Stability estimates for a twisted rod under terminal loads: a three-dimensional study

The stability of an inextensible unshearable elastic rod with quadratic strain energy density subject to end loads is considered. A self-contained proof in terms of local energy minimizers is presented and optimal bounds are obtained for the problem

The dynamics of bistable liquid crystal wells

A planar bistable liquid crystal device, reported in Tsakonas et al. [27], is modelled within the Landau-de Gennes theory for nematic liquid crystals. This planar device consists of an array of square micron-sized wells. We obtain six different classes of equilibrium profiles and these profiles are classified as diagonal or rotated solutions. In the strong anchoring case, we propose a Dirichlet boundary condition that mimics the experimentally imposed tangent boundary conditions. In the weak anchoring case, we present a suitable surface energy and study the multiplicity of solutions as a function of the anchoring strength. We find that diagonal solutions exist for all values of the anchoring strength W ≥ 0 while rotated solutions only exist for W ≥ Wc > 0, where Wc is a critical anchoring strength that has been computed numerically. We propose a dynamic model for the switching mechanisms based on only dielectric effects. For sufficiently strong external electric fields, we numerically demonstrate diagonal to rotated and rotated to diagonal switching by allowing for variable anchoring strength across the domain boundary

Singular Effect of Disorder on Electronic Transport in Strong Coupling Electron-Phonon Systems

We solve the disordered Holstein model in three dimensions considering the phonon variables to be classical. After mapping out the phases of the `clean' strong coupling problem, we focus on the effect of disorder at strong electron-phonon (EP) coupling. The presence of even weak disorder (i) enormously enhances the resistivity (\rho) at T=0, simultaneously suppressing the density of states at the Fermi level, (ii) suppresses the temperature dependent increase of \rho, and (iii) leads to a regime with d\rho/dT <0. We locate the origin of these anomalies in the disorder induced tendency towards polaron formation, and the associated suppression in effective carrier density and mobility. These results, explicitly at `metallic' density, are of direct relevance to disordered EP materials like covalent semiconductors, the manganites, and to anomalous transport in the A-15 compounds.Comment: Final versio

Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence

We study analytically the statistics of multiple sign changes in a discrete non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's are independent and identically distributed random variables each drawn from a symmetric and continuous distribution \rho(\phi). We show that the probability P_m(n) of m sign changes upto n steps is universal, i.e., independent of the distribution \rho(\phi). The mean and variance of the number of sign changes are computed exactly for all n>0. We show that the generating function {\tilde P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le p\le 1. We also show that in the natural scaling limit when m is large, n is large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large deviation function \Phi(x) is computed. The implications of these results for Ising spin glasses are discussed.Comment: 4 pages revtex, 1 eps figur

Universality and Scaling Behaviour of Injected Power in Elastic Turbulence in Worm-like Micellar Gel

We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a worm-like micellar gel formed by surfactant CTAT. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (pdf) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdfs can be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.Comment: 8 pages, 3 figure