Setting the quantum integrand of M-theory

In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-theory the E(8)-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions. In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction of heterotic M-theory on cylinders.Comment: 52 pages; revised version for publication in Commun. Math. Phys. corrects a few typo

Stereology of random lines through idealised composite particles of variable texture

Imperial Users onl

Quantization of anomaly coefficients in 6D N=(1,0)\mathcal{N}=(1,0) supergravity

We obtain new constraints on the anomaly coefficients of 6D $\mathcal{N}=(1,0)$ supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group $G$ should be an element of $2 H^4(BG;\mathbb{Z}) \otimes \Lambda_S$ where $\Lambda_S$ is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.Comment: 42 pages. v3: Some clarifications, typos correcte

A force balance system for the measurement of skin friction drag force in the presence of large vibrations and temperatures

Design of counterbalance system for skin friction drag measurements on hypersonic vehicle

Investigation of Systems and Techniques for Multicomponent Microforce Measurements on Wind Tunnel Models Semiannual Status Report, 15 Jul. 1965 - 15 Jan. 1966

Skin friction drag sensor and multicomponent microforce wind tunnel balance syste

Exploring constrained quantum control landscapes

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected `level sets' of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.Comment: 10 figure

Space station structures and dynamics test program

The design, construction, and operation of a low-Earth orbit space station poses unique challenges for development and implementation of new technology. The technology arises from the special requirement that the station be built and constructed to function in a weightless environment, where static loads are minimal and secondary to system dynamics and control problems. One specific challenge confronting NASA is the development of a dynamics test program for: (1) defining space station design requirements, and (2) identifying the characterizing phenomena affecting the station's design and development. A general definition of the space station dynamic test program, as proposed by MSFC, forms the subject of this report. The test proposal is a comprehensive structural dynamics program to be launched in support of the space station. The test program will help to define the key issues and/or problems inherent to large space structure analysis, design, and testing. Development of a parametric data base and verification of the math models and analytical analysis tools necessary for engineering support of the station's design, construction, and operation provide the impetus for the dynamics test program. The philosophy is to integrate dynamics into the design phase through extensive ground testing and analytical ground simulations of generic systems, prototype elements, and subassemblies. On-orbit testing of the station will also be used to define its capability

Institutional development work in the World Bank : a review of 84 bank projects

Institutional weakness is a critical constraint to economic development. The goal of this paper is to review the design of recent Bank projects to assess the quality of their institutional development (ID) components and the factors that may affect that quality. A major focus is Bank staffing and organization, and the following issues are addressed: (a) the quality of institutional analysis and ID components in the design of current Bank project; (b) the ID work that is being done in Bank projects; (c) qualifications needed for effective ID work; (d) the impact the Bank's organizational structure has on ID work; and (e) suggestions that can be made to broaden and strengthen the ID work in Bank projects.Banks&Banking Reform,Health Monitoring&Evaluation,Health Economics&Finance,Municipal Financial Management,Rural Portfolio Improvement

Evaluation of coatings for cobalt- and nickel-base superalloys, volume 2

The final results of an oxidation-reduction rig evaluation of aluminide coatings are presented, as applied to 1N-100 and B1900 nickel-base and X-10 and WI-52 cobalt-base alloys. Burner rigs were used which operated on JP-5 fuel and air, producing a gas velocity of 0.85 (2000 to 2500 ft/sec) at the specimen's leading edge. One-hour heating cycles were used with three minutes of air blast cooling. Results of testing at temperatures ranging from T sub max of 1850 to 2050 F indicate that coated B1900 has the longest oxidation life at all temperatures, followed by IN-100X-40WI-52, based on a weight change criterion. Coatings on nickel-base alloys provided more than twice the life of coating on cobalt-base alloys at comparable temperatures. The coatings with higher aluminum content and comparable thickness had longer lives. Silicon appeared to be a beneficial additive in the nickel-base alloy coatings for long term, low temperature life, but not for short term, high temperature performance. Chromium was identified in all coatings. Extrapolating the life results obtained to 1600 F, all the selected coatings on the four alloys would be protective for at least 10,000 hours