On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Characterization of titanium phosphate as electrolytes in fuel cells

Titanium phosphate is currently a promising material for proton exchange membrane fuel cells applications (PEMFC) allowing for operation at high temperature conditions. In this work, titanium phosphate was synthesized from tetra iso-propoxide (TTIP) and orthophosphoric acid (H3PO4) in different ratios by a sol gel method. High BET surface areas of 271 m(2).g(-1) were obtained for equimolar Ti:P samples whilst reduced surface areas were observed by varying the molar ratio either way. Highest proton conductivity of 5.4 x 10(-2) S.cm(-1) was measured at 20 degrees C and 93% relative humidity (RH). However, no correlation was observed between surface area and proton conductivity. High proton conductivity was directly attributed to hydrogen bonding in P-OH groups and the water molecules retained in the sample structure. The proton conductivity increased with relative humidity, indicating that the Grotthuss mechanism governed proton transport. Further, sample Ti/P with 1:9 molar ratio showed proton conductivity in the order of 10(-1) S.cm(-1) (5% RH) and similar to 1.6x10(-2) S.cm(-1) (anhydrous condition) at 200 degrees C. These proton conductivities were mainly attributed to excess acid locked into the functionalized TiP structure, thus forming ionisable protons.

A unified friction description and its application to the simulation of frictional instability using the finite element method

This article first summarizes some available experimental results on the frictional behaviour of contact interfaces, and briefly recalls typical frictional experiments and relationships, which are applicable for rock mechanics, and then a unified description is obtained to describe the entire frictional behaviour. It is formulated based on the experimental results and applied with a stick and slip decomposition algorithm to describe the stick-slip instability phenomena, which can describe the effects observed in rock experiments without using the so-called state variable, thus avoiding related numerical difficulties. This has been implemented to our finite element code, which uses the node-to-point contact element strategy proposed by the authors to handle the frictional contact between multiple finite-deformation bodies with stick and finite frictional slip, and applied here to simulate the frictional behaviour of rocks to show its usefulness and efficiency.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100 km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed ``hydrolytic weakening''. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.

Stirring in 3-d spherical models of convection in the Earth's mantle

On a global scale basalts from mid-ocean ridges are strikingly more homogeneous than basalts from intraplate volcanism. The observed geochemical heterogeneity argues strongly for the existence of distinct reservoirs in the Earth's mantle. It is an unresolved problem of Geodynamics as to how these findings can be reconciled with large-scale convection. We review observational constraints, and investigate stirring properties of numerical models of mantle convection. Conditions in the early Earth may have supported layered convection with rapid stirring in the upper layers. Material that has been altered near the surface is transported downwards by small-scale convection. Thereby a layer of homogeneous depleted material develops above pristine mantle. As the mantle cools over Earth history, the effects leading to layering become reduced and models show the large-scale convection favoured for the Earth today. Laterally averaged, the upper mantle below the lithosphere is least affected by material that has experienced near-surface differentiation. The geochemical signature obtained during the previous episode of small-scale convection may be preserved there for the longest time. Additionally, stirring is less effective in the high viscosity layer of the central lower mantle [1, 2], supporting the survival of medium-scale heterogeneities there. These models are the first, using 3-d spherical geometry and mostly Earth-like parameters, to address the suggested change of convective style. Although the models are still far from reproducing our planet, we find that proposal might be helpful towards reconciling geochemical and geophysical constraints.

Carrier lifetime and exciton saturation in a strain-balanced InGaAs/InAsP multiple-quantum-well

The bleaching of the n = 1 heavy-hole and light-hole exciton absorption has been studied at room temperature and zero bias in a strain-balanced InGaAs/InAsP multiple quantum well. Pump-probe spectroscopy was used to measure the decay of the light-hole absorption saturation, giving a hole lifetime of only 280 ps. As only 16 meV separates the light- and heavy-hole bands, the short escape time can be explained by thermalization between these bands followed by thermionic emission over the heavy-hole barrier. The saturation density was estimated to be 1 × 1016 cm-3; this is much lower than expected for tensile-strained wells where both heavy and light holes have large in-plane masses. © 1998 American Institute of Physics.

Pearl-chain waveguides written at megahertz repetition rate

Waveguides in the form of connected pearls, written with sub-30 fs pulses centered at 800 nm at a repetition rate of 10 MHz, show high changes of the refractive index and, as a consequence, simple in-coupling. The value of the refractive index modification of these waveguides is as high as 10-2, optical losses are 6 dB/cm (at 1.55 µm) and the mode field diameter is 8 µm at 670 nm.

Strain distributionand electronic property modifications in Si/Ge axial nanowires hetrostructures

Molecular dynamics simulations were carried out for Si/Ge axial nanowire heterostructures using modified effective atom method (MEAM) potentials. A Si–Ge MEAM interatomic cross potential was developed based on available experimental data and was used for these studies. The atomic distortions and strain distributions near the Si/Ge interfaces are predicted for nanowires with their axes oriented along the [111] direction. The cases of 10 and 25 nm diameter Si/Ge biwires and of 25 nm diameter Si/Ge/Si axial heterostructures with the Ge disk 1 nm thick were studied. Substantial distortions in the height of the atoms adjacent to the interface were found for the biwires but not for the Ge disks. Strains as high as 3.5% were found for the Ge disk and values of 2%–2.5% were found at the Si and Ge interfacial layers in the biwires. Deformation potential theory was used to estimate the influence of the strains on the band gap, and reductions in band gap to as small as 40% of bulk values are predicted for the Ge disks. The localized regions of increased strain and resulting energy minima were also found within the Si/Ge biwire interfaces with the larger effects on the Ge side of the interface. The regions of strain maxima near and within the interfaces are anticipated to be useful for tailoring band gaps and producing quantum confinement of carriers. These results suggest that nanowire heterostructures provide greater design flexibility in band structure modification than is possible with planar layer growth.

Faster radial strain relaxation in InAs-GaAs core-shell heterowires

The structure of wurtzite and zinc blende InAs-GaAs (001) core-shell nanowires grown by molecular beam epitaxy on GaAs (001) substrates has been investigated by transmission electron microscopy. Heterowires with InAs core radii exceeding 11 nm, strain relax through the generation of misfit dislocations, given a GaAs shell thickness greater than 2.5 nm. Strain relaxation is larger in radial directions than axial, particularly for shell thicknesses greater than 5.0 nm, consistent with molecular statics calculations that predict a large shear stress concentration at each interface corner. © 2012 American Institute of Physics.

Laser processing effect on magnetic properties of amorphous wires

A study was conducted to observe the laser processing effects on the magnetic properties of amorphous wires. Weekly interacting heterogeneous structures with different magnetic properties were formed by the local annealing by argon laser. Favourable changes were observed due to the creation of local stresses and structural interfaces.

Gain switching of an external cavity grating-coupled surface emitting laser with wide tunability

The gain-switched, single frequency operation of an external cavity grating-coupled surface emitting laser with a wavelength tuning range of 100 nm was presented. The light in the grating section was coupled out of the laser at a specific angle to the surface of the device. Analysis showed that within the driving current range, lasing in the device only occurred when the external cavity was properly aligned.

Longitudinal parametric oscillation in photorefractive sillenites: comparison between theory and experiment

By using an alternative setup for photorefractive parametric oscillation in which wave mixing between the recording beams is avoided it has become possible to make more detailed comparisons with the space-charge wave theory. In the present paper we compare the experimental features of longitudinal parametric oscillation observed in a crystal of Bi12SiO20 with the theoretical predictions.