On exact boundary controllability for linearly coupled wave equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A note on the controllability for the wave equation in nonsmooth plane domains

We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved part of the boundary, while in the straight part we impose homogeneous Dirichlet boundary condition. The initial state has finite energy and the control is square integrable. (c) 2005 Elsevier B.V. All rights reserved.

Exact boundary control for the wave equation in a polyhedral time-dependent domain

We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the boundary is given by the conormal derivative associated with the wave operator while in the fixed part the control is of Neuman type. For initial state H-1 x L-2 we obtain controls in L-2. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Energy decay for the linear Klein-Gordon equation and boundary control

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle na fronteira para um sistema de equações de ondas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

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.