197 research outputs found
The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
We give a direct calculation of the curvature of the Hitchin connection, in
geometric quantization on a symplectic manifold, using only differential
geometric techniques. In particular, we establish that the curvature acts as a
first-order operator on the quantum spaces. Projective flatness follows if the
K\"ahler structures do not admit holomorphic vector fields. Following Witten,
we define a complex variant of the Hitchin connection on the bundle of
prequantum spaces. The curvature is essentially unchanged, so projective
flatness holds in the same cases. Finally, the results are applied to quantum
Chern-Simons theory, both for compact and complex gauge groups
Using Enhanced Frequency Domain Decomposition as a Robust Technique to Harmonic Excitation in Operational Modal Analysis
Eliminating the Influence of Harmonic Components in Operational Modal Analysis
Operational modal analysis is used for determining the modal parameters of structures for which the input forces cannot be measured. However, the algorithms used assume that the input forces are stochastic in nature. While this is often the case for civil engineering structures, mechanical structures, in contrast, are subject inherently to deterministic forces due to the rotating parts in the machinery. These forces are seen as harmonic components in the responses, and their influence should be eliminated before extracting the modes in their vicinity. This paper describes a new method based on the well-known Enhanced Frequency Domain Decomposition (EFDD) technique for eliminating these harmonic components in the modal parameter extraction process. For assessing the quality of the method, various experiments were carried out where the results were compared with those obtained with pure stochastic excitation of the same structure. Good agreement was found and the method is shown to be an easy and robust tool for enhancing the EFDD technique for mechanical structures
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