Abstract By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from full symmetry group underlying lattice. This follows Ericksen’s suggestion which aimed at extending Landau-type theories to encompass behavior crystals undergoing structural phase transformation, with twinning, microstructure ...

In this paper, a new first-order, sphere-constraint-preserving numerical scheme is constructed for the Ericksen-Leslie equations with variable density. Firstly, by denoting orientation field vector $ \pmb{d} in polar coordinate, we rewrite system into an equivalent such that sphere constraint \lvert \pmb{d}\rvert = 1 can be still preserved at discrete level. Secondly, propose first-order discre...