By examining the locations of central black holes in two elliptical galaxies, M,32 and M,87, we derive constraints on the violation of the strong equivalence principle for purely gravitational objects, i.e. black holes, of less than about two-thirds,
$eta_N<0.68$ from the gravitational interaction of M,87 with its neighbours in the Virgo cluster. Although M,32 appears to be a good candidate for this technique, the high concentration of stars near its centre substantially weakens the constraints. On the other hand, if a central black hole is found in NGC 205 or one of the other satellite ellipticals of M,31, substantially better constraints could be obtained. In all cases the constraints could improve dramatically with better astrometry.
We use the worldline numerics technique to study a cylindrically symmetric model of magnetic flux tubes in a dense lattice and the non-local Casimir forces acting between regions of magnetic flux. Within a superconductor the magnetic field is constra
ined within magnetic flux tubes and if the background magnetic field is on the order the quantum critical field strength, $B_k = frac{m^2}{e} = 4.4 times 10^{13}$ Gauss, the magnetic field is likely to vary rapidly on the scales where acs{QED} effects are important. In this paper, we construct a cylindrically symmetric toy model of a flux tube lattice in which the non-local influence of acs{QED} on neighbouring flux tubes is taken into account. We compute the effective action densities using the worldline numerics technique. The numerics predict a greater effective energy density in the region of the flux tube, but a smaller energy density in the regions between the flux tubes compared to a locally-constant-field approximation. We also compute the interaction energy between a flux tube and its neighbours as the lattice spacing is reduced from infinity. Because our flux tubes exhibit compact support, this energy is entirely non-local and predicted to be zero in local approximations such as the derivative expansion. This Casimir-Polder energy can take positive or negative values depending on the distance between the flux tubes, and it may cause the flux tubes in neutron stars to form bunches. In addition to the above results we also discuss two important subtleties of determining the statistical uncertainties within the worldline numerics technique and recommend a form of jackknife analysis.
We give an overview of the worldline numerics technique, and discuss the parallel CUDA implementation of a worldline numerics algorithm. In the worldline numerics technique, we wish to generate an ensemble of representative closed-loop particle traje
ctories, and use these to compute an approximate average value for Wilson loops. We show how this can be done with a specific emphasis on cylindrically symmetric magnetic fields. The fine-grained, massive parallelism provided by the GPU architecture results in considerable speedup in computing Wilson loop averages. Furthermore, we give a brief overview of uncertainty analysis in the worldline numerics method. There are uncertainties from discretizing each loop, and from using a statistical ensemble of representative loops. The former can be minimized so that the latter dominates. However, determining the statistical uncertainties is complicated by two subtleties. Firstly, the distributions generated by the worldline ensembles are highly non-Gaussian, and so the standard error in the mean is not a good measure of the statistical uncertainty. Secondly, because the same ensemble of worldlines is used to compute the Wilson loops at different values of $T$ and $x_mathrm{ cm}$, the uncertainties associated with each computed value of the integrand are strongly correlated. We recommend a form of jackknife analysis which deals with both of these problems.
In this review article we provide an overview of the field of atomic structure of light atoms in strong magnetic fields. There is a very rich history of this field which dates back to the very birth of quantum mechanics. At various points in the past
significant discoveries in science and technology have repeatedly served to rejuvenate interest in atomic structure in strong fields, broadly speaking, resulting in three eras in the development of this field; the historical, the classical and the modern eras. The motivations for studying atomic structure have also changed significantly as time progressed. The review presents a chronological summary of the major advances that occurred during these eras and discusses new insights and impetus gained. The review is concluded with a description of the latest findings and the future prospects for one of the most remarkably cutting-edge fields of research in science today.
This paper presents new and efficient algorithms for matching stellar catalogues where the transformation between the coordinate systems of the two catalagoues is unknown and may include shearing. Finding a given object whether a star or asterism fro
m the first catalogue in the second is logarithmic in time rather than polynomial, yielding a dramatic speed up relative to a naive implementation. Both acceleration of the matching algorithm and the ability to solve for arbitrary affine transformations not only will allow the registration of stellar catalogues and images that are now impossible to use but also will find applications in machine vision and other imaging applications.
Diffraction is important when nearby substellar objects gravitationally lens distant stars. If the wavelength of the observation is comparable to the Schwarzschild radius of lensing object, diffraction leaves an observable imprint on the lensing sign
ature. The SKA may have sufficient sensitivity to detect the typical sources, giant stars in the bulge. The diffractive signatures in a lensing event break the degeneracies between the mass of the lens, its distance and proper motion.
