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symmetries of E_omega which preserve the 2-plectic structure on M.Comment: These preliminary results have been superseded by those given in arXiv:1009.297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

Extending the granularity of representation and control for the MIL-STD CAIS 1.0 node model

The Common APSE (Ada 1 Program Support Environment) Interface Set (CAIS) (DoD85) node model provides an excellent baseline for interfaces in a single-host development environment. To encompass the entire spectrum of computing, however, the CAIS model should be extended in four areas. It should provide the interface between the engineering workstation and the host system throughout the entire lifecycle of the system. It should provide a basis for communication and integration functions needed by distributed host environments. It should provide common interfaces for communications mechanisms to and among target processors. It should provide facilities for integration, validation, and verification of test beds extending to distributed systems on geographically separate processors with heterogeneous instruction set architectures (ISAS). Additions to the PROCESS NODE model to extend the CAIS into these four areas are proposed