Numerical Approximation of Liquid Crystal Flows

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9973285Technical Description:This project centers around the construction and analysis of algorithms for the simulation of the motion of nematic liquid crystals. Such algorithms will facilitate simulation of the manufacture and operation of devices (such as computer displays) built from liquid crystals. Equations characterizing the motion of liquid crystals were proposed by Ericksen and Leslie in the 1960's; however, until recently there were very few general results concerning the existence, uniqueness, and stability of these equations. Recent discoveries by F. Lin and C. Liu of new energy estimates enables many of these fundamental questions to be answered, which, in turn, facilitates the development and analysis of algorithms for the approximation of these equations. Preliminary results by the author, in collaboration with C. Liu, for a specific instance of the Ericksen--Leslie equations have been very promising, and this proposal outlines a program of research that will result in robust and reliable codes for the simulation of these equations in their full generality.Non-Technical Description:Over the past half century computers have stimulated a major change in the design and manufacture of virtually every industrial product produced in the U.S. Computer simulation of product strength, operation, and performance has replaced much of the expensive prototyping and testing phase required before any product is brought to market. In order to further reduce design and development costs better computer algorithms are required for each step of the manufacturing process, ranging from the simulation of advanced materials to the operation of complex systems. This project plans to draw upon recent theoretical breakthroughs to predict the behavior of materials like those found in modern liquid crystal computer displays. These materials exhibit many complex phenomena, and simulation and prediction of their properties requires modern high performance computers.