The Complementarity of Eastern and Western Hemisphere Long-Baseline Neutrino Oscillation Experiments

We present a general formalism for extracting information on the fundamental parameters associated with neutrino masses and mixings from two or more long baseline neutrino oscillation experiments. This formalism is then applied to the current most likely experiments using neutrino beams from the Japan Hadron Facility (JHF) and Fermilab's NuMI beamline. Different combinations of muon neutrino or muon anti-neutrino running are considered. To extract the type of neutrino mass hierarchy we make use of the matter effect. Contrary to naive expectation, we find that both beams using neutrinos is more suitable for determining the hierarchy provided that the neutrino energy divided by baseline ($E/L$) for NuMI is smaller than or equal to that of JHF. Whereas to determine the small mixing angle, $\theta_{13}$, and the CP or T violating phase $\delta$, one neutrino and the other anti-neutrino is most suitable. We make extensive use of bi-probability diagrams for both understanding and extracting the physics involved in such comparisons.Comment: 21 pages, Latex, 3 postscript figure

Reconstructing the Properties of Dark Energy using Standard Sirens

Future space-based gravity wave experiments such as the Big Bang Observatory (BBO), with their excellent projected, one sigma angular resolution, will measure the luminosity distance to a large number of gravity wave (GW) sources to high precision, and the redshift of the single galaxies in the narrow solid angles towards the sources will provide the redshifts of the gravity wave sources. One sigma BBO beams contain the actual source only in 68 per cent cases; the beams that do not contain the source may contain a spurious single galaxy, leading to misidentification. To increase the probability of the source falling within the beam, larger beams have to be considered, decreasing the chances of finding single galaxies in the beams. Saini, Sethi and Sahni (2010) argued, largely analytically, that identifying even a small number of GW source galaxies furnishes a rough distance-redshift relation, which could be used to further resolve sources that have multiple objects in the angular beam. In this work we further develop this idea by introducing a self-calibrating iterative scheme which works in conjunction with Monte-Carlo simulations to determine the luminosity distance to GW sources with progressively greater accuracy. This iterative scheme allows one to determine the equation of state of dark energy to within an accuracy of a few percent for a gravity wave experiment possessing a beam width an order of magnitude larger than BBO (and therefore having a far poorer angular resolution). This is achieved with no prior information about the nature of dark energy from other data sets such as SN Ia, BAO, CMB etc.Comment: 12 pages, 10 figures. Expanded discussion, additional references. Main results unchanged. Matches published versio

Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory

The multiphase Whitham modulation equations with $N$ phases have $2N$ characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for coalescence, where two characteristics change from hyperbolic to elliptic via collision. Firstly, a linear theory develops the structure of colliding characteristics involving the topological sign of characteristics and multiple Jordan chains, and secondly a nonlinear modulation theory is developed for transitions. The nonlinear theory shows that coalescing characteristics morph the Whitham equations into an asymptotically valid geometric form of the two-way Boussinesq equation. That is, coalescing characteristics generate dispersion, nonlinearity and complex wave fields. For illustration, the theory is applied to coalescing characteristics associated with the modulation of two-phase travelling-wave solutions of coupled nonlinear Schr\"odinger equations, highlighting how collisions can be identified and the relevant dispersive dynamics constructed.Comment: 40 pages, 2 figure

Concurrent extensions to the FORTRAN language for parallel programming of computational fluid dynamics algorithms

Experiments were conducted at NASA Ames Research Center to define multi-tasking software requirements for multiple-instruction, multiple-data stream (MIMD) computer architectures. The focus was on specifying solutions for algorithms in the field of computational fluid dynamics (CFD). The program objectives were to allow researchers to produce usable parallel application software as soon as possible after acquiring MIMD computer equipment, to provide researchers with an easy-to-learn and easy-to-use parallel software language which could be implemented on several different MIMD machines, and to enable researchers to list preferred design specifications for future MIMD computer architectures. Analysis of CFD algorithms indicated that extensions of an existing programming language, adaptable to new computer architectures, provided the best solution to meeting program objectives. The CoFORTRAN Language was written in response to these objectives and to provide researchers a means to experiment with parallel software solutions to CFD algorithms on machines with parallel architectures