Influence of supercoiling on the disruption of dsDNA

We propose that supercoiling energizes double-stranded DNA (dsDNA) so as to facilitate thermal fluctuations to an unzipped state. We support this with a model of two elastic rods coupled via forces that represent base pair interactions. Supercoiling is shown to lead to a spatially localized higher energy state in a small region of dsDNA consisting of a few base pairs. This causes the distance between specific base pairs to be extended, enhancing the thermal probability for their disruption. Our theory permits the development of an analogy between this unzipping transition and a second order phase transition, for which the possibility of a new set of critical exponents is identified

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation

In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirable properties and is such inferior from a physical point of view. Various applications of the SA-decomposition are discussed: the Cauchy relations (vanishing of A), the non-existence of elastic null Lagrangians, the decomposition of the elastic energy and of the acoustic wave propagation. The acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The Cauchy part governs the longitudinal wave propagation. We provide explicit examples of the effectiveness of the SA-decomposition. A complete class of anisotropic media is proposed that allows pure polarizations in arbitrary directions, similarly as in an isotropic medium.Comment: 1 figur

Untwisting of a Strained Cholesteric Elastomer by Disclination Loop Nucleation

The application of a sufficiently strong strain perpendicular to the pitch axis of a monodomain cholesteric elastomer unwinds the cholesteric helix. Previous theoretical analyses of this transition ignored the effects of Frank elasticity which we include here. We find that the strain needed to unwind the helix is reduced because of the Frank penalty and the cholesteric state becomes metastable above the transition. We consider in detail a previously proposed mechanism by which the topologically stable helical texture is removed in the metastable state, namely by the nucleation of twist disclination loops in the plane perpendicular to the pitch axis. We present an approximate calculation of the barrier energy for this nucleation process which neglects possible spatial variation of the strain fields in the elastomer, as well as a more accurate calculation based on a finite element modeling of the elastomer.Comment: 12 pages, 9 figure

A gauge theoretic approach to elasticity with microrotations

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page; revised and extended versio

On the strain-energy density in linear elasticity

Standard results from matrix theory are used to derive optimal upper and lower bounds for the strain-energy density in terms of the norm of the stress tensor in two and three dimensions. The approach also yields directly necessary and sufficient conditions for positive-definiteness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42704/1/10665_2005_Article_BF01535284.pd

Performance of CUF approach to analyze the structural behavior of slender bodies

This paper deals with the accurate evaluation of complete three-dimensional (3D) stress fields in beam structures with compact and bridge-like sections. A refined beam finite-element (FE) formulation is employed, which permits any-order expansions for the three displacement components over the section domain by means of the Carrera Unified Formulation (CUF). Classical (Euler-Bernoulli and Timoshenko) beam theories are considered as particular cases. Comparisons with 3D solid FE analyses are provided. End effects caused by the boundary conditions are investigated. Bending and torsional loadings are considered. The proposed formulation has shown its capability of leading to quasi-3D stress fields over the beam domain. Higher-order beam theories are necessary for the case of bridge-like sections. Various theories are also compared in terms of shear correction factors on the basis of definitions found in the open literature. It has been confirmed that different theories could lead to very different values of shear correction factors, the accuracy of which is subordinate to a great extent to the section geometries and loading conditions. However, an accurate evaluation of shear correction factors is obtained by means of the present higher-order theories

Relativistic nature of a magnetoelectric modulus of Cr_2O_3-crystals: a new 4-dimensional pseudoscalar and its measurement

Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we extract a 4-dimensional relativistic invariant pseudoscalar $\widetilde{\alpha}$. It is temperature dependent and of the order of 10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, $\widetilde{\alpha}$ is for Cr_2O_3 what Tellegen's gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.Comment: Revtex, 36 pages, 9 figures (submitted in low resolution, better quality figures are available from the authors