The Small Module Fixed Mirror Distributed Focus (FMDF) Photothermal Concentrator Study

The development of a general ray trace evaluation program called ICARUS, the study of novel Fresnel concepts, and the review of a report draft on novel Fresnel concepts are covered. ICARUS is documented, reports on the novel Fresnel concepts were previously submitted

Compensation for Primary Reflector Wavefront Error

The object of the invention is to compensate for errors in a large telescope primary reflector by making certain compensating deviations in a smaller, auxiliary reflector of the telescope. At least one intermediate element forms an image of the primary surface onto the secondary surface, so each point on the secondary surface corresponds to a point on the primary surface. The secondary surface is formed with a deviation from an ideal secondary surface, with the piston distance of each point on the actual secondary surface equal to the piston distance of a corresponding piston on the actual primary surface from the ideal primary surface. It is found that this results in electromagnetic (e.g., light) rays which strike a deviating area of the actual primary surface being brought to the same focus as if the actual primary surface did not have a diviation from an ideal primary surface

A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory

In the present paper we prove a classification (uniqueness) theorem for stationary, asymptotically flat black hole spacetimes with connected and non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling parameter $\alpha$. We show that such black holes are uniquely specified by the length of the horizon interval, angular momentum, electric and magnetic charge and the value of the dilaton field at infinity when the dilaton coupling parameter satisfies $0\le \alpha^2\le3$. The proof is based on the nonpositivity of the Riemann curvature operator on the space of the potentials. A generalization of the classification theorem for spacetimes with disconnected horizons is also given.Comment: 15 pages, v2 typos correcte

Differentially rotating disks of dust

We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer-Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Baecklund transformations to appropriate seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and Gravitation". Second version with minor correction

Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes

We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. The one type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of dust surrounded by such a ring. Both types of spacetime are regular everywhere (outside of the horizon in the case of the black hole) and fulfil the requirements of the positive energy theorem. However, it is shown that both the black hole and the disc can have negative Komar mass. Furthermore, there exists a continuous transition from discs to black holes even when their Komar masses are negative.Comment: 7 pages, 2 figures, document class iopart. v2: changes made (including title) to coincide with published versio

Intercomparison of ground-based and space solar flux measurements

Detailed temporal measurements of the solar flux at one location are performed. These data are then analyzed and compared to the potential of space measurements which allow one to consider the flux falling on areas of the earth. An important result of the research is that the temporal characteristics of the flux in the presence of a real atmosphere would be difficult to obtain from space and that the variations in the flux can be highly significant in regard to most solar conversion schemes. The detailed results of the research are presented. The instruments developed to separate the direct and scattered solar flux, the computer analysis methods developed, and the results of the research, presented as both graphical and tabular data, are discussed

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4

On the black hole limit of rotating fluid bodies in equilibrium

Recently, it was shown that the extreme Kerr black hole is the only candidate for a (Kerr) black hole limit of stationary and axisymmetric, uniformly rotating perfect fluid bodies with a zero temperature equation of state. In this paper, necessary and sufficient conditions for reaching the black hole limit are presented.Comment: 8 pages, v2: one footnote and one reference added, accepted for publication in CQ

The Ernst equation and ergosurfaces

We show that analytic solutions \mcE of the Ernst equation with non-empty zero-level-set of \Re \mcE lead to smooth ergosurfaces in space-time. In fact, the space-time metric is smooth near a "Ernst ergosurface" $E_f$ if and only if \mcE is smooth near $E_f$ and does not have zeros of infinite order there.Comment: 23 pages, 4 figures; misprints correcte

OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201