Optimal and efficient crossover designs for comparing test treatments with a control treatment

This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a crossover design to be simultaneously A-optimal and MV-optimal in a very large and appealing class of crossover designs. It is expected that these optimal designs are highly efficient in the entire class of crossover designs. Some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs. The model robustness of these newly discovered crossover designs is discussed.Comment: Published at http://dx.doi.org/10.1214/009053604000000887 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Locally D-optimal designs based on a class of composed models resulted from blending Emax and one-compartment models

A class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. The locally D-optimal (LD) design for a four-parameter composed model is found to be a saturated four-point uniform LD design with the two boundary points of the design space in the LD design support. For a five-parameter composed model, a sufficient condition for the LD design to require the minimum number of sampling time points is derived. Robust LD designs are also investigated for both models. It is found that an LD design with $k$ parameters is equivalent to an LD design with $k-1$ parameters if the linear parameter in the two composed models is a nuisance parameter. Assorted examples of LD designs are presented.Comment: Published in at http://dx.doi.org/10.1214/009053607000000776 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays

The task of decoupling, i.e., removing unwanted interactions in a system Hamiltonian and/or couplings with an environment (decoherence), plays an important role in controlling quantum systems. There are many efficient decoupling schemes based on combinatorial concepts like orthogonal arrays, difference schemes and Hadamard matrices. So far these (combinatorial) decoupling schemes have relied on the ability to effect sequences of instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To overcome the shortcomings of bang-bang control Viola and Knill proposed a method called Eulerian decoupling that allows the use of bounded-strength controls for decoupling. However, their method was not directly designed to take advantage of the composite structure of multipartite quantum systems. In this paper we define a combinatorial structure called an Eulerian orthogonal array. It merges the desirable properties of orthogonal arrays and Eulerian cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show that this structure gives rise to decoupling schemes with bounded-strength control Hamiltonians that can be applied to composite quantum systems with few body Hamiltonians and special couplings with the environment. Furthermore, we show how to construct Eulerian orthogonal arrays having good parameters in order to obtain efficient decoupling schemes.Comment: 8 pages, revte

Controlling quantum systems by embedded dynamical decoupling schemes

A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired perturbations of quantum systems significantly even for long interaction times. As a first application the stabilization of a quantum memory is discussed which is perturbed by one-and two-qubit interactions

Thermodynamic Vent System Performance Testing with Subcooled Liquid Methane and Gaseous Helium Pressurant

Due to its high specific impulse and favorable thermal properties for storage, liquid methane (LCH4) is being considered as a candidate propellant for exploration architectures. In order to gain an -understanding of any unique considerations involving micro-gravity pressure control with LCH4, testing was conducted at the Marshall Space Flight Center using the Multipurpose Hydrogen Test Bed (MHTB) to evaluate the performance of a spray-bar thermodynamic vent system (TVS) with subcooled LCH4 and gaseous helium (GHe) pressurant. Thirteen days of testing were performed in November 2006, with total tank heat leak conditions of about 715 W and 420 W at a fill level of approximately 90%. The TVS system was used to subcool the LCH4 to a liquid saturation pressure of approximately 55.2 kPa before the tank was pressurized with GHe to a total pressure of 165.5 kPa. A total of 23 TVS cycles were completed. The TVS successfully controlled the ullage pressure within a prescribed control band but did not maintain a stable liquid saturation pressure. This was likely. due to a TVS design not optimized for this particular propellant and test conditions, and possibly due to a large artificially induced heat input directly into the liquid. The capability to reduce liquid saturation pressure as well as maintain it within a prescribed control band, demonstrated that the TVS could be used to seek and maintain a desired liquid inlet temperature for an engine (at a cost of propellant lost through the TVS vent). One special test was conducted at the conclusion of the planned test activities. Reduction of the tank ullage pressure by opening the Joule-Thomson valve (JT) without operating the pump was attempted. The JT remained open for over 9300 seconds, resulting in an ullage pressure reduction of 30 kPa. The special test demonstrated the feasibility of using the JT valve for limited ullage pressure reduction in the event of a pump failure

Liquid Nitrogen (Oxygen Simulant) Thermodynamic Vent System Test Data Analysis

In designing systems for the long-term storage of cryogens in low-gravity (space) environments, one must consider the effects of thermal stratification on tank pressure that will occur due to environmental heat leaks. During low-gravity operations, a Thermodynamic Vent System (TVS) concept is expected to maintain tank pressure without propellant resettling. A series of TVS tests was conducted at NASA Marshall Space Flight Center (MSFC) using liquid nitrogen (LN2) as a liquid oxygen (LO2) simulant. The tests were performed at tank til1 levels of 90%, 50%, and 25%, and with a specified tank pressure control band. A transient one-dimensional TVS performance program is used to analyze and correlate the test data for all three fill levels. Predictions and comparisons of ullage pressure and temperature and bulk liquid saturation pressure and temperature with test data are presented

TankSIM: A Cryogenic Tank Performance Prediction Program

Accurate prediction of the thermodynamic state of the cryogenic propellants in launch vehicle tanks is necessary for mission planning and successful execution. Cryogenic propellant storage and transfer in space environments requires that tank pressure be controlled. The pressure rise rate is determined by the complex interaction of external heat leak, fluid temperature stratification, and interfacial heat and mass transfer. If the required storage duration of a space mission is longer than the period in which the tank pressure reaches its allowable maximum, an appropriate pressure control method must be applied. Therefore, predictions of the pressurization rate and performance of pressure control techniques in cryogenic tanks are required for development of cryogenic fluid long-duration storage technology and planning of future space exploration missions. This paper describes an analytical tool, Tank System Integrated Model (TankSIM), which can be used for modeling pressure control and predicting the behavior of cryogenic propellant for long-term storage for future space missions. It is written in the FORTRAN 90 language and can be compiled with any Visual FORTRAN compiler. A thermodynamic vent system (TVS) is used to achieve tank pressure control. Utilizing TankSIM, the following processes can be modeled: tank self-pressurization, boiloff, ullage venting, and mixing. Details of the TankSIM program and comparisons of its predictions with test data for liquid hydrogen and liquid methane will be presented in the final paper