Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

The tribology of linear tape recording systems

This thesis is devoted to the tribology at the head~to~tape interface of linear tape recording systems, OnStream ADRTM system being used as an experimental platform, Combining experimental characterisation with computer modelling, a comprehensive picture of the mechanisms involved in a tape recording system is drawn. The work is designed to isolate the mechanisms responsible for the physical spacing between head and tape with the aim of minimising spacing losses and errors and optimising signal output. Standard heads-used in ADR current products-and prototype heads- DLC and SPL coated and dummy heads built from a AI203-TiC and alternative single-phase ceramics intended to constitute the head tape-bearing surface-are tested in controlled environment for up to 500 hours (exceptionally 1000 hours), Evidences of wear on the standard head are mainly observable as a preferential wear of the TiC phase of the AI203-TiC ceramic, The TiC grains are believed to delaminate due to a fatigue wear mechanism, a hypothesis further confirmed via modelling, locating the maximum von Mises equivalent stress at a depth equivalent to the TiC recession (20 to 30 nm). Debris of TiC delaminated residues is moreover found trapped within the pole-tip recession, assumed therefore to provide three~body abrasive particles, thus increasing the pole-tip recession. Iron rich stain is found over the cycled standard head surface (preferentially over the pole-tip and to a lesser extent over the TiC grains) at any environment condition except high temperature/humidity, where mainly organic stain was apparent, Temperature (locally or globally) affects staining rate and aspect; stain transfer is generally promoted at high temperature. Humidity affects transfer rate and quantity; low humidity produces, thinner stains at higher rate. Stain generally targets preferentially head materials with high electrical conductivity, i.e. Permalloy and TiC. Stains are found to decrease the friction at the head-to-tape interface, delay the TiC recession hollow-out and act as a protective soft coating reducing the pole-tip recession. This is obviously at the expense of an additional spacing at the head-to-tape interface of the order of 20 nm. Two kinds of wear resistant coating are tested: diamond like carbon (DLC) and superprotective layer (SPL), 10 nm and 20 to 40 nm thick, respectively. DLC coating disappears within 100 hours due possibly to abrasive and fatigue wear. SPL coatings are generally more resistant, particularly at high temperature and low humidity, possibly in relation with stain transfer. 20 nm coatings are found to rely on the substrate wear behaviour whereas 40 nm coatings are found to rely on the adhesive strength at the coating/substrate interface. These observations seem to locate the wear-driving forces 40 nm below the surface, hence indicate that for coatings in the 10 nm thickness range-· i,e. compatible with high-density recording-the substrate resistance must be taken into account. Single-phase ceramic as candidate for wear-resistant tape-bearing surface are tested in form of full-contour dummy-heads. The absence of a second phase eliminates the preferential wear observed at the AI203-TiC surface; very low wear rates and no evidence of brittle fracture are observed.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

The application of computerised modelling techniques in manufacturing system design

The absence of a definitive approach to the design of manufacturing systems signifies the importance of a control mechanism to ensure the timely application of relevant design techniques. To provide effective control, design development needs to be continually assessed in relation to the required system performance, which can only be achieved analytically through computer simulation. The technique providing the only method of accurately replicating the highly complex and dynamic interrelationships inherent within manufacturing facilities and realistically predicting system behaviour. Owing to the unique capabilities of computer simulation, its application should support and encourage a thorough investigation of all alternative designs. Allowing attention to focus specifically on critical design areas and enabling continuous assessment of system evolution. To achieve this system analysis needs to efficient, in terms of data requirements and both speed and accuracy of evaluation. To provide an effective control mechanism a hierarchical or multi-level modelling procedure has therefore been developed, specifying the appropriate degree of evaluation support necessary at each phase of design. An underlying assumption of the proposal being that evaluation is quick, easy and allows models to expand in line with design developments. However, current approaches to computer simulation are totally inappropriate to support the hierarchical evaluation. Implementation of computer simulation through traditional approaches is typically characterized by a requirement for very specialist expertise, a lengthy model development phase, and a correspondingly high expenditure. Resulting in very little and rather inappropriate use of the technique. Simulation, when used, is generally only applied to check or verify a final design proposal. Rarely is the full potential of computer simulation utilized to aid, support or complement the manufacturing system design procedure. To implement the proposed modelling procedure therefore the concept of a generic simulator was adopted, as such systems require no specialist expertise, instead facilitating quick and easy model creation, execution and modification, through simple data inputs. Previously generic simulators have tended to be too restricted, lacking the necessary flexibility to be generally applicable to manufacturing systems. Development of the ATOMS manufacturing simulator, however, has proven that such systems can be relevant to a wide range of applications, besides verifying the benefits of multi-level modelling.

System identification of linear vibrating structures

Methods of dynamic modelling and analysis of structures, for example the finite element method, are well developed. However, it is generally agreed that accurate modelling of complex structures is difficult and for critical applications it is necessary to validate or update the theoretical models using data measured from actual structures. The techniques of identifying the parameters of linear dynamic models using Vibration test data have attracted considerable interest recently. However, no method has received a general acceptance due to a number of difficulties. These difficulties are mainly due to (i) Incomplete number of Vibration modes that can be excited and measured, (ii) Incomplete number of coordinates that can be measured, (iii) Inaccuracy in the experimental data (iv) Inaccuracy in the model structure. This thesis reports on a new approach to update the parameters of a finite element model as well as a lumped parameter model with a diagonal mass matrix. The structure and its theoretical model are equally perturbed by adding mass or stiffness and the incomplete number of eigen-data is measured. The parameters are then identified by an iterative updating of the initial estimates, by sensitivity analysis, using eigenvalues or both eigenvalues and eigenvectors of the structure before and after perturbation. It is shown that with a suitable choice of the perturbing coordinates exact parameters can be identified if the data and the model structure are exact. The theoretical basis of the technique is presented. To cope with measurement errors and possible inaccuracies in the model structure, a well known Bayesian approach is used to minimize the least squares difference between the updated and the initial parameters. The eigen-data of the structure with added mass or stiffness is also determined using the frequency response data of the unmodified structure by a structural modification technique. Thus, mass or stiffness do not have to be added physically. The mass-stiffness addition technique is demonstrated by simulation examples and Laboratory experiments on beams and an H-frame.

Exploratory data analysis with non-linear and missing data in geochemistry

Exploratory analysis of data seeks to find common patterns to gain insights into the structure and distribution of the data. In geochemistry it is a valuable means to gain insights into the complicated processes making up a petroleum system. Typically linear visualisation methods like principal components analysis, linked plots, or brushing are used. These methods can not directly be employed when dealing with missing data and they struggle to capture global non-linear structures in the data, however they can do so locally. This thesis discusses a complementary approach based on a non-linear probabilistic model. The generative topographic mapping (GTM) enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate more structure than a two dimensional principal components plot. The model can deal with uncertainty, missing data and allows for the exploration of the non-linear structure in the data. In this thesis a novel approach to initialise the GTM with arbitrary projections is developed. This makes it possible to combine GTM with algorithms like Isomap and fit complex non-linear structure like the Swiss-roll. Another novel extension is the incorporation of prior knowledge about the structure of the covariance matrix. This extension greatly enhances the modelling capabilities of the algorithm resulting in better fit to the data and better imputation capabilities for missing data. Additionally an extensive benchmark study of the missing data imputation capabilities of GTM is performed. Further a novel approach, based on missing data, will be introduced to benchmark the fit of probabilistic visualisation algorithms on unlabelled data. Finally the work is complemented by evaluating the algorithms on real-life datasets from geochemical projects.

An investigation into inductive parameter learning in complex hierarchical knowledge structures representing clinical expertise

This dissertation investigates the very important and current problem of modelling human expertise. This is an apparent issue in any computer system emulating human decision making. It is prominent in Clinical Decision Support Systems (CDSS) due to the complexity of the induction process and the vast number of parameters in most cases. Other issues such as human error and missing or incomplete data present further challenges. In this thesis, the Galatean Risk Screening Tool (GRiST) is used as an example of modelling clinical expertise and parameter elicitation. The tool is a mental health clinical record management system with a top layer of decision support capabilities. It is currently being deployed by several NHS mental health trusts across the UK. The aim of the research is to investigate the problem of parameter elicitation by inducing them from real clinical data rather than from the human experts who provided the decision model. The induced parameters provide an insight into both the data relationships and how experts make decisions themselves. The outcomes help further understand human decision making and, in particular, help GRiST provide more accurate emulations of risk judgements. Although the algorithms and methods presented in this dissertation are applied to GRiST, they can be adopted for other human knowledge engineering domains.

Using process-oriented holonic (PrOH) modelling to increase understanding of information systems

Methodologies for understanding business processes and their information systems (IS) are often criticized, either for being too imprecise and philosophical (a criticism often levied at softer methodologies) or too hierarchical and mechanistic (levied at harder methodologies). The process-oriented holonic modelling methodology combines aspects of softer and harder approaches to aid modellers in designing business processes and associated IS. The methodology uses holistic thinking and a construct known as the holon to build process descriptions into a set of models known as a holarchy. This paper describes the methodology through an action research case study based in a large design and manufacturing organization. The scientific contribution is a methodology for analysing business processes in environments that are characterized by high complexity, low volume and high variety where there are minimal repeated learning opportunities, such as large IS development projects. The practical deliverables from the project gave IS and business process improvements for the case study company.

The classification of HLA supertypes by GRID/CPCA and hierarchical clustering methods

Biological experiments often produce enormous amount of data, which are usually analyzed by data clustering. Cluster analysis refers to statistical methods that are used to assign data with similar properties into several smaller, more meaningful groups. Two commonly used clustering techniques are introduced in the following section: principal component analysis (PCA) and hierarchical clustering. PCA calculates the variance between variables and groups them into a few uncorrelated groups or principal components (PCs) that are orthogonal to each other. Hierarchical clustering is carried out by separating data into many clusters and merging similar clusters together. Here, we use an example of human leukocyte antigen (HLA) supertype classification to demonstrate the usage of the two methods. Two programs, Generating Optimal Linear Partial Least Square Estimations (GOLPE) and Sybyl, are used for PCA and hierarchical clustering, respectively. However, the reader should bear in mind that the methods have been incorporated into other software as well, such as SIMCA, statistiXL, and R.

Hierarchical approach to project planning:the case of a petroleum pipeline construction

Projects exposed to an uncertain environment must be adapted to deal with the effective integration of various planning elements and the optimization of project parameters. Time, cost, and quality are the prime objectives of a project that need to be optimized to fulfill the owner's goal. In an uncertain environment, there exist many other conflicting objectives that may also need to be optimized. These objectives are characterized by varying degrees of conflict. Moreover, an uncertain environment also causes several changes in the project plan throughout its life, demanding that the project plan be totally flexible. Goal programming (GP), a multiple criteria decision making technique, offers a good solution for this project planning problem. There the planning problem is considered from the owner's perspective, which leads to classifying the project up to the activity level. GP is applied separately at each level, and the formulated models are integrated through information flow. The flexibility and adaptability of the models lies in the ease of updating the model parameters at the required level through changing priorities and/or constraints and transmitting the information to other levels. The hierarchical model automatically provides integration among various element of planning. The proposed methodology is applied in this paper to plan a petroleum pipeline construction project, and its effectiveness is demonstrated.

Neural Networks for Modelling of Large Social Systems. Approaches for Mentality, Anticipating and Multivaluedness Accounting

It is consider the new global models for society of neuronet type. The hierarchical structure of society and mentality of individual are considered. The way for incorporating in model anticipatory (prognostic) ability of individual is considered. Some implementations of approach for real task and further research problems are described. Multivaluedness of models and solutions is discussed. Sensory-motor systems analogy also is discussed. New problems for theory and applications of neural networks are described.

Model Construction and Research using System Compositional Approach on Natural Hierarchical Neural Networks. Development of Computer Toolbox

System compositional approach to model construction and research of informational processes, which take place in biological hierarchical neural networks, is being discussed. A computer toolbox has been successfully developed for solution of tasks from this scientific sphere. A series of computational experiments investigating the work of this toolbox on olfactory bulb model has been carried out. The well-known psychophysical phenomena have been reproduced in experiments.

Multi-threaded parallel numerical modelling of femtosecond pulse propagation in laser machining

Femtosecond laser microfabrication has emerged over the last decade as a 3D flexible technology in photonics. Numerical simulations provide an important insight into spatial and temporal beam and pulse shaping during the course of extremely intricate nonlinear propagation (see e.g. [1,2]). Electromagnetics of such propagation is typically described in the form of the generalized Non-Linear Schrdinger Equation (NLSE) coupled with Drude model for plasma [3]. In this paper we consider a multi-threaded parallel numerical solution for a specific model which describes femtosecond laser pulse propagation in transparent media [4, 5]. However our approach can be extended to similar models. The numerical code is implemented in NVIDIA Graphics Processing Unit (GPU) which provides an effitient hardware platform for multi-threded computing. We compare the performance of the described below parallel code implementated for GPU using CUDA programming interface [3] with a serial CPU version used in our previous papers [4,5]. © 2011 IEEE.

An unsupervised Bayesian modelling approach to storyline detection from news articles

Storyline detection from news articles aims at summarizing events described under a certain news topic and revealing how those events evolve over time. It is a difficult task because it requires first the detection of events from news articles published in different time periods and then the construction of storylines by linking events into coherent news stories. Moreover, each storyline has different hierarchical structures which are dependent across epochs. Existing approaches often ignore the dependency of hierarchical structures in storyline generation. In this paper, we propose an unsupervised Bayesian model, called dynamic storyline detection model, to extract structured representations and evolution patterns of storylines. The proposed model is evaluated on a large scale news corpus. Experimental results show that our proposed model outperforms several baseline approaches.

Multi-threaded parallel simulation of non-local non-linear problems in ultrashort laser pulse propagation in the presence of plasma

We describe a parallel multi-threaded approach for high performance modelling of wide class of phenomena in ultrafast nonlinear optics. Specific implementation has been performed using the highly parallel capabilities of a programmable graphics processor. © 2011 SPIE.