33,378 research outputs found
Raising and Lowering operators of spin-weighted spheroidal harmonics
In this paper we generalize the spin-raising and lowering operators of
spin-weighted spherical harmonics to linear-in- spin-weighted
spheroidal harmonics where is an additional parameter present in the
second order ordinary differential equation governing these harmonics. One can
then generalize these operators to higher powers in . Constructing
these operators required calculating the -, - and -raising and
lowering operators (and various combinations of them) of spin-weighted
spherical harmonics which have been calculated and shown explicitly in this
paper
Interferometric detection of spin-polarized transport in the depletion layer of a metal-GaAs Schottky barrier
It is shown that the Kerr rotation of spin-polarized electrons is modulated
by the distance of the electrons from the sample surface. Time-resolved Kerr
rotation of optically-excited spin-polarized electrons in the depletion layer
of n-doped GaAs displays fast oscillations that originate from an interference
between the light reflected from the semiconductor surface and from the front
of the electron distribution moving into the semiconductor. Using this effect,
the dynamics of the photogenerated charge carriers in the depletion layer of
the biased Schottky barrier is measured.Comment: 10 pages, 4 figure
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Agreement of three tonometers with Goldmann Applanation Tonometry (GAT)
Micro-computed tomography pore-scale study of flow in porous media: Effect of voxel resolution
A fundamental understanding of flow in porous media at the pore-scale is necessary to be able to upscale average displacement processes from core to reservoir scale. The study of fluid flow in porous media at the pore-scale consists of two key procedures: Imaging - reconstruction of three-dimensional (3D) pore space images; and modelling such as with single and two-phase flow simulations with Lattice-Boltzmann (LB) or Pore-Network (PN) Modelling. Here we analyse pore-scale results to predict petrophysical properties such as porosity, single-phase permeability and multi-phase properties at different length scales. The fundamental issue is to understand the image resolution dependency of transport properties, in order to up-scale the flow physics from pore to core scale. In this work, we use a high resolution micro-computed tomography (micro-CT) scanner to image and reconstruct three dimensional pore-scale images of five sandstones (Bentheimer, Berea, Clashach, Doddington and Stainton) and five complex carbonates (Ketton, Estaillades, Middle Eastern sample 3, Middle Eastern sample 5 and Indiana Limestone 1) at four different voxel resolutions (4.4 µm, 6.2 µm, 8.3 µm and 10.2 µm), scanning the same physical field of view. Implementing three phase segmentation (macro-pore phase, intermediate phase and grain phase) on pore-scale images helps to understand the importance of connected macro-porosity in the fluid flow for the samples studied. We then compute the petrophysical properties for all the samples using PN and LB simulations in order to study the influence of voxel resolution on petrophysical properties. We then introduce a numerical coarsening scheme which is used to coarsen a high voxel resolution image (4.4 µm) to lower resolutions (6.2 µm, 8.3 µm and 10.2 µm) and study the impact of coarsening data on macroscopic and multi-phase properties. Numerical coarsening of high resolution data is found to be superior to using a lower resolution scan because it avoids the problem of partial volume effects and reduces the scaling effect by preserving the pore-space properties influencing the transport properties. This is evidently compared in this study by predicting several pore network properties such as number of pores and throats, average pore and throat radius and coordination number for both scan based analysis and numerical coarsened data
Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics
In this paper we study families of complex Hermite polynomials and construct
deformed versions of them, using a transformation. This
construction leads to the emergence of biorthogonal families of deformed
complex Hermite polynomials, which we then study in the context of a
two-dimensional model of noncommutative quantum mechanics.Comment: 17 page
Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
We present a novel analytic extraction of high-order post-Newtonian (pN)
parameters that govern quasi-circular binary systems. Coefficients in the pN
expansion of the energy of a binary system can be found from corresponding
coefficients in an extreme-mass-ratio inspiral (EMRI) computation of the change
in the redshift factor of a circular orbit at fixed angular
velocity. Remarkably, by computing this essentially gauge-invariant quantity to
accuracy greater than one part in , and by assuming that a subset of
pN coefficients are rational numbers or products of and a rational, we
obtain the exact analytic coefficients. We find the previously unexpected
result that the post-Newtonian expansion of (and of the change
in the angular velocity at fixed redshift factor) have
conservative terms at half-integral pN order beginning with a 5.5 pN term. This
implies the existence of a corresponding 5.5 pN term in the expansion of the
energy of a binary system.
Coefficients in the pN series that do not belong to the subset just described
are obtained to accuracy better than 1 part in at th pN
order. We work in a radiation gauge, finding the radiative part of the metric
perturbation from the gauge-invariant Weyl scalar via a Hertz
potential. We use mode-sum renormalization, and find high-order renormalization
coefficients by matching a series in to the large- behavior of
the expression for . The non-radiative parts of the perturbed metric
associated with changes in mass and angular momentum are calculated in the
Schwarzschild gauge
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