ICM-200305-0006 Order reconstruction in frustrated nematic twist cells Fulvio Bisi, 1, ∗ Eugene C. Gartland, Jr., 2 Riccardo Rosso, 1 and Epifanio G. Virga 1 1 Dipartimento di Matematica, Istituto Nazionale di Fisica della Materia, Universit` a di Pavia, via Ferrata 1, 27100 Pavia, Italy 2 Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA (Dated: May 20, 2003) Abstract Within the Landau-de Gennes theory of liquid crystals, we study the equilibrium configurations of a nematic cell with twist boundary conditions. Under the assumption that the order tensor Q be uniaxial on both bounding plates, we find three separate classes of solutions, one of which contains the absolute energy minimizer, a twist -like solution that exists for all values of the distance d between the plates. The solutions in the remaining two classes exist only if d exceeds a critical value d c . One class consists of metastable, twist-like solutions, while the other consists of unstable, exchange -like solutions, where the eigenvalues of Q are exchanged across the cell. When d = d c , the metastable solution relaxes back to the absolute energy minimizer, undergoing an order reconstruction somewhere within the cell. The critical distance d c equals in general a few biaxial coherence lengths. This scenario applies to all values of the boundary twist but π 2 , which thus appears as a very special case, though it is the one more studied in the literature. In fact, when the directors prescribed on the two plates are at right angles, two symmetric twist-like solutions merge continuously into an exchange-like solution at the critical value of d where the latter becomes unstable. Our analysis shows how the classical bifurcation associated with this phenomenon is unfolded by perturbing the boundary conditions. PACS numbers: 61.30.Gd, 61.30.Pq * Electronic address: bisi@dimat.unipv.it; URL: http://smmm.unipv.it Typeset by REVT E X 1