Analysis and Insights from a Dynamical Model of Nuclear Plant Safety Risk

In this paper, we expand upon previously reported results of a dynamical systems model for the impact of plant processes and programmatic performance on nuclear plant safety risk. We utilize both analytical techniques and numerical simulations typical of the analysis of nonlinear dynamical systems to obtain insights important for effective risk management. This includes use of bifurcation diagrams to show that period doubling bifurcations and regions of chaotic dynamics can occur. We also investigate the impact of risk mitigating functions (equipment reliability and loss prevention) on plant safety risk and demonstrate that these functions are capable of improving risk to levels that are better than those that are represented in a traditional risk assessment. Next, we analyze the system response to the presence of external noise and obtain some conclusions with respect to the allocation of resources to ensure that safety is maintained at optimal levels. In particular, we demonstrate that the model supports the importance of management and regulator attention to plants that have demonstrated poor performance by providing an external stimulus to obtain desired improvements. Equally important, the model suggests that excessive intervention, by either plant management or regulatory authorities, can have a deleterious impact on safety for plants that are operating with very effective programs and processes. Finally, we propose a modification to the model that accounts for the impact of plant risk culture on process performance and plant safety risk. We then use numerical simulations to demonstrate the important safety benefits of a strong risk culture.Nonlinear Dynamical Systems, Process Model, Risk Management

Comment on Performance of Different Synchronization Measures in Real Data: A Case Study on Electroencephalographic Signals

Quian Quiroga [Phys. Rev. E 65, 041903 (2002)] reported a similar performance of several linear and nonlinear measures of synchronization when applied to the rat electrocorticogram (ECoG). However, they found that the mutual information measure did not produce robust estimates of synchronization when compared to other measures. We reexamined their data using a histogram method with adaptive partitioning and found the mutual information to be a useful measure of regional ECoG interdependence

Kolmogorov-Smirnov Test Distinguishes Attractors with Similar Dimensions

Recent advances in nonlinear dynamics have led to more informative characterizations of complex signals making it possible to probe correlations in data to which traditional linear statistical and spectral analyses were not sensitive. Many of these new tools require detailed knowledge of small scale structures of the attractor; knowledge that can be acquired only from relatively large amounts of precise data that are not contaminated by noise-not the kind of data one usually obtains from experiments. There is a need for tools that can take advantage of \u27\u27coarse-grained\u27\u27 information, but which nevertheless remain sensitive to higher-order correlations in the data. We propose that the correlation integral, now much used as an intermediate step in the calculation of dimensions and entropies, can be used as such a tool and that the Kolmogorov-Smirnov test is a convenient and reliable way of comparing correlation integrals quantitatively. This procedure makes it possible to distinguish between attractors with similar dimensions. For example, it can unambiguously distinguish (p \u3c 10(-8)) the Lorenz, Rossler, and Mackey-Glass (delay = 17) attractors whose correlation dimensions are within 1% of each other. We also show that the Kolmogorov-Smirnov test is a convenient way of comparing a data set with its surrogates

Dipole-dipole spin relaxation in solids. The unrestricted hopping model and the methyl proton - non-methyl proton interaction

We report proton Zeeman relaxation rates R as a function of temperature T at 8.5 and 53 MHz in polycrystalline 1,9-dimethylphenanthrene (1,9-DMP) and l-trideuteriomethyl-9-methylphenanthrene (1, 9-DMP[1-d3]). The data are interpreted using a Davidson-Cole spectral density for intramolecular reorientation and the implications of this are discussed. R vs T−1data for 1,9-DMP[1-d3] are used to determine the parameters that characterize the reorientation of the 9-methyl group. By assuming that the parameters characterizing the dynamics of the 9-methyl group are the same in 1,9-DMP and 1,9-DMP[1-d3], we subtract out the R vs T−1 contribution of the 9-methyl group in 1,9-DMP to determine the parameters that characterize the dynamics of the 1-methyl group. We find that the barrier for reorientation of the 9-methyl group is larger than the barrier for the 1-methyl group and this is discussed in terms of the various contributions to the barrier

Correlation-Dimension Calculations for Broadband Intensity Fluctuations in Emission from a Heavily Saturated Source of Amplified Spontaneous Emission

Broadband intensity fluctuations from a heavily saturated source of amplified spontaneous emission (ASE) operating on the 3.51-μm transition of xenon show no evidence of a dynamical origin represented by a low-dimensional underlying chaotic attractor. The broadband coupled-mode fluctuations in ASE thus seem to be stochastic when contrasted with the recently reported deterministic nature of similar broadband fluctuations of single-mode lasers operating on the same transition

Correlation-Dimension Calculations for Broadband Intensity Fluctuations in Emission from a Heavily Saturated Source of Amplified Spontaneous Emission

Broadband intensity fluctuations from a heavily saturated source of amplified spontaneous emission (ASE) operating on the 3.51-μm transition of xenon show no evidence of a dynamical origin represented by a low-dimensional underlying chaotic attractor. The broadband coupled-mode fluctuations in ASE thus seem to be stochastic when contrasted with the recently reported deterministic nature of similar broadband fluctuations of single-mode lasers operating on the same transition

Dipole-dipole spin relaxation in solids. The unrestricted hopping model and the methyl proton - non-methyl proton interaction

We report proton Zeeman relaxation rates R as a function of temperature T at 8.5 and 53 MHz in polycrystalline 1,9-dimethylphenanthrene (1,9-DMP) and l-trideuteriomethyl-9-methylphenanthrene (1, 9-DMP[1-d3]). The data are interpreted using a Davidson-Cole spectral density for intramolecular reorientation and the implications of this are discussed. R vs T−1data for 1,9-DMP[1-d3] are used to determine the parameters that characterize the reorientation of the 9-methyl group. By assuming that the parameters characterizing the dynamics of the 9-methyl group are the same in 1,9-DMP and 1,9-DMP[1-d3], we subtract out the R vs T−1 contribution of the 9-methyl group in 1,9-DMP to determine the parameters that characterize the dynamics of the 1-methyl group. We find that the barrier for reorientation of the 9-methyl group is larger than the barrier for the 1-methyl group and this is discussed in terms of the various contributions to the barrier

Comparative Study of Embedding Methods

Embedding experimental data is a common first step in many forms of dynamical analysis. The choice of appropriate embedding parameters (dimension and lag) is crucial to the success of the subsequent analysis. We argue here that the optimal embedding of a time series cannot be determined by criteria based solely on the time series itself. Therefore we base our analysis on an examination of systems that have explicit analytic representations. A comparison of analytically obtained results with those obtained by an examination of the corresponding time series provides a means of assessing the comparative success of different embedding criteria. The assessment also includes measures of robustness to noise. The limitations of this study are explicitly delineated. While bearing these limitations in mind, we conclude that for the examples considered here, the best identification of the embedding dimension was achieved with a global false nearest neighbors argument, and the best value of lag was identified by the mutual information function

Semiclassical Analysis of a Detuned Ring Laser with a Saturable Absorber: New Results for the Steady States

This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately