Temporal finite elements in the dynamic analysis of structures

This thesis demonstrates that the use of finite elements need not be confined to space alone, but that they may also be used in the time domain, It is shown that finite element methods may be used successfully to obtain the response of systems to applied forces, including, for example, the accelerations in a tall structure subjected to an earthquake shock. It is further demonstrated that at least one of these methods may be considered to be a practical alternative to more usual methods of solution. A detailed investigation of the accuracy and stability of finite element solutions is included, and methods of applications to both single- and multi-degree of freedom systems are described. Solutions using two different temporal finite elements are compared with those obtained by conventional methods, and a comparison of computation times for the different methods is given. The application of finite element methods to distributed systems is described, using both separate discretizations in space and time, and a combined space-time discretization. The inclusion of both viscous and hysteretic damping is shown to add little to the difficulty of the solution. Temporal finite elements are also seen to be of considerable interest when applied to non-linear systems, both when the system parameters are time-dependent and also when they are functions of displacement. Solutions are given for many different examples, and the computer programs used for the finite element methods are included in an Appendix.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Intermediate asymptotics in nonlinear optical systems

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

Bandwidth management of WiMAX systems and performance modeling

WiMAX has been introduced as a competitive alternative for metropolitan broadband wireless access technologies. It is connection oriented and it can provide very high data rates, large service coverage, and flexible quality of services (QoS). Due to the large number of connections and flexible QoS supported by WiMAX, the uplink access in WiMAX networks is very challenging since the medium access control (MAC) protocol must efficiently manage the bandwidth and related channel allocations. In this paper, we propose and investigate a cost-effective WiMAX bandwidth management scheme, named the WiMAX partial sharing scheme (WPSS), in order to provide good QoS while achieving better bandwidth utilization and network throughput. The proposed bandwidth management scheme is compared with a simple but inefficient scheme, named the WiMAX complete sharing scheme (WCPS). A maximum entropy (ME) based analytical model (MEAM) is proposed for the performance evaluation of the two bandwidth management schemes. The reason for using MEAM for the performance evaluation is that MEAM can efficiently model a large-scale system in which the number of stations or connections is generally very high, while the traditional simulation and analytical (e.g., Markov models) approaches cannot perform well due to the high computation complexity. We model the bandwidth management scheme as a queuing network model (QNM) that consists of interacting multiclass queues for different service classes. Closed form expressions for the state and blocking probability distributions are derived for those schemes. Simulation results verify the MEAM numerical results and show that WPSS can significantly improve the network's performance compared to WCPS.

Control integrated finite state machine design for photovoltaic module integrated converter

The operation state of photovoltaic Module Integrated Converter (MIC) is subjected to change due to different source and load conditions, while state-swap is usually implemented with flow chart based sequential controller in the past research. In this paper, the signatures for different operational states are evaluated and investigated, which lead to an effective control integrated finite state machine (CIFSM), providing real-time state-swap as fast as the local control loop. The proposed CIFSM is implemented digitally for a boost type MIC prototype and tested under a variety of load and source conditions. The test results prove the effectiveness of the proposed CIFSM design.

Modelling the human accommodation system using finite element analysis

The human accommodation system has been extensively examined for over a century, with a particular focus on trying to understand the mechanisms that lead to the loss of accommodative ability with age (Presbyopia). The accommodative process, along with the potential causes of presbyopia, are disputed; hindering efforts to develop methods of restoring accommodation in the presbyopic eye. One method that can be used to provide insight into this complex area is Finite Element Analysis (FEA). The effectiveness of FEA in modelling the accommodative process has been illustrated by a number of accommodative FEA models developed to date. However, there have been limitations to these previous models; principally due to the variation in data on the geometry of the accommodative components, combined with sparse measurements of their material properties. Despite advances in available data, continued oversimplification has occurred in the modelling of the crystalline lens structure and the zonular fibres that surround the lens. A new accommodation model was proposed by the author that aims to eliminate these limitations. A novel representation of the zonular structure was developed, combined with updated lens and capsule modelling methods. The model has been designed to be adaptable so that a range of different age accommodation systems can be modelled, allowing the age related changes that occur to be simulated. The new modelling methods were validated by comparing the changes induced within the model to available in vivo data, leading to the definition of three different age models. These were used in an extended sensitivity study on age related changes, where individual parameters were altered to investigate their effect on the accommodative process. The material properties were found to have the largest impact on the decline in accommodative ability, in particular compared to changes in ciliary body movement or zonular structure. Novel data on the importance of the capsule stiffness and thickness was also established. The new model detailed within this thesis provides further insight into the accommodation mechanism, as well as a foundation for future, more detailed investigations into accommodation, presbyopia and accommodative restoration techniques.

Intermediate asymptotics in nonlinear optical systems

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

Assessing the queuing process using data envelopment analysis:an application in health centres

Queuing is one of the very important criteria for assessing the performance and efficiency of any service industry, including healthcare. Data Envelopment Analysis (DEA) is one of the most widely-used techniques for performance measurement in healthcare. However, no queue management application has been reported in the health-related DEA literature. Most of the studies regarding patient flow systems had the objective of improving an already existing Appointment System. The current study presents a novel application of DEA for assessing the queuing process at an Outpatients’ department of a large public hospital in a developing country where appointment systems do not exist. The main aim of the current study is to demonstrate the usefulness of DEA modelling in the evaluation of a queue system. The patient flow pathway considered for this study consists of two stages; consultation with a doctor and pharmacy. The DEA results indicated that waiting times and other related queuing variables included need considerable minimisation at both stages.

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.