Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

Pole tip recession in linear tape systems

The tribology of linear tape storage system including Linear Tape Open (LTO) and Travan5 was investigated by combining X-ray Photoelectron Spectroscopy (XPS), Auger Electron Spectroscopy (AES), Optical Microscopy and Atomic Force Microscopy (AFM) technologies. The purpose of this study was to understand the tribology mechanism of linear tape systems then projected recording densities may be achieved in future systems. Water vapour pressure or Normalized Water Content (NWC) rather than the Relative Humidity (RH) values (as are used almost universally in this field) determined the extent of PTR and stain (if produced) in linear heads. Approximately linear dependencies were found for saturated PTR increasing with normalized water content increasing over the range studied using the same tape. Fe Stain (if produced) preferentially formed on the head surfaces at the lower water contents. The stain formation mechanism had been identified. Adhesive bond formation is a chemical process that is governed by temperature. Thus the higher the contact pressure, the higher the contact temperature in the interface of head and tape, was produced higher the probability of adhesive bond formation and the greater the amount of transferred material (stain). Water molecules at the interface saturate the surface bonds and makes adhesive junctions less likely. Tape polymeric binder formulation also has a significant role in stain formation, with the latest generation binders producing less transfer of material. This is almost certainly due to higher cohesive bonds within the body of the magnetic layer. TiC in the two-phase ceramic tape-bearing surface (AlTiC) was found to oxidise to form TiO2.The oxidation rate of TiC increased with water content increasing. The oxide was less dense than the underlying carbide; hence the interface between TiO2 oxide and TiC was stressed. Removals of the oxide phase results in the formation of three-body abrasive particles that were swept across the tape head, and gave rise to three-body abrasive wear, particularly in the pole regions. Hence, PTR and subsequent which signal loss and error growth. The lower contact pressure of the LTO system comparing with the Travan5 system ensures that fewer and smaller three-body abrasive particles were swept across the poles and insulator regions. Hence, lower contact pressure, as well as reducing stain in the same time significantly reduces PTR in the LTO system.

Creep and fatigue of a single crystal nickel base superalloy

The introduction of single crystal casting techniques has led to the development of existing nickel-base superalloys to produce materials with optimum mechanical properties in the single crystal condition. As single crystals are known to be anisotropic, a study is needed to determine the general mechanical properties of these materials, and determine the effects of crystal orientation upon them. A study has been carried out to identify the effect of orientation and temperature on the creep and fatigue properties of a development single crystal superalloy, SRR 99. Creep testing and crystal rotation experiments have been made on SRR 99 and an earlier development alloy, SRR 9. Fatigue experiments at elevated temperatures have been carried out on both notched and un-notched specimens of alloy SRR 99. To aid in this analysis, several analytical techniques have been employed including Laue x-ray orientation analysis, measurement of strain by photographic methods and microstructural examination. Crystal rotation experiments have indicated that shear of 1 precipitates by lbrace111rbrace< 112> slip systems is operative during primary creep deformation at temperatures of 750oC and 850oC. The effect of orientation variation obtained by standard casting practices was not found to be significant. Creep rupture was found to be associated with multiple crack initiation from micropores. Fatigue crack initiation in un-notched specimens was found to be related to microporosity and microstructural defects. Failure was predominantly by crystallographic crack growth on lbrace111rbrace planes. The use of linear elastic fracture mechanics to describe fatigue crack propagation in alloy SRR 99 was found to be acceptable at temperatures up to 850oC. Variation of temperature, frequency and crystal orientation was found to have only moderate effect upon crack propagation rates.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Deformations of the pneumatic tyre

A mathematical model is developed for the general pneumatic tyre. The model will permit the investigations of tyre deformations produced by arbitrary external loading, and will enable estimates to be made of the distributions of applied and reactive forces. The principle of Finite Elements is used to idealise the composite tyre structure, each element consisting of a triangle of double curvature with varying thickness. Large deflections of' the structure are accomodated by the use of an iterative sequence of small incremental steps, each of' which obeys the laws of linear mechanics. The theoretical results are found to compare favourably with the experimental test data obtained from two different types of ttye construction. However, limitations in the discretisation process has prohibited accurate assessments to be made of stress distributions in the regions of high stress gradients ..

Synthesis and evaluation of polystyrene based soluble polymeric supports for organic synthesis

Several copolymers of linear polystyrene were prepared for evaluation as soluble polymeric supports for organic synthesis. These polymers were utilized for the synthesis of ?2-isoxazoline compounds. The target compounds were synthesized via 1,3-dipolar cycloaddition reactions between polymer bound alkenes and nitrile oxides generated in situ from their corresponding aldoximes. The cleaved ?2-isoxazoline compounds were tested for biological activity against Mycobacterium fortuitum. To compare the success of these linear polystyrene copolymers, some of the ?2-isoxazoline compounds synthesized on soluble polymeric supports were also prepared via traditional crosslinked polymer supports. The polymer-bound ?2-isoxazolines were also tested for antimicrobial activity. In addition attempts were made to prepare polymers containing the ?2-isoxazolines but anchored by non-hydrolysable bonds. Although the copolymers of polystyrene gave good loading capacity in mmol/g, and being soluble in chlorinated solvents it was possible to monitor the reactions by 1H NMR spectroscopy, the cleavage of the polymer bound products proved to be quite troublesome. Product purification was not as straightforward as it was anticipated. Isolation of the cleaved target compounds proved to be time consuming and laborious when compared to the traditional organic synthesis and solid phase organic synthesis (SPOS). Polymer-bound ?2-isoxazolines close to the polymer backbone exhibited some biological activity against Staphylococcus aureus. Polymers with substitution at the para-position of the aryl substituent at position 3 of isoxazoline ring showed antimicrobial activity.

The Kinematics of interference mechanisms in certain machining operations

The mechanism of "Helical Interference" in milled slots is examined and a coherent theory for the geometry of such surfaces is presented. An examination of the relevant literature shows a fragmented approach to the problem owing to its normally destructive nature, so a complete analysis is developed for slots of constant lead, thus giving a united and exact theory for many different setting parameters and a range of cutter shapes. For the first time, a theory is developed to explain the "Interference Surface" generated in variable lead slots for cylindrical work and attention is drawn to other practical surfaces, such as cones, where variable leads are encountered. Although generally outside the scope of this work, an introductory analysis of these cases is considered in order to develop the cylindrical theory. Special emphasis is laid upon practical areas where the interference mechanism can be used constructively and its application as the rake face of a cutting tool is discussed. A theory of rake angle for such cutting tools is given for commonly used planes, and relative variations in calculated rake angle between planes is examined. Practical tests are conducted to validate both constant lead and variable lead theories and some design improvements to the conventional dividing head are suggested in order to manufacture variable lead workpieces, by use of a "superposed" rotation. A prototype machine is manufactured and its kinematic principle given for both linear and non-linearly varying superposed rotations. Practical workpieces of the former type are manufactured and compared with analytical predictions,while theoretical curves are generated for non-linear workpieces and then compared with those of linear geometry. Finally suggestions are made for the application of these principles to the manufacture of spiral bevel gears, using the "Interference Surface" along a cone as the tooth form.

Effect of poor curing conditions and remedies on the durability of steel in concrete

An investigation was undertaken to study the effect of poor curing simulating hot climatic conditions and remedies on the durability of steel in concrete. Three different curing environments were used i.e. (1) Saturated Ca(OH)2 solution at 20°C, (2) Saturated Ca(OH)2 solution at 50°C and (3) Air at 50°C at 30% relative humidity. The third curing condition corresponding to the temperature and relative humidity typical of Middle Eastern Countries. The nature of the hardened cement paste matrix, cured under the above conditions was studied by means of Mercury Intrusion Porosimetry for measuring pore size distribution. The results were represented as total pore volume and initial pore entry diameter. The Scanning Electron Microscope was used to look at morphological changes during hydration, which were compared to the Mercury Intrusion Porosimetry results. X-ray defraction and Differential Thermal Analysis techniques were also employed for looking at any phase transformations. Polymer impregnation was used to reduce the porosity of the hardened cement pastes, especially in the case of the poorly cured samples. Carbonation rates of unimpregnated and impregnated cements were determined. Chloride diffusion studies were also undertaken to establish the effect of polymer impregnation and blending of the cements. Finally the corrosion behaviour of embedded steel bars was determined by the technique of Linear Polarisation. The steel was embedded in both untreated and polymer impregnated hardened cement pastes placed in either a solution containing NaCl or an environmental cabinet which provided carbonation at 40°C and 50% relative humidity.

Dielectric relaxation of polysiloxanes and kerr effect of p-phenylene vinylene oligomers

The dielectric relaxation behaviour of a series of cyclic and linear poly(dimethylsiloxanes) with overline nn in the range 28 to 99 has been studied, as a function of temperature (142.0K-157.5K) and frequency (12-105Hz). Activation energies for the -relaxation process, Davidson-Cole empirical distribution factors, , and mean-square dipole moments per repeat unit, < 2> , have been calculated. Differences in values of H_act reflected restricted dipolar rotation for the cyclic structures, compared to the linear structures, over the range of molecular weights studied. The dielectric relaxation behaviour of a series of linear oligomers of methyl phenyl siloxane, with n in the range 4 to 10, a series of linear fractions of poly(methyl phenyl siloxane), with overline n_n in the range 31 to 1370, and a cyclic oligomer of mehyl phenyl siloxane, with n = 10, has been studied as a function of temperature (155.5K-264.0K) and frequency (12-105Hz). Activation energies for the -relaxation process, Davidson-Cole and Cole-Cole empirical distribution factors, and , respectively, and mean-square dipole moments per repeat unit have been calculated. The reduced flexibility of short methyl phenyl siloxane chains, compared to dimethyl siloxane chains, was apparent from a comparison of dipole moment ratios. The dilectric relaxation behaviour of poly(methyl hydrogen siloxane) and poly(n-hexyl methyl siloxane) has been studied as a function of temperature and frequency. A polysiloxane liquid crystal has been synthesised and its dielectric relaxation behaviour has been studied, as a function of temperature and frequency, in the liquid crystalline phase and below T_g. Poly(p-phenylene vinylene) and related oligomers have been synthesised and characterised by a variety of experimental techniques. The Kerr effect of two oligomeric fractions, in solution in PPG 2025, has been measured. The electrical conductivities of the undoped and I_2-doped polymer and oligomers have been measured.

An optical study of human ocular dimensions

Many workers have studied the ocular components which occur in eyes exhibiting differing amounts of central refractive error but few have ever considered the additional information that could be derived from a study of peripheral refraction. Before now, peripheral refraction has either been measured in real eyes or has otherwise been modelled in schematic eyes of varying levels of sophistication. Several differences occur between measured and modelled results which, if accounted for, could give rise to more information regarding the nature of the optical and retinal surfaces and their asymmetries. Measurements of ocular components and peripheral refraction, however, have never been made in the same sample of eyes. In this study, ocular component and peripheral refractive measurements were made in a sample of young near-emmetropic, myopic and hyperopic eyes. The data for each refractive group was averaged. A computer program was written to construct spherical surfaced schematic eyes from this data. More sophisticated eye models were developed making use of linear algebraic ray tracing program. This method allowed rays to be traced through toroidal aspheric surfaces which were translated or rotated with respect to each other. For simplicity, the gradient index optical nature of the crystalline lens was neglected. Various alterations were made in these eye models to reproduce the measured peripheral refractive patterns. Excellent agreement was found between the modelled and measured peripheral refractive values over the central 70o of the visual field. This implied that the additional biometric features incorporated in each eye model were representative of those which were present in the measured eyes. As some of these features are not otherwise obtainable using in vivo techniques, it is proposed that the variation of refraction in the periphery offers a very useful optical method for studying human ocular component dimensions.

A solar-powered reverse osmosis system for high recovery of freshwater from saline groundwater

Desalination of groundwater is essential in arid regions that are remote from both seawater and freshwater resources. Desirable features of a groundwater desalination system include a high recovery ratio, operation from a sustainable energy source such as solar, and high water output per unit of energy and land. Here we propose a new system that uses a solar-Rankine cycle to drive reverse osmosis (RO). The working fluid such as steam is expanded against a power piston that actuates a pump piston which in turn pressurises the saline water thus passing it through RO membranes. A reciprocating crank mechanism is used to equalise the forces between the two pistons. The choice of batch mode in preference to continuous flow permits maximum energy recovery and minimal concentration polarisation in the vicinity of the RO membrane. This study analyses the sizing and efficiency of the crank mechanism, quantifies energy losses in the RO separation and predicts the overall performance. For example, a system using a field of linear Fresnel collectors occupying 1000 m2 of land and raising steam at 200 °C and 15.5 bar could desalinate 350 m3/day from saline water containing 5000 ppm of sodium chloride with a recovery ratio of 0.7.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

The role of organoclay in promoting co-continuous morphology in high-density poly(ethylene)/poly(amide) 6 blends

The effect of organically modified clay on the morphology, rheology and mechanical properties of high-density polyethylene (HDPE) and polyamide 6 (PA6) blends (HDPE/PA6 = 75/25 parts) is studied. Virgin and filled blends were prepared by melt compounding the constituents using a twin-screw extruder. The influence of the organoclay on the morphology of the hybrid was deeply investigated by means of wide-angle X-ray diffractometry, transmission and scanning electron microscopies and quantitative extraction experiments. It has been found that the organoclay exclusively places inside the more hydrophilic polyamide phase during the melt compounding. The extrusion process promotes the formation of highly elongated and separated organoclay-rich PA6 domains. Despite its low volume fraction, the filled minor phase eventually merges once the extruded pellets are melted again, giving rise to a co-continuous microstructure. Remarkably, such a morphology persists for long time in the melt state. A possible compatibilizing action related to the organoclay has been investigated by comparing the morphology of the hybrid blend with that of a blend compatibilized using an ethylene–acrylic acid (EAA) copolymer as a compatibilizer precursor. The former remains phase separated, indicating that the filler does not promote the enhancement of the interfacial adhesion. The macroscopic properties of the hybrid blend were interpreted in the light of its morphology. The melt state dynamics of the materials were probed by means of linear viscoelastic measurements. Many peculiar rheological features of polymer-layered silicate nanocomposites based on single polymer matrix were detected for the hybrid blend. The results have been interpreted proposing the existence of two distinct populations of dynamical species: HDPE not interacting with the filler, and a slower species, constituted by the organoclay-rich polyamide phase, which slackened dynamics stabilize the morphology in the melt state. In the solid state, both the reinforcement effect of the filler and the co-continuous microstructure promote the enhancement of the tensile modulus. Our results demonstrate that adding nanoparticles to polymer blends allows tailoring the final properties of the hybrid, potentially leading to high-performance materials which combine the advantages of polymer blends and the merits of polymer nanocomposites.

Compensation of nonlinear fibre impairments in coherent systems employing spectrally efficient modulation formats

We investigate electronic mitigation of linear and non-linear fibre impairments and compare various digital signal processing techniques, including electronic dispersion compensation (EDC), single-channel back-propagation (SC-BP) and back-propagation with multiple channel processing (MC-BP) in a nine-channel 112 Gb/s PM-mQAM (m=4,16) WDM system, for reaches up to 6,320 km. We show that, for a sufficiently high local dispersion, SC-BP is sufficient to provide a significant performance enhancement when compared to EDC, and is adequate to achieve BER below FEC threshold. For these conditions we report that a sampling rate of two samples per symbol is sufficient for practical SC-BP, without significant penalties.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.