Measuring the three-dimensional shear from simulation data, with applications to weak gravitational lensing

We have developed a new three-dimensional algorithm, based on the standard P$^3$M method, for computing deflections due to weak gravitational lensing. We compare the results of this method with those of the two-dimensional planar approach, and rigorously outline the conditions under which the two approaches are equivalent. Our new algorithm uses a Fast Fourier Transform convolution method for speed, and has a variable softening feature to provide a realistic interpretation of the large-scale structure in a simulation. The output values of the code are compared with those from the Ewald summation method, which we describe and develop in detail. With an optimal choice of the high frequency filtering in the Fourier convolution, the maximum errors, when using only a single particle, are about 7 per cent, with an rms error less than 2 per cent. For ensembles of particles, used in typical $N$-body simulations, the rms errors are typically 0.3 per cent. We describe how the output from the algorithm can be used to generate distributions of magnification, source ellipticity, shear and convergence for large-scale structure.Comment: 22 pages, latex, 11 figure

Solving Einstein's Equations With Dual Coordinate Frames

A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original ``inertial'' coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.Comment: Updated to agree with published versio

Dispersion and polarization conversion of whispering gallery modes in arbitrary cross-section nanowires

We investigate theoretically the optical properties of Nano-Wires (NWs) with cross sections having either discrete or cylindrical symmetry. The material forming the wire is birefringent, showing a different dielectric response in the plane and along the axis of the wire, which is typically the case for wires made of wurtzite materials, such as ZnO or GaN. We look for solutions of Maxwell`s equations having the proper symmetry. The dispersions and the linewidths versus angle of incident light for the modes having high momentum in the cross-section plane, so called whispering gallery modes, are calculated. We put a special emphasis on the case of hexagonal cross sections. The energy positions of the modes for a set of azimuthal quantum numbers are shown. We demonstrate the dependence of the energy splitting between TE and TM modes versus birefringence. The polarization conversion from TE to TM with increase of the axial wave vectoris discussed for both cylindrical and discrete symmetry.Comment: 9 pages, 10 figure