Mathematical model for the dc-ac inverter for the Space Shuttle

The reader is informed of what was done for the mathematical modeling of the dc-ac inverter for the Space Shuttle. The mathematical modeling of the dc-ac inverter is an essential element in the modeling of the electrical power distribution system of the Space Shuttle. The electrical power distribution system which is present on the Space Shuttle is made up to 3 strings each having a fuel cell which provides dc to those systems which require dc, and the inverters which convert the dc to ac for those elements which require ac. The inverters are units which are 2 wire structures for the main dc inputs and 2 wire structures for the ac output. When 3 are connected together a 4 wire wye connection results on the ac side. The method of modeling is performed by using a Least Squares curve fitting method. A computer program is presented for implementation of the model along with graphs and tables to demonstrate the accuracy of the model

Development of parallel algorithms for electrical power management in space applications

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met

Relation between classical communication capacity and entanglement capability for two-qubit unitary operations

Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an ensemble may be increased via a two-qubit unitary operation by twice the operation's capacity for entanglement.Comment: 12 pages, published version plus minor correction

High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.Comment: ITP.SB-93-22,17 page

Implementation of multipartite unitary operations with limited resources

A general method for implementing weakly entangling multipartite unitary operations using a small amount of entanglement and classical communication is presented. For the simple Hamiltonian \sigma_z\otimes\sigma_z this method requires less entanglement than previously known methods. In addition, compression of multiple operations is applied to reduce the average communication required.Comment: 7 pages, 4 figures, comments welcom

On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: comment on B. Brown (1983) and Roehrig (1988)

This note revisits the identification theorems of B. Brown (1983) and Roehrig (1988). We describe an error in the proofs of the main identification theorems in these papers, and provide an important counterexample to the theorems on the identification of the reduced form. Specifically, contrary to the theorems, the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of those papers. We conclude the note with a conjecture that it may be possible to use classical exclusion restrictions to recover some of the key implications of the theorems.Simultaneous equations, Non-separable errors

Expectations for extreme-mass-ratio bursts from the Galactic Centre

When a compact object on a highly eccentric orbit about a much more massive body passes through periapsis it emits a short gravitational wave signal known as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs provide a novel means of extracting information about the MBH; an EMRB from the Galactic MBH could be highly informative regarding the MBH's mass and spin if the orbital periapsis is small enough. However, to be a useful astronomical tool EMRBs must be both informative and sufficiently common to be detectable with a space-based interferometer. We construct a simple model to predict the event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts in a two year mission lifetime for LISA. Stellar mass black holes dominate the event rate. Creating a sample of 100 mission realisations, we calculate what we could learn about the MBH. On average, we expect to be able to determine the MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published versio

Critical random graphs: limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and letting n go to infinity yields a non-trivial sequence of limit metric spaces C = (C_1, C_2, ...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R_+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak, Pittel and Wierman by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure

Observing the Galaxy's massive black hole with gravitational wave bursts

An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object, in our case a stellar mass object about a 10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the spacetime of massive black holes (MBHs). We conduct an investigation of the properties of EMRBs and how they could allow us to constrain the parameters, such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu = 10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) + 4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good constraints on both the MBH's mass and spin. Closer orbits provide better constraints, with the best giving accuracies of better than one part in 10^4 for both the mass and spin parameter.Comment: 25 pages, 17 figures, 1 appendix. One more typo fixe