Courant algebroids from categorified symplectic geometry

In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed nondegenerate (n+1)-form. The case relevant to classical string theory is when n=2 and is called "2-plectic geometry". Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, there is a Lie 2-algebra of observables associated to any 2-plectic manifold. String theory, closed 3-forms and Lie 2-algebras also play important roles in the theory of Courant algebroids. Courant algebroids are vector bundles which generalize the structures found in tangent bundles and quadratic Lie algebras. It is known that a particular kind of Courant algebroid (called an exact Courant algebroid) naturally arises in string theory, and that such an algebroid is classified up to isomorphism by a closed 3-form on the base space, which then induces a Lie 2-algebra structure on the space of global sections. In this paper we begin to establish precise connections between 2-plectic manifolds and Courant algebroids. We prove that any manifold M equipped with a 2-plectic form omega gives an exact Courant algebroid E_omega over M with Severa class [omega], and we construct an embedding of the Lie 2-algebra of observables into the Lie 2-algebra of sections of E_omega. We then show that this embedding identifies the observables as particular infinitesimal symmetries of E_omega which preserve the 2-plectic structure on M.Comment: These preliminary results have been superseded by those given in arXiv:1009.297

The impact of fourth generation computers on NASTRAN

The impact of 'fourth generation' computers (STAR 100 or ILLIAC 4) on NASTRAN is considered. The desired characteristics of large programs designed for execution on 4G machines are described

The potential application of the blackboard model of problem solving to multidisciplinary design

The potential application of the blackboard model of problem solving to multidisciplinary design is discussed. Multidisciplinary design problems are complex, poorly structured, and lack a predetermined decision path from the initial starting point to the final solution. The final solution is achieved using data from different engineering disciplines. Ideally, for the final solution to be the optimum solution, there must be a significant amount of communication among the different disciplines plus intradisciplinary and interdisciplinary optimization. In reality, this is not what happens in today's sequential approach to multidisciplinary design. Therefore it is highly unlikely that the final solution is the true optimum solution from an interdisciplinary optimization standpoint. A multilevel decomposition approach is suggested as a technique to overcome the problems associated with the sequential approach, but no tool currently exists with which to fully implement this technique. A system based on the blackboard model of problem solving appears to be an ideal tool for implementing this technique because it offers an incremental problem solving approach that requires no a priori determined reasoning path. Thus it has the potential of finding a more optimum solution for the multidisciplinary design problems found in today's aerospace industries

DeMAID: A Design Manager's Aide for Intelligent Decomposition user's guide

A design problem is viewed as a complex system divisible into modules. Before the design of a complex system can begin, the couplings among modules and the presence of iterative loops is determined. This is important because the design manager must know how to group the modules into subsystems and how to assign subsystems to design teams so that changes in one subsystem will have predictable effects on other subsystems. Determining these subsystems is not an easy, straightforward process and often important couplings are overlooked. Moreover, the planning task must be repeated as new information become available or as the design specifications change. The purpose of this research is to develop a knowledge-based tool called the Design Manager's Aide for Intelligent Decomposition (DeMAID) to act as an intelligent advisor for the design manager. DeMaid identifies the subsystems of a complex design problem, orders them into a well-structured format, and marks the couplings among the subsystems to facilitate the use of multilevel tools. DeMAID also provides the design manager with the capability of examining the trade-offs between sequential and parallel processing. This type of approach could lead to a substantial savings or organizing and displaying a complex problem as a sequence of subsystems easily divisible among design teams. This report serves as a User's Guide for the program