An analytical solver for the multi-group two-dimensional neutron-diffusion equation by integral transform techniques

In this work, we present an analytical solver for neutron diffusion in a rectangular two-dimensional geometry by a two-step integral transform procedure. To this end, we consider a regionwise homogeneous problem for two energy groups, i.e. fast and thermal neutrons, respectively. Each region has its specific physical properties, specified by cross-sections and diffusion constants. The problem is set up by two coupled bi-dimensional diffusion equations in agreement with general perturbation theory. These are solved by integral transforms Laplace transform and generalized integral transform technique yielding analytical expressions for the scalar neutron fluxes. The solutions for neutron fluxes are presented for fast and thermal neutrons in the four regions

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

Measurements of Charged Current Reactions of νe\nu_e on 12C^{12}C

Charged Current reactions of $\nu_e$ on $^{12}C$ have been studied using a $\mu^+$ decay-at-rest $\nu_e$ beam at the Los Alamos Neutron Science Center. The cross section for the exclusive reaction $^{12}C(\nu_e,e^-)^{12}N_{g.s.}$ was measured to be $(8.9\pm0.3\pm0.9)\times10^{-42}$ cm$^2$. The observed energy dependence of the cross section and angular distribution of the outgoing electron agree well with theoretical expectations. Measurements are also presented for inclusive transitions to $^{12}N$ excited states, $^{12}C(\nu_e,e^-)^{12}N^*$ and compared with theoretical expectations. The measured cross section, $(4.3\pm0.4\pm0.6)\times10^{-42}$ cm$^2$, is somewhat lower than previous measurements and than a continuum random phase approximation calculation. It is in better agreement with a recent shell model calculation.Comment: 34 pages, 18 figures, accepted to PRC, replaced with the accepted on

Evidence for nu_mu -> nu_e Oscillations from Pion Decay in Flight Neutrinos

A search for nu_mu -> nu_e oscillations has been conducted at the Los Alamos Meson Physics Facility using nu_mu from pi^+ decay in flight. An excess in the number of beam-related events from the C(nu_e,e^-)X inclusive reaction is observed. The excess is too large to be explained by normal nu_e contamination in the beam at a confidence level greater than 99%. If interpreted as an oscillation signal, the observed oscillation probability of (2.6 +- 1.0 +- 0.5) x 10^{-3} is consistent with the previously reported nu_mu_bar -> nu_e_bar oscillation evidence from LSND.Comment: 70 pages (LaTeX), 32 figures (PostScript), submitted to Phys. Rev. C. Additional information at http://nu1.lampf.lanl.gov/~lsn

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Probing Sterile Neutrino Parameters with Double Chooz, Daya Bay and RENO

In this work, we present a realistic analysis of the potential of the present-day reactor experiments Double Chooz, Daya Bay and RENO for probing the existence of sterile neutrinos. We present exclusion regions for sterile oscillation parameters for each of these experiments, using simulations with realistic estimates of systematic errors and detector resolutions, and compare the sterile parameter sensitivity regions we obtain with the existing bounds from other reactor experiments. We find that these experimental set-ups give significant bounds on the parameter \Theta_{ee} especially in the low sterile oscillation region 0.01 < \Delta m_{41}^2 < 0.05 eV^2. These bounds can add to our understanding of the sterile neutrino sector since there is still a tension in the allowed regions from different experiments for sterile parameters.Comment: 12 pages, 5 figure

Evidence for Neutrino Oscillations from Muon Decay at Rest

A search for nu_bar_mu to nu_bar_e oscillations has been conducted at the Los Alamos Meson Physics Facility using nu_bar_mu from mu+ decay at rest. The nu_bar_e are detected via the reaction (nu_bar_e,p) -> (e+,n), correlated with the 2.2 MeV gamma from (n,p) -> (d,gamma). The use of tight cuts to identify e+ events with correlated gamma rays yields 22 events with e+ energy between 36 and 60 MeV and only 4.6 (+/- 0.6) background events. The probability that this excess is due entirely to a statistical fluctuation is 4.1E-08. A chi^2 fit to the entire e+ sample results in a total excess of 51.8 (+18.7) (-16.9) (+/- 8.0) events with e+ energy between 20 and 60 MeV. If attributed to nu_bar_mu -> nu_bar_e oscillations, this corresponds to an oscillation probability (averaged over the experimental energy and spatial acceptance) of 0.0031 (+0.0011) (-0.0010) (+/- 0.0005).Comment: 57 pages, 34 figures, revtex, additional information available at http://nu1.lampf.lanl.gov/~lsnd

Measurements of the reactions 12C + nu_e -> e- + 12N g.s. and 12C + nu_e -> e- + 12N

Charged current reactions of nu_e on 12C have been studied using a mu decay-at-rest nu_e beam from the Los Alamos Meson Physics Facility. More than 500 events from the exclusive reaction 12C + nu_e -> e- + 12N g.s. were measured in a large Liquid Scintillator Neutrino Detector (LSND). The observed energy dependence of the cross section and the angular distribution of the outgoing electron agree well with theoretical expectations. Measurements are also presented for inclusive transitions to 12N excited states, 12C + nu_e -> e- + 12N and compared with theoretical expectations. Results are consistent with a recent Continuum Random Phase Approximation (CRPA) calculation.Comment: Figures included with psfi

Evidence for νˉμ→νˉe\bar\nu_\mu\to\bar\nu_e Oscillations from the LSND Experiment at LAMPF

A search for $\bar\nu_{\mu}\to \bar\nu_{e}$ oscillations has been conducted at the Los Alamos Meson Physics Facility by using $\bar\nu_\mu$ from $\mu^+$ decay at rest. The $\bar\nu_e$ are detected via the reaction $\bar\nu_e\,p \rightarrow e^{+}\,n$, correlated with a $\gamma$ from $np\rightarrow d\gamma$ ($2.2\,{\rm MeV}$). The use of tight cuts to identify $e^+$ events with correlated $\gamma$ rays yields 22 events with $e^+$ energy between 36 and $60\,{\rm MeV}$ and only $4.6 \pm 0.6$ background events. A fit to the $e^+$ events between 20 and $60\,{\rm MeV}$ yields a total excess of $51.8^{+18.7}_{-16.9} \pm 8.0$ events. If attributed to $\bar \nu_\mu \rightarrow \bar \nu_e$ oscillations, this corresponds to an oscillation probability of ($0.31^{+0.11}_{-0.10} \pm 0.05$)\%.Comment: 4 pages, 3 figures, revtex, psfig. additional information available at http://nu1.lampf.lanl.gov/~lsnd