Photonic band structure of highly deformable, self-assembling systems

We calculate the photonic band structure at normal incidence of highly deformable, self-assembling systems - cholesteric elastomers subjected to external stress. Cholesterics display brilliant reflection and lasing owing to gaps in their photonic band structure. The band structure of cholesteric elastomers varies sensitively with strain, showing new gaps opening up and shifting in frequency. A novel prediction of a total band gap is made, and is expected to occur in the vicinity of the previously observed de Vries bandgap, which is only for one polarisation

Termination Of Newton/Chord Iterations And The Method Of Lines

. Many ordinary differential equation and differential algebraic equation codes terminate the nonlinear iteration for the corrector equation when the difference between successive iterates (the step) is sufficiently small. This termination criterion avoids the expense of evaluating the nonlinear residual at the final iterate. Similarly, Jacobian information is not usually computed at every time step, but only when certain tests indicate that the cost of a new Jacobian is justified by the improved performance in the nonlinear iteration. In this paper, we show how an out-of-date Jacobian coupled with moderate ill-conditioning can lead to premature termination of the corrector iteration and suggest ways in which this situation can be detected and remedied. As an example, we consider the method of lines solution of Richards' equation, which models flow through variably-saturated porous media. When the solution to this problem has a sharp moving front, and the Jacobian is even slightly ill-..