Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Robust multivariable control of complex biological processes

This paper addresses advanced control of a biological nutrient removal (BNR) activated sludge process. Based on a previously validated distributed parameter model of the BNR activated sludge process, we present robust multivariable controller designs for the process, involving loop shaping of plant model, robust stability and performance analyses. Results from three design case studies showed that a multivariable controller with stability margins of 0.163, 0.492 and 1.062 measured by the normalised coprime factor, multiplicative and additive uncertainties respectively give the best results for meeting performance robustness specifications. The controller robustly stabilises effluent nutrients in the presence of uncertainties with the behaviour of phosphorus accumulating organisms as well as to effectively attenuate major disturbances introduced as step changes. This study also shows that, performance of the multivariable robust controller is superior to multi-loops SISO PI controllers for regulating the BNR activated sludge process in terms of robust stability and performance and controlling the process using inlet feed flowrate is infeasible. (C) 2003 Elsevier Ltd. All rights reserved.

The early sperm gets the good egg: mating order effects in free spawners

Mating order can have important consequences for the fertilization success of males whose ejaculates compete to fertilize a clutch of eggs. Despite an excellent body of literature on mating-order effects in many animals, they have rarely been considered in marine free-spawning invertebrates, where both sexes release gametes into the water column. In this study, we show that in such organisms, mating order can have profound repercussions for male reproductive success. Using in vitro fertilization for two species of sea urchin we found that the 'fertilization history' of a clutch of eggs strongly influenced the size distribution of unfertilized eggs, and consequently the likelihood that they will be fertilized. Males that had first access to a batch of eggs enjoyed elevated fertilization success because they had privileged access to the largest and therefore most readily fertilizable eggs within a clutch. By contrast, when a male's sperm were exposed to a batch of unfertilized eggs left over from a previous mating event, fertilization rates were reduced, owing to smaller eggs remaining in egg clutches previously exposed to sperm. Because of this size-dependent fertilization, the fertilization history of eggs also strongly influenced the size distribution of offspring, with first-spawning males producing larger, and therefore fitter, offspring. These findings suggest that when there is variation in egg size, mating order will influence not only the quantity but also the quality of offspring sired by competing males.

Noninertial observers in special relativity and clock synchronization debates

Selleri's arguments that a consideration of noninertial reference frames in the framework of special relativity identify absolute simultaneity as being Nature's choice of synchronization are considered. In the case of rectilinearly accelerating rockets, it is argued by considering two rockets which maintain a fixed proper separation rather than a fixed separation relative to the inertial frame in which they start from rest, that what seems the most natural choice for a simultaneity convention is problem-dependent and that Einstein's definition is the most natural (though still conventional) choice in this case. In addition, the supposed problems special relativity has with treating a rotating disk, namely how a pulse of light traveling around the circumference of the disk can have a local speed of light equal to c everywhere but a global speed not equal to c, and how coordinate transformations to the disk can give the Lorentz transformations in the limit of large disk radius but small angular velocity, are addressed. It is shown that the theory of Fermi frames solves both of these problems. It is also argued that the question of defining simultaneity relative to a uniformly rotating disk does riot need to be resolved in order to resolve Ehrenfest's paradox.

Reduced genetic diversity and significant genetic differentiation after translocation: Comparison of the remnant and translocated populations of bridled nailtail wallabies (Onychogalea fraenata)

Loss of genetic diversity and increased population differentiation from source populations are common problems associated with translocation programmes established from captive-bred stock or a small number of founders. The bridled nailtail wallaby is one of the most endangered macropods in Australia, having been reduced to a single remnant population in the last 100 years. A translocated population of bridled nailtail wallabies was established using animals sourced directly from the remnant population (wild-released) as well as the progeny of animals collected for a captive breeding programme (captive-bred). The aims of this study were to compare genetic diversity among released animals and their wild-born progeny to genetic diversity observed in the remnant population, and to monitor changes in genetic diversity over time as more animals were released into the population. Heterozygosity did not differ between the translocated and remnant population; however, allelic diversity was significantly reduced across all released animals and their wild-born progeny. Animals bred in captivity and their wild-born progeny were also significantly differentiated from the source population after just four generations. Wild-released animals, however, were representative of the source population and several alleles were unique to this group. Both heterozygosity and allelic diversity among translocated animals decreased over time with the additional release of captive-bred animals, as no new genetic stock was added to the population. Captive breeding programmes can provide large numbers of animals for release, but this study highlights the importance of sourcing animals directly from remnant populations in order to maintain genetic diversity and minimise genetic drift.

Reflexive optokinetic nystagmus in younger and older observers under photopic and mesopic viewing conditions

PURPOSE. To investigate the effect of age on optokinetic nystagmus (OKN) in response to stimuli designed to preferentially stimulate the M-pathway. METHOD. OKN was recorded in 10 younger (32.3 +/- 5.98 years) and 10 older (65.6 +/- 6.53) subjects with normal vision. Vertical gratings of 0.43 or 1.08 cpd drifting at 5 degrees/s or 20 degrees/s and presented at either 8% or 80% contrast were displayed on a large screen as full-field stimulation, central stimulation within a central Gaussian-blurred window of 15 diameter, or peripheral stimulation outside this window. All conditions apart from the high-contrast condition were presented in a random order at two light levels, mesopic (1.8 cdm(-2)) and photopic (71.5 cdm(-2)). RESULTS. Partial-field data indicated that central stimulation, mesopic light levels, and lower temporal frequency each significantly increased slow-phase velocity (SPV). Although there was no overall difference between groups for partial-field stimulation, full-field stimulation, or low-contrast stimulation, a change in illumination revealed a significant interaction with age: there was a larger decrease in SPV going from photopic to mesopic conditions for the older group than the younger group, especially for higher temporal frequency stimulation. CONCLUSIONS. OKN becomes reflexive in conditions conducive to M-pathway stimulation, and this rOKN response is significantly diminished in older healthy adults than in younger healthy adults, indicative of decreased M-pathway sensitivity.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Teleportation with a uniformly accelerated partner

In this work, we give a description of the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies-Unruh radiation in Rob's frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in noninertial frames.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Fixed bed reactors with catalyst poisoning - first order kinetics.

The long performance of an isothermal fixed bed reactor undergoing catalyst poisoning is theoretically analyzed using the dispersion model. First order reaction with dth order deactivation is assumed and the model equations are solved by matched asymptotic expansions for large Peclet number. Simple closed-form solutions, uniformly valid in time, are obtained.

Gypsum solubility in seawater, and its application to bauxite residue amelioration

The solubilities and dissolution rates of three gypsum sources (analytical grade (AG), phosphogypsum (PG) and mined gypsum (MG)) with six MG size fractions ((mm) > 2.0, 1.0-2.0, 0.5-1.0, 0.25-0.5, 0.125-0.25, and < 0.125) were investigated in triple deionised water (TDI) and seawater to examine their suitability for bauxite residue amelioration. Gypsum solubility was greater in seawater (3.8 g L 1) than TDI (2.9 g L 1) due to the ionic strength effect, with dissolution in both TDI and seawater following first order kinetics. Dissolution rate constants varied with gypsum source (AR > PG > MG) due to reactivity and surface area differences, with 1:20 gypsum:solution suspensions reaching saturation within 15 s (AR) to 30 min (MG > 2.0). The ability of bauxite residue to adsorb Ca from solution was also examined. The quantity of the total solution Ca adsorbed was found to be small (5 %). These low rates of solution Ca adsorption combined with the comparatively rapid dissolution rates preclude the application of gypsum to the residue sand/seawater slurry as a method for residue amelioration. Instead, direct field application to the residue would ensure more efficient gypsum use. In addition, the formation of a sparingly soluble CaCO3 coating around the gypsum particles after mixing in a highly alkaline seawater/supernatant liquor (SNL) solution greatly reduced the rate of gypsum dissolution.

The kinetics of NO and N2O reduction over coal chars in fluidised-bed combustion

This paper presents a comprehensive and critical review of the mechanisms and kinetics of NO and N2O reduction reaction with coal chars under fluidised-bed combustion conditions (FBC). The heterogeneous reactions of NO and N2O with char/carbon surface have been well recognised as the most important processes in reducing both NOx and N2O in situ FBC. Compared to NO-carbon reactions in FBC, the reactions of N2O with chars have been relatively less understood and studied. Beginning with the overall reaction schemes for both NO and N2O reduction, the paper extensively discusses the reaction mechanisms including the effects of active surface sites. Generally, NO- and N2O-carbon reactions follow a series of step reactions. However, questions remain concerning the role of adsorbed phases of NO and N2O, and the behaviour of different surface sites. Important kinetics factors such as the rate expressions, kinetics parameters as well as the effects of surface area and pore structure are discussed in detail. The main factors influencing the reduction of NO and N2O in FBC conditions are the chemical and physical properties of chars, and the operating parameters of FBC such as temperature, presence of CO, O-2 and pressure. It is shown that under similar conditions, N2O is more readily reduced on the char surface than NO. Temperature was found to be a very important parameter in both NO and N2O reduction. It is generally agreed that both NO- and N2O-carbon reactions follow first-order reaction kinetics with respect to the NO and N2O concentrations. The kinetic parameters for NO and N2O reduction largely depend on the pore structure of chars. The correlation between the char surface area and the reactivities of NO/N2O-char reactions is considered to be of great importance to the determination of the reaction kinetics. The rate of NO reduction by chars is strongly enhanced by the presence of CO and O-2, but these species may not have significant effects on the rate of N2O reduction. However, the presence of these gases in FBC presents difficulties in the study of kinetics since CO cannot be easily eliminated from the carbon surface. In N2O reduction reactions, ash in chars is found to have significant catalytic effects, which must be accounted for in the kinetic models and data evaluation. (C) 1997 Elsevier Science Ltd.

Catalytic activities and coking characteristics of oxides-supported Ni catalysts for CH4 reforming with carbon dioxide

Catalytic activities and deactivation characteristics of oxides-supported nickel catalysts for the reaction of methane reforming with carbon dioxide were investigated. The dynamic carbon deposition on various nickel catalysts was also studied by a thermogravimetric method. Among the catalysts prepared, Ni/La2O3, Ni/alpha-Al2O3, Ni/SiO2, and Ni/CeO2 showed very high CH4 and CO2 conversions and moderate deactivation whereas Ni/MgO and Ni/TiO2 had lower conversions when the Ni reduction was conducted at 500 degrees C. When Ni/MgO catalyst was reduced at 800 degrees C, it exhibited not only comparable conversions of CH4 and CO2 with other active catalysts but also much longer period of stability without deactivation. The amount of carbon deposited in Ni-based catalysts varied depending on the nature of support and followed the order of Ni/La2O3 > Ni/alpha-Al2O3 > Ni/SiO2 > Ni/MgO > Ni/CeO2 at 700 degrees C. The carbons formed on the catalyst surface showed different structural and chemical properties, and these in turn affected the catalytic activity of the catalysts.

Chirality of reduced haloperidol in humans

In vitro, cytosolic human ketone reductases catalyse the stereospecific (i.e. >99%) formation of S(-) reduced haloperidol (RHP) from haloperidol (HP). Whether this situation is reflected in patients taking the drug is unknown. In this study in nine patients taking HP, only 73.2+/-18.2% of the RHP excreted in urine was the S(-) enantiomer. Thus, enzymes other than cytosolic ketone reductases must be responsible for the formation of the minor enantiomer. (C) 1998 Elsevier Science B.V./ECNP.

Crystal structures of reduced and oxidized DsbA: investigation of domain motion and thiolate stabilization

Background: The redox proteins that incorporate a thioredoxin fold have diverse properties and functions. The bacterial protein-folding factor DsbA is the most oxidizing of the thioredoxin family. DsbA catalyzes disulfide-bond formation during the folding of secreted proteins, The extremely oxidizing nature of DsbA has been proposed to result from either domain motion or stabilizing active-site interactions in the reduced form. In the domain motion model, hinge bending between the two domains of DsbA occurs as a result of redox-related conformational changes. Results: We have determined the crystal structures of reduced and oxidized DsbA in the same crystal form and at the same pH (5.6). The crystal structure of a lower pH form of oxidized DsbA has also been determined (pH 5.0). These new crystal structures of DsbA, and the previously determined structure of oxidized DsbA at pH 6.5, provide the foundation for analysis of structural changes that occur upon reduction of the active-site disulfide bond. Conclusions: The structures of reduced and oxidized DsbA reveal that hinge bending motions do occur between the two domains. These motions are independent of redox state, however, and therefore do not contribute to the energetic differences between the two redox states, instead, the observed domain motion is proposed to be a consequence of substrate binding. Furthermore, DsbA's highly oxidizing nature is a result of hydrogen bond, electrostatic and helix-dipole interactions that favour the thiolate over the disulfide at the active site.