Deckelnick and Dziuk (2009) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of Willmore flow/elastic flow of closed curves in R, d ≥ 2. We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in Barrett, Garcke, and Nürnberg (2007b, 2008b, 2010b)...

Underlying the nuclear envelope (NE) of most eukaryotic cells is the nuclear lamina, a meshwork consisting largely of coiled-coil nuclear intermediate filament proteins that play a critical role in nuclear organization and gene expression, and are vital for the structural stability of the NE/nucleus. By confocal microscopy and micromanipulation of the NE in living cells and isolated nuclei, we ...

We present an investigation of the phase diagram of cholesteric liquid crystals within the framework of Landau-de Gennes theory. The free energy is modified to incorporate all three Frank elastic constants and to allow for a temperature dependent pitch in the cholesteric phase. It is found that the region of stability of the cubic blue phases depends significantly on the value of the elastic co...

We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general k-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case k = 2. In this case we identify three types of radial profiles: with two, three of full five components an...

A critical analysis of the conditions elastic stability crystal structures different symmetry as restrictions imposed on their constants c ij has been carried out. It is shown that all crystals, except for cubic ones, are described by polynomials from second to sixth powers . Necessary and sufficient crystals presented explicitly. Keywords: Elastic stability, Symmetry, constants, Stability cond...