Three Flavor Neutrino Oscillations in Matter: Flavor Diagonal Potentials, the Adiabatic Basis and the CP phase

We discuss the three neutrino flavor evolution problem with general, flavor-diagonal, matter potentials and a fully parameterized mixing matrix that includes CP violation, and derive expressions for the eigenvalues, mixing angles and phases. We demonstrate that, in the limit that the mu and tau potentials are equal, the eigenvalues and matter mixing angles theta_12 and theta_13 are independent of the CP phase, although theta_23 does have CP dependence. Since we are interested in developing a framework that can be used for S matrix calculations of neutrino flavor transformation, it is useful to work in a basis that contains only off-diagonal entries in the Hamiltonian. We derive the "non-adiabaticity" parameters that appear in the Hamiltonian in this basis. We then introduce the neutrino S matrix, derive its evolution equation and the integral solution. We find that this new Hamiltonian, and therefore the S matrix, in the limit that the mu and tau neutrino potentials are the same, is independent of both theta_23 and the CP violating phase. In this limit, any CP violation in the flavor basis can only be introduced via the rotation matrices, and so effects which derive from the CP phase are then straightforward to determine. We show explicitly that the electron neutrino and electron antineutrino survival probability is independent of the CP phase in this limit. Conversely, if the CP phase is nonzero and mu and tau matter potentials are not equal, then the electron neutrino survival probability cannot be independent of the CP phase

How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a coarse-grained description of the behavior that accurately describes the invariant properties of an underlying chaotic attractor. In particular, measures of the rate of information production--the topological and metric entropy rates--can be estimated from the outputs of Markov or generating partitions. Here we develop Bayesian inference for k-th order Markov chains as a method to finding generating partitions and estimating entropy rates from finite samples of discretized data produced by coarse-grained dynamical systems.Comment: 8 pages, 1 figure; http://cse.ucdavis.edu/~cmg/compmech/pubs/hrct.ht

Bayesian Structural Inference for Hidden Processes

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological epsilon-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be epsilon-machines, irrespective of estimated transition probabilities. Properties of epsilon-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.Comment: 20 pages, 11 figures, 1 table; supplementary materials, 15 pages, 11 figures, 6 tables; http://csc.ucdavis.edu/~cmg/compmech/pubs/bsihp.ht

Feasibility Study of SDAS Instrumentation's Ability to Identify Mobile Launcher (ML)/Crawler-Transporter (CT) Modes During Rollout Operations

The Space Launch System (SLS) and its Mobile Launcher (ML) will be transported to the launch pad via the Crawler-Transporter (CT) system. Rollout (i.e., transportation) loads produce structural loads on the integrated SLS/Orion Multi-Purpose Crew Vehicle (MPCV) launch vehicle which are of a concern with respect to fatigue. As part of the risk reduction process and in addition to the modal building block test approach that has been adopted by the SLS Program, acceleration data will be obtained during rollout for use in modal parameter estimation. There are several occurrences where the ML/CT will be transported either into the Vertical Assembly Building (VAB) or to the launch pad and back without the SLS stack as part of the Kennedy Space Center (KSC) Exploration Ground Systems (EGS) Integrated Test and Checkout (ITCO). NASA KSC EGS has instrumentation installed on both the ML and CT to record data during rollout, at the launch pad, and during liftoff. The EGS instrumentation on the ML, which includes accelerometers, is referred to as the Sensor Data Acquisition System (SDAS). The EGS instrumentation on the CT, which also includes accelerometers, is referred to as the CT Data Acquisition System (CTDAS). The forces and accelerations applied to the ML and CT during a rollout event will be higher than any of the planned building block modal tests. This can be very beneficial in helping identify nonlinear behavior in the structure. Developing modal parameters from the same test hardware in multiple boundary conditions and under multiple levels of excitation is a key step in developing a well correlated FEM. The purpose of this study was three fold. First, determine the target modes of the ML/CT in its rollout configuration. Second, determine if the test degrees of freedom (DOF) corresponding to the layout of the SDAS/CTDAS accelerometers (i.e. position and orientation) is sufficient to identify the target modes. Third, determine if the Generic Rollout Forcing Functions (GRFF's) is sufficient for identifying the ML/CT target modes accounting for variations in CT speed, modal damping, and sensor/ambient background noise levels. The finding from the first part of this study identified 28 target modes of the ML/CT rollout configuration based upon Modal Effective Mass Fractions (MEFF) and engineering judgement. The finding from the second part of this study showed that the SDAS/CTDAS accelerometers (i.e. position and orientation) are able to identify a sufficient number of the target modes to support model correlation of the ML/CT FEM. The finding from the third part of this study confirms the GRFFs sufficiently excite the ML/CT such that varying quantities of the defined target modes should be able to be extracted when utilizing an Experimental Modal Analysis (EMA) Multi-Input Multi-Output (MIMO) analysis approach. An EMA analysis approach was used because Operational Modal Analysis (OMA) tools were not available and the GRFFs were sufficiently uncorrelated. Two key findings from this third part of the study are that the CT speed does not show a significant impact on the ability to extract the modal parameters and that keeping the ambient background noise observed at each accelerometer location at or below 30 grms is essential to the success of this approach

Abundance stratification in Type Ia supernovae - V. SN 1986G bridging the gap between normal and subluminous SNe Ia

A detailed spectroscopic analysis of SN 1986G has been performed. SN 1986G `bridges the gap' between normal and sub luminous type Ia supernova (SNe Ia). The abundance tomography technique is used to determine the abundance distribution of the elements in the ejecta. SN 1986G was found to be a low energy Chandrasekhar mass explosion. Its kinetic energy was 70% of the standard W7 model (0.9x10$^{51}$erg). Oxygen dominates the ejecta from the outermost layers down to $\sim$9000kms$^{-1}$ , intermediate mass elements (IME) dominate from $\sim$ 9000kms$^{-1}$ to $\sim$ 3500kms$^{-1}$ with Ni and Fe dominating the inner layers $<\sim$ 3500kms$^{-1}$. The final masses of the main elements in the ejecta were found to be, O=0.33M, IME=0.69M, stable NSE=0.21M, $^{56}$Ni=0.14M. An upper limit of the carbon mass is set at C=0.02M. The spectra of SN1986G consist of almost exclusively singly ionised species. SN1986G can be thought of as a low luminosity extension of the main population of SN Ia, with a large deflagration phase that produced more IMEs than a standard SN Ia.Comment: Accepted for publication in MNRAS, update

Resilience of Hierarchical Critical Infrastructure Networks

Concern over the resilience of critical infrastructure networks has increased dramatically over the last decade due to a number of well documented failures and the significant disruption associated with these. This has led to a large body of research that has adopted graph-theoretic based analysis in order to try and improve our understanding of infrastructure network resilience. Many studies have asserted that infrastructure networks possess a scale-free topology which is robust to random failures but sensitive to targeted attacks at highly connected hubs. However, many studies have ignored that many networks in addition to their topological connectivity may be organised either logically or spatially in a hierarchical system which may significantly change their response to perturbations. In this paper we explore if hierarchical network models exhibit significantly different higher-order topological characteristics compared to other network structures and how this impacts on their resilience to a number of different failure types. This is achieved by investigating a suite of synthetic networks as well as a suite of ‘real world’ spatial infrastructure networks