Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity

2000 Mathematics Subject Classification: 53C24, 53C65, 53C21.

Suppression of grain boundary relaxation in Zr-doped BiFeO3 thin films

Here, we present the results of temperature dependent dielectric studies on chemical solution processed Zr-doped BiFeO3 (BFO) thin films deposited on Pt/Si substrates. We find that in contrast to the undoped BFO films, Zr doping at Fe-site suppresses the low frequency dielectric relaxation originating from the grain boundaries, attributed to the increased dipolar rigidity due to stronger Zr-O bonds. Temperature dependent dc conductivity obtained from impedance and modulus analyses shows two distinct conduction processes occurring inside the grains. At temperature below similar to 423K, conductivity is nearly temperature independent, while in the high temperature regime (above similar to 423K), conduction is governed by the long range movement of oxygen vacancies with an activation energy of similar to 1eV. (C) 2014 AIP Publishing LLC.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Biotribological assessment for artificial synovial joints : the role of boundary lubrication

Biotribology, the study of lubrication, wear and friction within the body, has become a topic of high importance in recent times as we continue to encounter debilitating diseases and trauma that destroy function of the joints. A highly successful surgical procedure to replace the joint with an artificial equivalent alleviates dysfunction and pain. However, the wear of the bearing surfaces in prosthetic joints is a significant clinical problem and more patients are surviving longer than the life expectancy of the joint replacement. Revision surgery is associated with increased morbidity and mortality and has a far less successful outcome than primary joint replacement. As such, it is essential to ensure that everything possible is done to limit the rate of revision surgery. Past experience indicates that the survival rate of the implant will be influenced by many parameters, of primary importance, the material properties of the implant, the composition of the synovial fluid and the method of lubrication. In prosthetic joints, effective boundary lubrication is known to take place. The interaction of the boundary lubricant and the bearing material is of utmost importance. The identity of the vital active ingredient within synovial fluid (SF) to which we owe the near frictionless performance of our articulating joints has been the quest of researchers for many years. Once identified, tribo tests can determine what materials and more importantly what surfaces this fraction of SF can function most optimally with. Surface-Active Phospholipids (SAPL) have been implicated as the body’s natural load bearing lubricant. Studies in this thesis are the first to fully characterise the adsorbed SAPL detected on the surface of retrieved prostheses and the first to verify the presence of SAPL on knee prostheses. Rinsings from the bearing surfaces of both hip and knee prostheses removed from revision operations were analysed using High Performance Liquid Chromatography (HPLC) to determine the presence and profile of SAPL. Several common prosthetic materials along with a novel biomaterial were investigated to determine their tribological interaction with various SAPLs. A pin-on-flat tribometer was used to make comparative friction measurements between the various tribo-pairs. A novel material, Pyrolytic Carbon (PyC) was screened as a potential candidate as a load bearing prosthetic material. Friction measurements were also performed on explanted prostheses. SAPL was detected on all retrieved implant bearing surfaces. As a result of the study eight different species of phosphatidylcholines were identified. The relative concentrations of each species were also determined indicating that the unsaturated species are dominant. Initial tribo tests employed a saturated phosphatidylcholine (SPC) and the subsequent tests adopted the addition of the newly identified major constituents of SAPL, unsaturated phosphatidylcholine (USPC), as the test lubricant. All tribo tests showed a dramatic reduction in friction when synthetic SAPL was used as the lubricant under boundary lubrication conditions. Some tribopairs showed more of an affinity to SAPL than others. PyC performed superior to the other prosthetic materials. Friction measurements with explanted prostheses verified the presence and performance of SAPL. SAPL, in particular phosphatidylcholine, plays an essential role in the lubrication of prosthetic joints. Of particular interest was the ability of SAPLs to reduce friction and ultimately wear of the bearing materials. The identification and knowledge of the lubricating constituents of SF is invaluable for not only the future development of artificial joints but also in developing effective cures for several disease processes where lubrication may play a role. The tribological interaction of the various tribo-pairs and SAPL is extremely favourable in the context of reducing friction at the bearing interface. PyC is highly recommended as a future candidate material for use in load bearing prosthetic joints considering its impressive tribological performance.

Nanoparticle melting as a Stefan moving boundary problem

The melting of spherical nanoparticles is considered from the perspective of heat flow in a pure material and as a moving boundary (Stefan) problem. The dependence of the melting temperature on both the size of the particle and the interfacial tension is described by the Gibbs-Thomson effect, and the resulting two-phase model is solved numerically using a front-fixing method. Results show that interfacial tension increases the speed of the melting process, and furthermore, the temperature distribution within the solid core of the particle exhibits behaviour that is qualitatively different to that predicted by the classical models without interfacial tension.

The moderating role of self-efficacy on the relationship between emotional exhaustion and job strain for boundary-spanning service employees

Appropriate behaviours toward customers often requires employees to suppress some genuine emotions and/or express other emotions; genuine or contrived. Managing one's emotions in this way gives rise to emotional exhaustion. This can have consequences for psychological ill health, in the form of work place strain, and ultimately employee's desire to leave. This student examines the relationships between emotional management, emotional exhaustion and turnover intentions amongst diversional therapy professionals. We find that some forms of emotional management have a significant impact on emotional exhaustion and that this predicts workplace strain. Furthermore, the deleterious effects of emotional exhaustion are mitigated somewhat for employees who have strong beliefs in their ability to provide good service, compared to employees with lower self efficacy beliefs.