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.

An improved novelty criterion for resource allocating networks

Online model order complexity estimation remains one of the key problems in neural network research. The problem is further exacerbated in situations where the underlying system generator is non-stationary. In this paper, we introduce a novelty criterion for resource allocating networks (RANs) which is capable of being applied to both stationary and slowly varying non-stationary problems. The deficiencies of existing novelty criteria are discussed and the relative performances are demonstrated on two real-world problems : electricity load forecasting and exchange rate prediction.

The effect of blending on selected physical properties of crude oils and their products

A study was made of the effect of blending practice upon selected physical properties of crude oils, and of various base oils and petroleum products, using a range of binary mixtures. The crudes comprised light, medium and heavy Kuwait crude oils. The properties included kinematic viscosity, pour point, boiling point and Reid vapour pressure. The literature related to the prediction of these properties, and the changes reported to occur on blending, was critically reviewed as a preliminary to the study. The kinematic viscosity of petroleum oils in general exhibited non-ideal behaviour upon blending. A mechanism was proposed for this behaviour which took into account the effect of asphaltenes content. A correlation was developed, as a modification of Grunberg's equation, to predict the viscosities of binary mixtures of petroleum oils. A correlation was also developed to predict the viscosities of ternary mixtures. This correlation showed better agreement with experimental data (< 6% deviation for crude oils and 2.0% for base oils) than currently-used methods, i.e. ASTM and Refutas methods. An investigation was made of the effect of temperature on the viscosities of crude oils and petroleum products at atmospheric pressure. The effect of pressure on the viscosity of crude oil was also studied. A correlation was developed to predict the viscosity at high pressures (up to 8000 psi), which gave significantly better agreement with the experimental data than the current method due to Kouzel (5.2% and 6.0% deviation for the binary and ternary mixtures respectively). Eyring's theory of viscous flow was critically investigated, and a modification was proposed which extends its application to petroleum oils. The effect of blending on the pour points of selected petroleum oils was studied together with the effect of wax formation and asphaltenes content. Depression of the pour point was always obtained with crude oil binary mixtures. A mechanism was proposed to explain the pour point behaviour of the different binary mixtures. The effects of blending on the boiling point ranges and Reid vapour pressures of binary mixtures of petroleum oils were investigated. The boiling point range exhibited ideal behaviour but the R.V.P. showed negative deviations from it in all cases. Molecular weights of these mixtures were ideal, but the densities and molar volumes were not. The stability of the various crude oil binary mixtures, in terms of viscosity, was studied over a temperature range of 1oC - 30oC for up to 12 weeks. Good stability was found in most cases.

Phase equilibrium studies at moderate pressures

The theory of vapour-liquid equilibria is reviewed, as is the present status or prediction methods in this field. After discussion of the experimental methods available, development of a recirculating equilibrium still based on a previously successful design (the modified Raal, Code and Best still of O'Donnell and Jenkins) is described. This novel still is designed to work at pressures up to 35 bar and for the measurement of both isothermal and isobaric vapour-liquid equilibrium data. The equilibrium still was first commissioned by measuring the saturated vapour pressures of pure ethanol and cyclohexane in the temperature range 77-124°C and 80-142°C respectively. The data obtained were compared with available literature experimental values and with values derived from an extended form of the Antoine equation for which parameters were given in the literature. Commissioning continued with the study of the phase behaviour of mixtures of the two pure components as such mixtures are strongly non-ideal, showing azeotopic behaviour. Existing data did not exist above one atmosphere pressure. Isothermal measurements were made at 83.29°C and 106.54°C, whilst isobaric measurements were made at pressures of 1 bar, 3 bar and 5 bar respectively. The experimental vapour-liquid equilibrium data obtained are assessed by a standard literature method incorporating a themodynamic consistency test that minimises the errors in all the measured variables. This assessment showed that reasonable x-P-T data-sets had been measured, from which y-values could be deduced, but that the experimental y-values indicated the need for improvements in the design of the still. The final discussion sets out the improvements required and outlines how they might be attained.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

Possibilities and limitations of coded aperture imaging

We have simulated the performance of various apertures used in Coded Aperture Imaging - optically. Coded pictures of extended and continuous-tone planar objects from the Annulus, Twin Annulus, Fresnel Zone Plate and the Uniformly Redundant Array have been decoded using a noncoherent correlation process. We have compared the tomographic capabilities of the Twin Annulus with the Uniformly Redundant Arrays based on quadratic residues and m-sequences. We discuss the ways of reducing the 'd. c.' background of the various apertures used. The non-ideal System-Point-Spread-Function inherent in a noncoherent optical correlation process produces artifacts in the reconstruction. Artifacts are also introduced as a result of unwanted cross-correlation terms from out-of-focus planes. We find that the URN based on m-sequences exhibits good spatial resolution and out-of-focus behaviour when imaging extended objects.

Clogging in horizontal subsurface flow constructed wetlands

Horizontal Subsurface Flow Treatment Wetlands (HSSF TWs) are used by Severn Trent Water as a low-cost tertiary wastewater treatment for rural locations. Experience has shown that clogging is a major operational problem that reduces HSSF TW lifetime. Clogging is caused by an accumulation of secondary wastewater solids from upstream processes and decomposing leaf litter. Clogging occurs as a sludge layer where wastewater is loaded on the surface of the bed at the inlet. Severn Trent systems receive relatively high hydraulic loading rates, which causes overland flow and reduces the ability to mineralise surface sludge accumulations. A novel apparatus and method, the Aston Permeameter, was created to measure hydraulic conductivity in situ. Accuracy is ±30 %, which was considered adequate given that conductivity in clogged systems varies by several orders of magnitude. The Aston Permeameter was used to perform 20 separate tests on 13 different HSSF TWs in the UK and the US. The minimum conductivity measured was 0.03 m/d at Fenny Compton (compared with 5,000 m/d clean conductivity), which was caused by an accumulation of construction fines in one part of the bed. Most systems displayed a 2 to 3 order of magnitude variation in conductivity in each dimension. Statistically significant transverse variations in conductivity were found in 70% of the systems. Clogging at the inlet and outlet was generally highest where flow enters the influent distribution and exits the effluent collection system, respectively. Surface conductivity was lower in systems with dense vegetation because plant canopies reduce surface evapotranspiration and decelerate sludge mineralisation. An equation was derived to describe how the water table profile is influenced by overland flow, spatial variations in conductivity and clogging. The equation is calibrated using a single parameter, the Clog Factor (CF), which represents the equivalent loss of porosity that would reproduce measured conductivity according to the Kozeny-Carman Equation. The CF varies from 0 for ideal conditions to 1 for completely clogged conditions. Minimum CF was 0.54 for a system that had recently been refurbished, which represents the deviation from ideal conditions due to characteristics of non-ideal media such as particle size distribution and morphology. Maximum CF was 0.90 for a 15 year old system that exhibited sludge accumulation and overland flow across the majority of the bed. A Finite Element Model of a 15 m long HSSF TW was used to indicate how hydraulics and hydrodynamics vary as CF increases. It was found that as CF increases from 0.55 to 0.65 the subsurface wetted area increases, which causes mean hydraulic residence time to increase from 0.16 days to 0.18 days. As CF increases from 0.65 to 0.90, the extent of overland flow increases from 1.8 m to 13.1 m, which reduces hydraulic efficiency from 37 % to 12 % and reduces mean residence time to 0.08 days.

Mass transfer and chemical reaction on a distillation plate

A multistage distillation column in which mass transfer and a reversible chemical reaction occurred simultaneously, has been investigated to formulate a technique by which this process can be analysed or predicted. A transesterification reaction between ethyl alcohol and butyl acetate, catalysed by concentrated sulphuric acid, was selected for the investigation and all the components were analysed on a gas liquid chromatograph. The transesterification reaction kinetics have been studied in a batch reactor for catalyst concentrations of 0.1 - 1.0 weight percent and temperatures between 21.4 and 85.0 °C. The reaction was found to be second order and dependent on the catalyst concentration at a given temperature. The vapour liquid equilibrium data for six binary, four ternary and one quaternary systems are measured at atmospheric pressure using a modified Cathala dynamic equilibrium still. The systems with the exception of ethyl alcohol - butyl alcohol mixtures, were found to be non-ideal. Multicomponent vapour liquid equilibrium compositions were predicted by a computer programme which utilised the Van Laar constants obtained from the binary data sets. Good agreement was obtained between the predicted and experimental quaternary equilibrium vapour compositions. Continuous transesterification experiments were carried out in a six stage sieve plate distillation column. The column was 3" in internal diameter and of unit construction in glass. The plates were 8" apart and had a free area of 7.7%. Both the liquid and vapour streams were analysed. The component conversion was dependent on the boilup rate and the reflux ratio. Because of the presence of the reaction, the concentration of one of the lighter components increased below the feed plate. In the same region a highly developed foam was formed due to the presence of the catalyst. The experimental results were analysed by the solution of a series of simultaneous enthalpy and mass equations. Good agreement was obtained between the experimental and calculated results.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Tracking of non-stationary time-series using resource allocating RBF networks

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Using electricity load data and training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise and forgetting factors for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. We also find that a recently-proposed alternative novelty criterion, found to be more robust in stationary environments, does not fare so well in the non-stationary case due to the need for filter adaptability during training.

The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Multi-valued control problems and mixture density network

We have proposed a novel robust inversion-based neurocontroller that searches for the optimal control law by sampling from the estimated Gaussian distribution of the inverse plant model. However, for problems involving the prediction of continuous variables, a Gaussian model approximation provides only a very limited description of the properties of the inverse model. This is usually the case for problems in which the mapping to be learned is multi-valued or involves hysteritic transfer characteristics. This often arises in the solution of inverse plant models. In order to obtain a complete description of the inverse model, a more general multicomponent distributions must be modeled. In this paper we test whether our proposed sampling approach can be used when considering an arbitrary conditional probability distributions. These arbitrary distributions will be modeled by a mixture density network. Importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The effectiveness of the importance sampling from an arbitrary conditional probability distribution will be demonstrated using a simple single input single output static nonlinear system with hysteretic characteristics in the inverse plant model.

Biocomposites of non-crosslinked natural and synthetic polymers

Biocomposite films comprising a non-crosslinked, natural polymer (collagen) and a synthetic polymer, poly(var epsilon-caprolactone) (PCL), have been produced by impregnation of lyophilised collagen mats with a solution of PCL in dichloromethane followed by solvent evaporation. This approach avoids the toxicity problems associated with chemical crosslinking. Distinct changes in film morphology, from continuous surface coating to open porous format, were achieved by variation of processing parameters such as collagen:PCL ratio and the weight of the starting lyophilised collagen mat. Collagenase digestion indicated that the collagen content of 1:4 and 1:8 collagen:PCL biocomposites was almost totally accessible for enzymatic digestion indicating a high degree of collagen exposure for interaction with other ECM proteins or cells contacting the biomaterial surface. Much reduced collagen exposure (around 50%) was measured for the 1:20 collagen:PCL materials. These findings were consistent with the SEM examination of collagen:PCL biocomposites which revealed a highly porous morphology for the 1:4 and 1:8 blends but virtually complete coverage of the collagen component by PCL in the1:20 samples. Investigations of the attachment and spreading characteristics of human osteoblast (HOB) cells on PCL films and collagen:PCL materials respectively, indicated that HOB cells poorly recognised PCL but attachment and spreading were much improved on the biocomposites. The non-chemically crosslinked, collagen:PCL biocomposites described are expected to provide a useful addition to the range of biomaterials and matrix systems for tissue engineering.

Detection of signals corrupted by the combination of Gaussian and Non-Gaussian noise

The detection of signals in the presence of noise is one of the most basic and important problems encountered by communication engineers. Although the literature abounds with analyses of communications in Gaussian noise, relatively little work has appeared dealing with communications in non-Gaussian noise. In this thesis several digital communication systems disturbed by non-Gaussian noise are analysed. The thesis is divided into two main parts. In the first part, a filtered-Poisson impulse noise model is utilized to calulate error probability characteristics of a linear receiver operating in additive impulsive noise. Firstly the effect that non-Gaussian interference has on the performance of a receiver that has been optimized for Gaussian noise is determined. The factors affecting the choice of modulation scheme so as to minimize the deterimental effects of non-Gaussian noise are then discussed. In the second part, a new theoretical model of impulsive noise that fits well with the observed statistics of noise in radio channels below 100 MHz has been developed. This empirical noise model is applied to the detection of known signals in the presence of noise to determine the optimal receiver structure. The performance of such a detector has been assessed and is found to depend on the signal shape, the time-bandwidth product, as well as the signal-to-noise ratio. The optimal signal to minimize the probability of error of; the detector is determined. Attention is then turned to the problem of threshold detection. Detector structure, large sample performance and robustness against errors in the detector parameters are examined. Finally, estimators of such parameters as. the occurrence of an impulse and the parameters in an empirical noise model are developed for the case of an adaptive system with slowly varying conditions.