Time-dependent Schr\"odinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states

Using the transformations from paper I, we show that the Schr\"odinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is deomonstrated.Comment: LaTeX, 22 pages, new format, edited, with added discussion of the classical motio

Displacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras

In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schr\"odinger equation for systems with potentials $V(x,\tau)=g^{(2)}(\tau)x^2+g^{(1)}(\tau)x +g^{(0)}(\tau)$. We describe a set of number-operator eigenstates states, $\{\Psi_n(x,\tau)\}$, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, $\Psi_0$, and a displacement squeeze operator derived using the Lie symmetries, we construct squeezed states and compute expectation values for position and momentum as a function of time, $\tau$. We prove a general expression for the uncertainty relation for position and momentum in terms of the squeezing parameters. Specific examples, all corresponding to choices of $V(x,\tau)$ and having isomorphic Lie algebras, will be dealt with in the following paper (II).Comment: 23 pages, LaTe

Recent Results on "Approximations to Optimal Alarm Systems for Anomaly Detection"

An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario

An Investigation of State-Space Model Fidelity for SSME Data

In previous studies, a variety of unsupervised anomaly detection techniques for anomaly detection were applied to SSME (Space Shuttle Main Engine) data. The observed results indicated that the identification of certain anomalies were specific to the algorithmic method under consideration. This is the reason why one of the follow-on goals of these previous investigations was to build an architecture to support the best capabilities of all algorithms. We appeal to that goal here by investigating a cascade, serial architecture for the best performing and most suitable candidates from previous studies. As a precursor to a formal ROC (Receiver Operating Characteristic) curve analysis for validation of resulting anomaly detection algorithms, our primary focus here is to investigate the model fidelity as measured by variants of the AIC (Akaike Information Criterion) for state-space based models. We show that placing constraints on a state-space model during or after the training of the model introduces a modest level of suboptimality. Furthermore, we compare the fidelity of all candidate models including those embodying the cascade, serial architecture. We make recommendations on the most suitable candidates for application to subsequent anomaly detection studies as measured by AIC-based criteria

Multivariate Optimization of Neutron Detectors Through Modeling

Due to the eminent shortage of 3He, there exists a significant need to develop a new (or optimize an existing) neutron detection system which would reduce the dependency on the current 3He-based detectors for Domestic Nuclear Detection Office (DNDO) applications. The purpose of this research is to develop a novel methodology for optimizing candidate neutron detector designs using multivariate statistical analysis of Monte Carlo radiation transport code (MCNPX) models. The developed methodology allows the simultaneous optimization of multiple detector parameters with respect to multiple response parameters which measure the overall performance of a candidate neutron detector. This is achieved by applying three statistical strategies in a sequential manner (namely factorial design experiments, response surface methodology, and constrained multivariate optimization) to results generated from MCNPX calculations. Additionally, for organic scintillators, a methodology incorporating the light yield non-proportionality is developed for inclusion into the simulated pulse height spectra (PHS). A Matlab® program was developed to post-process the MCNPX standard and PTRAC output files to automate the process of generating the PHS thus allowing the inclusion of nonlinear light yield equations (Birks equations) into the simulation of the PHS for organic scintillators. The functionality of the developed methodology is demonstrated on the successful multivariate optimization of three neutron detection systems which utilize varied approaches to satisfying the DNDO criteria for an acceptable alternative neutron detector. The first neutron detection system optimized is a 3He-based radiation portal monitor (RPM) based on a generalized version of a currently deployed system. The second system optimized is a 6Li-loaded polymer composite scintillator in the form of a thin film. The final system optimized is a 10B-based plastic scintillator sandwiched between two standard plastic scintillators. Results from the multivariate optimization analysis include not only the identification of which factors significantly affect detector performance, but also the determination of optimum levels for those factors with simultaneous consideration of multiple detector performance responses. Based on the demonstrated functionality of the developed multivariate optimization methodology, application of the methodology in the development process of new candidate neutron detector designs is warranted

Transportable Modular Balance of Plant Study for Small Nuclear Power Plants

The purpose of this research is to develop a conceptual design for a balance of plant (BOP) layout to coordinate with small nuclear power plants and to demonstrate the feasibility of transporting this BOP via US waterways. The Westinghouse International Reactor, Innovative and Secure (IRIS) is used as the primary plant for the base-case study. IRIS is an advanced design pressurized water reactor (PWR) with a power rating of 1000MWt (approximately 335 MWe). A Matlab® script file, named BOSCO, automates the process of calculating the BOP component sizes for different initial conditions, enabling the use of different primary systems and/or initial conditions without difficulty. The results are used to create 3-D solid models of the components. These solid models are used to design a layout for a barge-mounted balance of plant. The feasibility of transporting the primary and the secondary systems via two separate barges traveling from the Gulf of Mexico to Chattanooga, TN has been analyzed. Limitations imposed by locks, dams, bridges, aerial power crossings, and river channel depths determine the maximum allowable barge dimensions. The final dimensions for both the reactor building and turbine-generator building barges are 30 meters wide, 100 meters long, with 2.74 meters draft. The reactor building barge displaces approximately 4992 metric tons, while the turbine-generator building barge displaces approximately 2195 metric tons. Figures containing visualizations of plant components layout and solid modeling have been developed and are presented. Further travel up the Tennessee River with a barge of these dimensions is currently restricted due to width limitations imposed by several locks and dams

Time-dependent Schr\"odinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations

In this paper, we focus on a general class of Schr\"odinger equations that are time-dependent and quadratic in X and P. We transform Schr\"odinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ``time'' variable. We derive mathematical constraints forthe transformation and introduce two examples.Comment: LaTeX, 18 pages, new format, edite

Texture Analysis Of Rice Cakes

Snack foods represent a dynamic segment of the food industry, as new products are continually being developed to satisfy changes in consumer trends. This highly competitive market features many products that have short life cycles, and a requirement for rapid development that puts pressure on aspects of the product development process such as shelf life studies, flavour profile development etc. Knowing a products limitations with respect to shelf life and storage is of critical importance before launching. In dry cereal foods, like rice cakes, breakfast cereals and extruded products, knowing the effects of storage on texture is of importance to ensure a high quality product reaches the consumer ..

Near Real-Time Optimal Prediction of Adverse Events in Aviation Data

The prediction of anomalies or adverse events is a challenging task, and there are a variety of methods which can be used to address the problem. In this paper, we demonstrate how to recast the anomaly prediction problem into a form whose solution is accessible as a level-crossing prediction problem. The level-crossing prediction problem has an elegant, optimal, yet untested solution under certain technical constraints, and only when the appropriate modeling assumptions are made. As such, we will thoroughly investigate the resilience of these modeling assumptions, and show how they affect final performance. Finally, the predictive capability of this method will be assessed by quantitative means, using both validation and test data containing anomalies or adverse events from real aviation data sets that have previously been identified as operationally significant by domain experts. It will be shown that the formulation proposed yields a lower false alarm rate on average than competing methods based on similarly advanced concepts, and a higher correct detection rate than a standard method based upon exceedances that is commonly used for prediction