
different van der Waals (vdW) functionals. In our QMC calculations, we use
accurate correlated trial wave functions including three-body Jastrow factors,
and backflow transformations. We consider two benzene molecules in the parallel
displaced (PD) geometry, and find that by highly optimizing the wave function
and introducing more dynamical correlation into the wave function, we compute
the weak chemical binding energy between aromatic rings accurately. We find
optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol,
respectively. The best estimate of the CCSD(T)/CBS limit is -2.65(2) kcal/mol
[E. Miliordos et al, J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate
that QMC methods give chemical accuracy for weakly bound van der Waals
molecular interactions, comparable to results from the best quantum chemistry
methods.Comment: Accepted for publication in the Journal of Chemical Physics, Vol.
143, Issue 11, 201
Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo
We study the low-pressure (0 to 10 GPa) phase diagram of crystalline benzene
using quantum Monte Carlo (QMC) and density functional theory (DFT) methods. We
consider the , , and structures as the best candidates
for phase I and phase II. We perform diffusion quantum Monte Carlo (DMC)
calculations to obtain accurate static phase diagrams as benchmarks for modern
van der Waals density functionals. We use density functional perturbation
theory to compute phonon contribution in the free-energy calculations. Our DFT
enthalpy-pressure phase diagram indicates that the and
structures are the most stable phases within the studied pressure range. The
DMC Gibbs free-energy calculations predict that the room temperature to
phase transition occurs at 2.1(1) GPa. This prediction is consistent
with available experimental results at room temperature. Our DMC calculations
show an estimate of 50.60.5 kJ/mol for crystalline benzene lattice energy
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