Weak Energy: Form and Function

The equation of motion for a time-independent weak value of a quantum mechanical observable contains a complex valued energy factor - the weak energy of evolution. This quantity is defined by the dynamics of the pre-selected and post-selected states which specify the observable's weak value. It is shown that this energy: (i) is manifested as dynamical and geometric phases that govern the evolution of the weak value during the measurement process; (ii) satisfies the Euler-Lagrange equations when expressed in terms of Pancharatnam (P) phase and Fubini-Study (FS) metric distance; (iii) provides for a PFS stationary action principle for quantum state evolution; (iv) time translates correlation amplitudes; (v) generalizes the temporal persistence of state normalization; and (vi) obeys a time-energy uncertainty relation. A similar complex valued quantity - the pointed weak energy of an evolving state - is also defined and several of its properties in PFS-coordinates are discussed. It is shown that the imaginary part of the pointed weak energy governs the state's survival probability and its real part is - to within a sign - the Mukunda-Simon geometric phase for arbitrary evolutions or the Aharonov-Anandan (AA) phase for cyclic evolutions. Pointed weak energy gauge transformations and the PFS 1-form are discussed and the relationship between the PFS 1-form and the AA connection 1-form is established.Comment: To appear in "Quantum Theory: A Two-Time Success Story"; Yakir Aharonov Festschrif

Insight into High-quality Aerodynamic Design Spaces through Multi-objective Optimization

An approach to support the computational aerodynamic design process is presented and demonstrated through the application of a novel multi-objective variant of the Tabu Search optimization algorithm for continuous problems to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and ultimately of the whole engine. The integrated system developed for this purpose is described. This combines the optimizer with an existing geometry parameterization scheme and a well- established CFD package. The system’s performance is illustrated through case studies – one two-dimensional, one three-dimensional – in which flow characteristics important to the overall performance of turbomachinery blades are optimized. By showing the designer the trade-off surfaces between the competing objectives, this approach provides considerable insight into the design space under consideration and presents the designer with a range of different Pareto-optimal designs for further consideration. Special emphasis is given to the dimensionality in objective function space of the optimization problem, which seeks designs that perform well for a range of flow performance metrics. The resulting compressor blades achieve their high performance by exploiting complicated physical mechanisms successfully identified through the design process. The system can readily be run on parallel computers, substantially reducing wall-clock run times – a significant benefit when tackling computationally demanding design problems. Overall optimal performance is offered by compromise designs on the Pareto trade-off surface revealed through a true multi-objective design optimization test case. Bearing in mind the continuing rapid advances in computing power and the benefits discussed, this approach brings the adoption of such techniques in real-world engineering design practice a ste

Additional application of the NASCAP code. Volume 1: NASCAP extension

The NASCAP computer program comprehensively analyzes problems of spacecraft charging. Using a fully three dimensional approach, it can accurately predict spacecraft potentials under a variety of conditions. Several changes were made to NASCAP, and a new code, NASCAP/LEO, was developed. In addition, detailed studies of several spacecraft-environmental interactions and of the SCATHA spacecraft were performed. The NASCAP/LEO program handles situations of relatively short Debye length encountered by large space structures or by any satellite in low earth orbit (LEO)

Analysis of the charging of the SCATHA (P78-2) satellite

The charging of a large object in polar Earth orbit was investigated in order to obtain a preliminary indication of the response of the shuttle orbiter to such an environment. Two NASCAP (NASA Charging Analyzer Program) models of SCATHA (Satellite Charging at High Altitudes) were used in simulations of charging events. The properties of the satellite's constituent materials were compiled and representations of the experimentally observed plasma spectra were constructed. Actual charging events, as well as those using test environments, were simulated. Numerical models for the simulation of particle emitters and detectors were used to analyze the operation of these devices onboard SCATHA. The effect of highly charged surface regions on the charging conductivity within a photosheath was used to interpret results from the onboard electric field experiment. Shadowing calculations were carried out for the satellite and a table of effective illuminated areas was compiled

Additional application of the NASCAP code. Volume 2: SEPS, ion thruster neutralization and electrostatic antenna model

The interactions of spacecraft systems with the surrounding plasma environment were studied analytically for three cases of current interest: calculating the impact of spacecraft generated plasmas on the main power system of a baseline solar electric propulsion stage (SEPS), modeling the physics of the neutralization of an ion thruster beam by a plasma bridge, and examining the physical and electrical effects of orbital ambient plasmas on the operation of an electrostatically controlled membrane mirror. In order to perform these studies, the NASA charging analyzer program (NASCAP) was used as well as several other computer models and analytical estimates. The main result of the SEPS study was to show how charge exchange ion expansion can create a conducting channel between the thrusters and the solar arrays. A fluid-like model was able to predict plasma potentials and temperatures measured near the main beam of an ion thruster and in the vicinity of a hollow cathode neutralizer. Power losses due to plasma currents were shown to be substantial for several proposed electrostatic antenna designs

Robust design optimisation of gas turbine compression systems

Engineering design commonly assumes nominal values for uncertain parameters to simplify the design process: the design of a gas turbine, or one of its modules, is generally approached with some specific operating conditions in mind (its design point). Unfortunately, engine components never exactly meet their specifications and do not operate at just one condition, but over a range of power settings. This simplification can then lead to a product that exhibits performance significantly worse than nominal in real-world conditions. This problem is exacerbated in the presence of heavily optimised designs, which tend to lie in extreme regions of the design space.15 In gas turbine design, safe and satisfactory off-design operation must be guaranteed and is generally evaluated before moving to the next phase of the design process. This approach, while guaranteeing that some minimum requirements are met, introduces a further loop in the design process and does not ensure the final design will be optimal with respect to this new requirement. The introduction of some robustness considerations into the design process can reduce the level of fragmentation and iteration typical of gas turbine engine design and produce further (and more robust) improvements relative to the traditional method. In this study, two approaches for dealing with off-design performance analysis are presented, integrated into an automatic optimisation system and applied to the preliminary design of a core compression system from a three-spool modern turbofan engine. Designs that are more robust than those found if only design-point performance is considered are successfully identified

Multi-Objective Optimisation of Aero-Engine Compressors

The design of a new aero-engine compressor is a complex task: design objectives are almost always conflicting, the design space is large, nonlinear and highly constrained, and the effects of some geometrical changes can be difficult to predict. Computational fluid dynamics (CFD) is now widely used in real-world applications and especially in the design of turbomachinery. However, the large design space and the time required for the numerical simulation of the whole turbomachine make the use of CFD in the early phases of the design process infeasible: preliminary design relies on a number of physical and empirical relations, still quite similar to those used in the early history of turbomachinery design. In this study, 87 independent parameters were used to define the geometry of a 7-stage compressor, the performance of which was evaluated using proprietary design codes for mean-line, multi-stage analysis. The effects on efficiency and surge margin of changing 44 design variables were analysed and their optimal values found by means of deterministic (gradient-based) and meta-heuristic (Tabu Search [TS]) optimisation methods. The results show clearly how the use of meta-heuristic optimisation tools can improve the preliminary design of turbomachinery, allowing a more thorough but still rapid exploration of the design space to identify the most promising regions that will then be verified and further analysed with higher fidelity tools. The results also reveal the impact of introducing various constraints into the design process, highlighting the effects of design decomposition

Induced polarization at a paraelectric/superconducting interface

We examine the modified electronic states at the interface between superconducting and ferro(para)-electric heterostructures. We find that electric polarization $P$ and superconducting $\psi$ order parameters can be significantly modified due to coupling through linear terms brought about by explicit symmetry breaking at the interface. Using an effective action and a Ginzburg-Landau formalism, we show that an interaction term linear in the electric polarization will modify the superconducting order parameter $\psi$ at the interface. This also produces modulation of a ferroelectric polarization. It is shown that a paraelectric-superconductor interaction will produce an interface-induced ferroelectric polarization.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.