Solving the Optimal Mistuning Problem by Symmetry: A General Framework for Extending Flutter Boundaries in Turbomachines via Mistuning

A general framework is presented for analyzing and optimizing stability increases due to mistuning. The framework given is model independent and is based primarily on symmetry arguments. Difficult practical issues are transformed to tractable mathematical questions. It is shown that mistuning analysis reduces to a block circular matrix eigenvalue/vector problem which can be solved efficiently even for large problems. Similarly, the optimization becomes a standard linear constraint quadratic programming problem and can be solved numerically. Since the methods given are model independent, they can be applied to various models and allow the researcher to easily conclude which models accurately capture mistuning, and which do not. A simple quasi-steady model for flutter in a cascade is used to illustrate and validate results in this paper

Continuation of low altitude satellite interaction problem investigation Final report

Continuation of low-altitude satellite interaction problem study using Monte Carlo metho

Higgs-mass predictions

A compilation of Higgs-mass predictions is proposedComment: This is the last version. Only addition: today's update by Kahana & Kahan

Adaptive computation of gravitational waves from black hole interactions

We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$ modes simultaneously, allowing the study of wave perturbations of black holes with arbitrary 3D structure, as would be present when studying the full set of nonlinear Einstein equations describing a perturbed black hole. This class of equations forms an excellent testbed to explore the computational issues of simulating black spacetimes using a three dimensional adaptive mesh refinement code. Using this code, we present results from the first fully resolved 3D solution of the equations describing perturbed black holes. We discuss both fixed and adaptive mesh refinement, refinement criteria, and the computational savings provided by adaptive techniques in 3D for such model problems of distorted black holes.Comment: 16 Pages, RevTeX, 13 figure

Automatic techniques for detecting and exploiting symmetry in model checking

The application of model checking is limited due to the state-space explosion problem – as the number of components represented by a model increase, the worst case size of the associated state-space grows exponentially. Current techniques can handle limited kinds of symmetry, e.g. full symmetry between identical components in a concurrent system. They avoid the problem of automatic symmetry detection by requiring the user to specify the presence of symmetry in a model (explicitly, or by annotating the associated specification using additional language keywords), or by restricting the input language of a model checker so that only symmetric systems can be specified. Additionally, computing unique representatives for each symmetric equivalence class is easy for these limited kinds of symmetry. We present a theoretical framework for symmetry reduction which can be applied to explicit state model checking. The framework includes techniques for automatic symmetry detection using computational group theory, which can be applied with no additional user input. These techniques detect structural symmetries induced by the topology of a concurrent system, so our framework includes exact and approximate techniques to efficiently exploit arbitrary symmetry groups which may arise in this way. These techniques are also based on computational group theoretic methods. We prove that our framework is logically sound, and demonstrate its general applicability to explicit state model checking. By providing a new symmetry reduction package for the SPIN model checker, we show that our framework can be feasibly implemented as part of a system which is widely used in both industry and academia. Through a study of SPIN users, we assess the usability of our automatic symmetry detection techniques in practice