Developed from an advanced course on mathematical physics at the University of Pavia, considers the equilibrium of liquid crystals strictly from a mathematical perspective, but in the style of modern continuum mechanics to provide insights into topics traditionally treated by physics and chemistry. Explains two variational theories, the classical one by Zocher, Oseen, and Frank; and a new mathematical formulation by Ericksen. Uses the methods of variational calculus. Annotation copyright Book News, Inc. Portland, Or.
The programme of this book was projected in a survey written by J.L. Ericksen for SIAM News (see issue No. 4, November 1987). After a sentence inoculating the reader with the germs of hope: Clearly, [ liquid crystals] are [ materials] of growing importance from a technological point of view, and their development entails a healthy interaction between science and technology, Ericksen remarks that applied mathematicians should heed: To a large extent, the research has been done by non-mathemati cians. Frank Leslie, a mathematician who is weB known to workers in the field for his important contributions, is a notable exception. However, from a mathematical viewpoint, develop ment has been slow, aIthough the situation is beginning to change. This faint vein of optimism was justified by the outcomes of the pro gramme presented by J.L. Ericksen himself and D. Kinderlehrer as part of the activities during the academic year 1984-85 at the Institute for Mathematics and its Applications at Minneapolis. As Ericksen says, expert analysts were Ethen] introduced to and became fascinated with some of the [ unsolved] issues. They have already proved deep and beautiful results with interesting physical implications. In particular, we are now seeing the rapid development of a mathematicaBy sound, nonlinear static theory of defects, some thing that does not exist for any other kind of material.
Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.
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