Transient temperature rises in a sandwich-structured composite induced by a dithering or rotating laser beam

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Zhou, Hong
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rotating or dithering Gaussian laser beam
non-homogeneous heat equation
composite sandwich structure
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2012
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Abstract
We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b∗ (6.7314863965), the only equilibrium state is isotropic and it is stable; when b∗ 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state.
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IOSR Journal of Engineering (IOSRJEN), Vol.2 Issue 2, pages 234-246, 2012
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https://hdl.handle.net/10945/40945
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Transient temperature rises in a sandwich-structured composite induced by a dithering or rotating laser beam, IOSR Journal of Engineering (IOSRJEN), Vol.2 Issue 2, pages 234-246, 2012
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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