Hierarchical control and optimisation of the Tennessee Eastman process

Based on integrated system optimisation and parameter estimation a method is described for on-line steady state optimisation which compensates for model-plant mismatch and solves a non-linear optimisation problem by iterating on a linear - quadratic representation. The method requires real process derivatives which are estimated using a dynamic identification technique. The utility of the method is demonstrated using a simulation of the Tennessee Eastman benchmark chemical process.

Variable step-size LMS blind CDMA multiuser detectors

Adaptive least mean square (LMS) filters with or without training sequences, which are known as training-based and blind detectors respectively, have been formulated to counter interference in CDMA systems. The convergence characteristics of these two LMS detectors are analyzed and compared in this paper. We show that the blind detector is superior to the training-based detector with respect to convergence rate. On the other hand, the training-based detector performs better in the steady state, giving a lower excess mean-square error (MSE) for a given adaptation step size. A novel decision-directed LMS detector which achieves the low excess MSE of the training-based detector and the superior convergence performance of the blind detector is proposed.

Long-term effect of volcanic forcing on ocean heat content

Explosive volcanic eruptions cause episodic negative radiative forcing of the climate system. Using coupled atmosphere-ocean general circulation models (AOGCMs) subjected to historical forcing since the late nineteenth century, previous authors have shown that each large volcanic eruption is associated with a sudden drop in ocean heat content and sea-level from which the subsequent recovery is slow. Here we show that this effect may be an artefact of experimental design, caused by the AOGCMs not having been spun up to a steady state with volcanic forcing before the historical integrations begin. Because volcanic forcing has a long-term negative average, a cooling tendency is thus imposed on the ocean in the historical simulation. We recommend that an extra experiment be carried out in parallel to the historical simulation, with constant time-mean historical volcanic forcing, in order to correct for this effect and avoid misinterpretation of ocean heat content changes

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Forecasting the future: an overview of the strategic planning of the Bournemouth and Poole conurbation

An important part of strategic planning’s purpose should be to attempt to forecast the future, not simply to belatedly respond to events, or accept the future as inevitable. This paper puts forward a conceptual approach for seeking to achieve these aims and uses the Bournemouth and Poole area in Dorset as a vehicle for applying the basic methodology. The area has been chosen because of the significant issues that it currently faces in planning terms; and its future development possibilities. In order that alternative future choices for the area – different ‘developmental trajectories’ – can be evaluated, they must be carefully and logically constructed. Four Futures for Bournemouth/Poole have been put forward; they are titled and colour-coded: Future One is Maximising Growth – Golden Prospect which seeks to achieve the highest level of economic prosperity of the area; Future Two is Incremental Growth – Solid Silver which attempts to facilitate a steady, continuing, controlled pattern of the development for the area; Future Three is Steady State – Cobalt Blue which suggests that people in the area could be more concerned with preserving their quality of life in terms of their leisure and recreation rather than increasing wealth; Future Four is Environment First – Jade Green which makes the area’s environmental protection its top priority even at the possible expense of economic prosperity. The scenarios proposed here are not sacrosanct. Nor are they simply confined to the Bournemouth and Poole area. In theory, suitably modified, they could use in a variety of different contexts. Consideration of the scenarios – wherever located - might then generate other, additional scenarios. These are called hybrids, alloys and amalgams. Likewise it might identify some of them as inappropriate or impossible. Most likely, careful consideration of the scenarios will suggest hybrid scenarios, in which features from different scenarios are combined to produce alternative or additional futures for consideration. The real issue then becomes how best to fashion such a future for the particular area under consideration

Reduced complexity set-point following in self-tuning control

An external input signal is incorporated into a self-tuning controller which, although it is based on a CARMA system model, employs a state-space framework for control law calculations. Steady-state set point following can then be accomplished even when only a recursive least squares parameter estimation scheme is used, despite the fact that the disturbance affecting the system may well be coloured.

An isotope dilution model for partitioning phenylalanine uptake by the liver of lactating dairy cows

An isotope dilution model for partitioning phenylalanine uptake by the liver of the lactating dairy cow was constructed and solved in the steady state. If assumptions are made, model solution permits calculation of the rate of phenylalanine uptake from portal vein and hepatic arterial blood supply, phenylalanine release into the hepatic vein, phenylalanine oxidation and synthesis, and degradation of hepatic constitutive and export proteins. The model requires the measurement of plasma fow rate through the liver in combination with phenylalanine concentrations and plateau isotopic enrichments in arterial, portal and hepatic plasma during a constant infusion of [1-13C]phenylalanine tracer. The model can be applied to other amino acids with similar metabolic fates and will provide a means for assessing the impact of hepatic metabolism on amino acid availability to peripheral tissues. This is of particular importance for the dairy cow when considering the requirements for milk protein synthesis and the negative environmental impact of excessive nitrogen excretion.

An ocean modelling and assimilation guide to using GOCE geoid products

We review the procedures and challenges that must be considered when using geoid data derived from the Gravity and steady-state Ocean Circulation Explorer (GOCE) mission in order to constrain the circulation and water mass representation in an ocean 5 general circulation model. It covers the combination of the geoid information with timemean sea level information derived from satellite altimeter data, to construct a mean dynamic topography (MDT), and considers how this complements the time-varying sea level anomaly, also available from the satellite altimeter. We particularly consider the compatibility of these different fields in their spatial scale content, their temporal rep10 resentation, and in their error covariances. These considerations are very important when the resulting data are to be used to estimate ocean circulation and its corresponding errors. We describe the further steps needed for assimilating the resulting dynamic topography information into an ocean circulation model using three different operational fore15 casting and data assimilation systems. We look at methods used for assimilating altimeter anomaly data in the absence of a suitable geoid, and then discuss different approaches which have been tried for assimilating the additional geoid information. We review the problems that have been encountered and the lessons learned in order the help future users. Finally we present some results from the use of GRACE geoid in20 formation in the operational oceanography community and discuss the future potential gains that may be obtained from a new GOCE geoid.

The relationship between land–ccean surface temperature contrast and radiative forcing

Previous work has demonstrated that observed and modeled climates show a near-time-invariant ratio of mean land to mean ocean surface temperature change under transient and equilibrium global warming. This study confirms this in a range of atmospheric models coupled to perturbed sea surface temperatures (SSTs), slab (thermodynamics only) oceans, and a fully coupled ocean. Away from equilibrium, it is found that the atmospheric processes that maintain the ratio cause a land-to-ocean heat transport anomaly that can be approximated using a two-box energy balance model. When climate is forced by increasing atmospheric CO2 concentration, the heat transport anomaly moves heat from land to ocean, constraining the land to warm in step with the ocean surface, despite the small heat capacity of the land. The heat transport anomaly is strongly related to the top-of-atmosphere radiative flux imbalance, and hence it tends to a small value as equilibrium is approached. In contrast, when climate is forced by prescribing changes in SSTs, the heat transport anomaly replaces ‘‘missing’’ radiative forcing over land by moving heat from ocean to land, warming the land surface. The heat transport anomaly remains substantial in steady state. These results are consistent with earlier studies that found that both land and ocean surface temperature changes may be approximated as local responses to global mean radiative forcing. The modeled heat transport anomaly has large impacts on surface heat fluxes but small impacts on precipitation, circulation, and cloud radiative forcing compared with the impacts of surface temperature change. No substantial nonlinearities are found in these atmospheric variables when the effects of forcing and surface temperature change are added.

Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change

Atmosphere–ocean general circulation models (AOGCMs) predict a weakening of the Atlantic meridional overturning circulation (AMOC) in response to anthropogenic forcing of climate, but there is a large model uncertainty in the magnitude of the predicted change. The weakening of the AMOC is generally understood to be the result of increased buoyancy input to the north Atlantic in a warmer climate, leading to reduced convection and deep water formation. Consistent with this idea, model analyses have shown empirical relationships between the AMOC and the meridional density gradient, but this link is not direct because the large-scale ocean circulation is essentially geostrophic, making currents and pressure gradients orthogonal. Analysis of the budget of kinetic energy (KE) instead of momentum has the advantage of excluding the dominant geostrophic balance. Diagnosis of the KE balance of the HadCM3 AOGCM and its low-resolution version FAMOUS shows that KE is supplied to the ocean by the wind and dissipated by viscous forces in the global mean of the steady-state control climate, and the circulation does work against the pressure-gradient force, mainly in the Southern Ocean. In the Atlantic Ocean, however, the pressure-gradient force does work on the circulation, especially in the high-latitude regions of deep water formation. During CO2-forced climate change, we demonstrate a very good temporal correlation between the AMOC strength and the rate of KE generation by the pressure-gradient force in 50–70°N of the Atlantic Ocean in each of nine contemporary AOGCMs, supporting a buoyancy-driven interpretation of AMOC changes. To account for this, we describe a conceptual model, which offers an explanation of why AOGCMs with stronger overturning in the control climate tend to have a larger weakening under CO2 increase

Orientational behaviour of thermotropic and lyotropic liquid crystal polymer systems under shear flow

A comparison is made of the development of global orientation during shearing of lyotropic solutions of hydroxypropylcellulose with that observed for the thermotropic phase of hydroxypropylcellulose. At shear rates the behaviour of the two systems is similar, both during steady-state shear, and in terms of relaxation following cessation of shear flow. At low shear rates, the levels of orientation observed for the thermotropic system are substantially greater than observed for the lyotropic solutions. The relationship of these differences to variations in molecular parameters, viscous stress and to director tumbling is discussed.

Time-resolved in situ X-ray scattering studies of aqueous hydroxypropylcellulose solutions

The evolution of the global orientation parameter for a series of aqueous hydroxypropylcellulose solutions both during and following the cessation of a steady-state shear flow is reported. Time-resolved orientation measurements were made in situ through a novel X-ray rheometer coupled with a two-dimensional electronic X-ray camera, and using an intense X-ray source at the LURE synchrotron. After the cessation of flow, the global orientation decreases from the steady-state orientation level to zero following shear flow at low shear rate or to a small but finite value after flow at a high shear rate. The decrease of orientation with time shows different behaviour, dependent upon the previously applied shear rate.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Precise calculations of the existence of multiple AMOC equilibria in coupled climate models Part I: equilibrium states

This study examines criteria for the existence of two stable states of the Atlantic Meridional Overturning Circulation (AMOC) using a combination of theory and simulations from a numerical coupled atmosphere–ocean climate model. By formulating a simple collection of state parameters and their relationships, the authors reconstruct the North Atlantic Deep Water (NADW) OFF state behavior under a varying external salt-flux forcing. This part (Part I) of the paper examines the steady-state solution, which gives insight into the mechanisms that sustain the NADW OFF state in this coupled model; Part II deals with the transient behavior predicted by the evolution equation. The nonlinear behavior of the Antarctic Intermediate Water (AAIW) reverse cell is critical to the OFF state. Higher Atlantic salinity leads both to a reduced AAIW reverse cell and to a greater vertical salinity gradient in the South Atlantic. The former tends to reduce Atlantic salt export to the Southern Ocean, while the latter tends to increases it. These competing effects produce a nonlinear response of Atlantic salinity and salt export to salt forcing, and the existence of maxima in these quantities. Thus the authors obtain a natural and accurate analytical saddle-node condition for the maximal surface salt flux for which a NADW OFF state exists. By contrast, the bistability indicator proposed by De Vries and Weber does not generally work in this model. It is applicable only when the effect of the AAIW reverse cell on the Atlantic salt budget is weak.