Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

We derive an orthotropic model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data

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Transport properties of the metallic state of overdoped cuprate superconductors from an anisotropic marginal Fermi liquid model

We consider the implications of a phenomenological model self-energy for the charge transport properties of the metallic phase of the overdoped cuprate superconductors. The self-energy is the sum of two terms with characteristic dependencies on temperature, frequency, location on the Fermi surface, and doping. The first term is isotropic over the Fermi surface, independent of doping, and has the frequency and temperature dependence characteristic of a Fermi liquid. The second term is anisotropic over the Fermi surface (vanishing at the same points as the superconducting energy gap), strongly varies with doping (scaling roughly with $T_c$, the superconducting transition temperature), and has the frequency and temperature dependence characteristic of a marginal Fermi liquid. Previously it has been shown this self-energy can describe a range of experimental data including angle-dependent magnetoresistance (ADMR) and quasi-particle renormalisations determined from specific heat, quantum oscillations, and angle-resolved photo-emission spectroscopy (ARPES). Without introducing new parameters and neglecting vertex corrections we show that this model self-energy can give a quantitative description of the temperature and doping dependence of a range of reported transport properties of Tl2201 samples. These include the intra-layer resistivity, the frequency dependent optical conductivity, the intra-layer magnetoresistance, and the Hall coefficient. The temperature dependence of the latter two are particularly sensitive to the anisotropy of the scattering rate and to the shape of the Fermi surface. In contrast, the temperature dependence of the Hall angle is dominated by the Fermi liquid contribution to the self-energy that determines the scattering rate in the nodal regions of the Fermi surface.Comment: 17 pages, 16 figure

Skyrmions in the Moore-Read state at nu=5/2

We study charged excitations of the non-abelian Moore-Read liquid at filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of non-zero well widths, we find that at sufficiently low Zeeman energy it is energetically favourable for charge e/4 quasiholes to bind into "skyrmions" of charge e/2. We show that skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations. We comment on the consequences for the activated transport.Comment: 4 pages, 3 figure

Soil deformations caused by soft-ground tunnelling

This thesis discusses the interaction between methods of tunnelling in soil and sources of ground loss. Two distinct phases of settlement in cohesive soils are identified. Short-term settlements are caused by loss of ground into the tunnel and long term settlements are caused by consolidation of the ground around the tunnel. A stochastic model of ground movements caused by volume loss into the tunnel is developed in order to explain in-situ observations. Consolidation settlement is estimated with the aid of flow nets developed by finite difference numerical modelling. These nets are also used to estimate the contribution of seepage to tunnel face instability. Field observations of ground movements caused by tunnelling In soft, cohesive ground were made at three sites. These measurements were taken In order not only to add to the store of case history evidence already available, but also in a direct attempt to confirm or disprove the theoretical model. Tunnelling conditions were different in each case. One tunnel was shield-driven in laminated clay, one was shield-driven with the aid of compressed air support In alluvial organic slit, and one was driven without a shield in stiff, stony clay. These case histories confirm that settlement troughs of Gaussian configuration were developed, agreeing with the stochastic model, and that long-term consolidation may develop in clay soils on the removal of compressed air support from the tunnel