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

Tantilla oolitica

Number of Pages: 1Integrative BiologyGeological Science

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 $Pbca$, $P4_32_12$, and $P2_1/c$ 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 $Pbca$ and $P2_1/c$ structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature $Pbca$ to $P2_1/c$ 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 50.6$\pm$0.5 kJ/mol for crystalline benzene lattice energy