Improved MATLAB GUIs for learning frequency response methods

The author developed two GUIs for asymptotic Bode plots and identification from such plots aimed at improving the learning of frequency response methods: these were presented at UKACC Control 2012. Student feedback and reflection by the author suggested various improvements to these GUIs, which have now been implemented. This paper reviews the earlier work, describes the improvements, and includes positive feedback from the students on the GUIs and how they have helped their understanding of the methods.

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

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.

Quartz crystal microbalance monitoring of density changes in mesoporous TiO2 phytate films during redox and ion exchange processes

Nanofilm deposits of TiO2 nanoparticle phytates are formed on gold electrode surfaces by 'directed assembly' methods. Alternate exposure of a 3-mercapto-propionic acid modified gold surface to (i) a TiO2 sol and (ii) an aqueous phytic acid solution (pH 3) results in layer-by-layer formation of a mesoporous film. Ru(NH3)(6)(3+) is shown to strongly adsorb/accumulate into the mesoporous structure whilst remaining electrochemically active. Scanning the electrode potential into a sufficiently negative potential range allows the Ru(NH3)(6)(3+) complex to be reduced to Ru(NH3)(6)(2+) which undergoes immediate desorption. When applied to a gold coated quartz crystal microbalance (QCM) sensor, electrochemically driven adsorption and desorption processes in the mesoporous structure become directly detectable as a frequency response, which corresponds directly to a mass or density change in the membrane. The frequency response (at least for thin films) is proportional to the thickness of the mass-responsive film, which suggests good mechanical coupling between electrode and film. Based on this observation, a method for the amplified QCM detection of small mass/density changes is proposed by conducting measurements in rigid mesoporous structures. (C) 2003 Elsevier Science B.V. All rights reserved.

Designing dietary interventions: a reappraisal of the demographic and socio-economic determinants of dietary choice in the UK

The facilitation of healthier dietary choices by consumers is one of the key elements of the UK Government’s food strategy. Designing and targeting dietary interventions requires a clear understanding of the determinants of dietary choice. Conventional analysis of the determinants of dietary choice has focused on mean response functions which may mask significant differences in the dietary behaviour of different segments of the population. In this paper we use a quantile regression approach to investigate how food consumption behaviour varies amongst UK households in different segments of the population, especially in the upper and lower quantiles characterised by healthy or unhealthy consumption patterns. We find that the effect of demographic determinants of dietary choice on households that exhibit less healthy consumption patterns differs significantly from that on households that make healthier consumption choices. A more nuanced understanding of the differences in the behavioural responses of households making less-healthy eating choices provides useful insights for the design and targeting of measures to promote healthier diets.

Microcontroller-based peak current mode control using digital slope compensation

Microcontroller-based peak current mode control of a buck converter is investigated. The new solution uses a discrete time controller with digital slope compensation. This is implemented using only a single-chip microcontroller to achieve desirable cycle-by-cycle peak current limiting. The digital controller is implemented as a two-pole, two-zero linear difference equation designed using a continuous time model of the buck converter and a discrete time transform. Subharmonic oscillations are removed with digital slope compensation using a discrete staircase ramp. A 16 W hardware implementation directly compares analog and digital control. Frequency response measurements are taken and it is shown that the crossover frequency and expected phase margin of the digital control system match that of its analog counterpart.

Temporal coupling between stimulus-evoked neural activity and hemodynamic responses from individual cortical columns

Using previously published data from the whisker barrel cortex of anesthetized rodents (Berwick et al 2008 J. Neurophysiol. 99 787–98) we investigated whether highly spatially localized stimulus-evoked cortical hemodynamics responses displayed a linear time-invariant (LTI) relationship with neural activity. Presentation of stimuli to individual whiskers of 2 s and 16 s durations produced hemodynamics and neural activity spatially localized to individual cortical columns. Two-dimensional optical imaging spectroscopy (2D-OIS) measured hemoglobin responses, while multi-laminar electrophysiology recorded neural activity. Hemoglobin responses to 2 s stimuli were deconvolved with underlying evoked neural activity to estimate impulse response functions which were then convolved with neural activity evoked by 16 s stimuli to generate predictions of hemodynamic responses. An LTI system more adequately described the temporal neuro-hemodynamics coupling relationship for these spatially localized sensory stimuli than in previous studies that activated the entire whisker cortex. An inability to predict the magnitude of an initial 'peak' in the total and oxy- hemoglobin responses was alleviated when excluding responses influenced by overlying arterial components. However, this did not improve estimation of the hemodynamic responses return to baseline post-stimulus cessation.

Evaluating forecasts from SETAR models of exchange rates

We consider the forecasting performance of two SETAR exchange rate models proposed by Kräger and Kugler [J. Int. Money Fin. 12 (1993) 195]. Assuming that the models are good approximations to the data generating process, we show that whether the non-linearities inherent in the data can be exploited to forecast better than a random walk depends on both how forecast accuracy is assessed and on the ‘state of nature’. Evaluation based on traditional measures, such as (root) mean squared forecast errors, may mask the superiority of the non-linear models. Generalized impulse response functions are also calculated as a means of portraying the asymmetric response to shocks implied by such models.

The ocean's role in polar climate change: asymmetric Arctic and Antarctic responses to greenhouse gas and ozone forcing

In recent decades, the Arctic has been warming and sea ice disappearing. By contrast, the Southern Ocean around Antarctica has been (mainly) cooling and sea-ice extent growing. We argue here that interhemispheric asymmetries in the mean ocean circulation, with sinking in the northern North Atlantic and upwelling around Antarctica, strongly influence the sea-surface temperature (SST) response to anthropogenic greenhouse gas (GHG) forcing, accelerating warming in the Arctic while delaying it in the Antarctic. Furthermore, while the amplitude of GHG forcing has been similar at the poles, significant ozone depletion only occurs over Antarctica. We suggest that the initial response of SST around Antarctica to ozone depletion is one of cooling and only later adds to the GHG-induced warming trend as upwelling of sub-surface warm water associated with stronger surface westerlies impacts surface properties. We organize our discussion around ‘climate response functions’ (CRFs), i.e. the response of the climate to ‘step’ changes in anthropogenic forcing in which GHG and/or ozone-hole forcing is abruptly turned on and the transient response of the climate revealed and studied. Convolutions of known or postulated GHG and ozone-hole forcing functions with their respective CRFs then yield the transient forced SST response (implied by linear response theory), providing a context for discussion of the differing warming/cooling trends in the Arctic and Antarctic. We speculate that the period through which we are now passing may be one in which the delayed warming of SST associated with GHG forcing around Antarctica is largely cancelled by the cooling effects associated with the ozone hole. By mid-century, however, ozone-hole effects may instead be adding to GHG warming around Antarctica but with diminished amplitude as the ozone hole heals. The Arctic, meanwhile, responding to GHG forcing but in a manner amplified by ocean heat transport, may continue to warm at an accelerating rate.

Sensory enhancement, a pilot perceptual study of subdermal magnetic implants

Subdermal magnetic implants originated as an art form in the world of body modification. To date an in depth scientific analysis of the benefits of this implant has yet to be established. This research explores the concept of sensory extension of the tactile sense utilising this form of implantation. This relatively simple procedure enables the tactile sense to respond to static and alternating magnetic fields. This is not to say that the underlying biology of the system has changed; i.e. the concept does not increase our tactile frequency response range or sensitivity to pressure, but now does invoke a perceptual response to a stimulus that is not innately available to humans. Within this research two social surveys have been conducted in order to ascertain one, the social acceptance of the general notion of human enhancement, and two the perceptual experiences of individuals with the magnetic implants themselves. In terms of acceptance to the notion of sensory improvement (via implantation) ~39% of the general population questioned responded positively with a further ~25% of the respondents answering with the indecisive response. Thus with careful dissemination a large proportion of individuals may adopt this technology much like this if it were to become available for consumers. Interestingly of the responses collected from the magnetic implants survey ~60% of the respondents actually underwent the implant for magnetic vision purposes. The main contribution of this research however comes from a series of psychophysical testing. In which 7 subjects with subdermal magnetic implants, were cross compared with 7 subjects that had similar magnets superficially attached to their dermis. The experimentation examined multiple psychometric thresholds of the candidates including intensity, frequency and temporal. Whilst relatively simple, the experimental setup for the perceptual experimentation conducted was novel in that custom hardware and protocols were created in order to determine the subjective thresholds of the individuals. Abstract iv The overall purpose of this research is to utilise this concept in high stress scenarios, such as driving or piloting; whereby alerts and warnings could be relayed to an operator without intruding upon their other (typically overloaded) exterior senses (i.e. the auditory and visual senses). Hence each of the thresholding experiments were designed with the intention of utilising the results in the design of signals for information transfer. The findings from the study show that the implanted group of subjects significantly outperformed the superficial group in the absolute intensity threshold experiment, i.e. the implanted group required significantly less force than the superficial group in order to perceive the stimulus. The results for the frequency difference threshold showed no significant difference in the two groups tested. Interestingly however at low frequencies, i.e. 20 and 50 Hz, the ability of the subjects tested to discriminate frequencies significantly increased with more complex waveforms i.e. square and sawtooth, when compared against the typically used sinewave. Furthermore a novel protocol for establishing the temporal gap detection threshold during a temporal numerosity study has been established in this thesis. This experiment measured the subjects’ capability to correctly determine the number of concatenated signals presented to them whilst the time between the signals, referred to as pulses, tended to zero. A significant finding was that when altering the length of, the frequency of, and the number of cycles of the pulses, the time between pulses for correct recognition altered. This finding will ultimately aid in the design of the tactile alerts for this method of information transfer. Preliminary development work for the use of this method of input to the body, in an automotive scenario, is also presented within this thesis in the form of a driving simulation. The overall goal of which is to present warning alerts to a driver, such as rear-to-end collision, or excessive speeds on roads, in order to prevent incidents and penalties from occurring. Discussion on the broader utility of this implant has been presented, reflecting on its potential use as a basis for vibrotactile, and sensory substitution, devices. This discussion furthers with postulations on its use as a human machine interface, as well as how a similar implant could be used within the ear as a hearing aid device.

A comparative value of electricity storage within GB market mechanisms

This paper investigates the value of a generic storage system within two GB market mechanisms and one ancillary service provision: the wholesale power market, the Balancing Mechanism and Firm Frequency Response (FFR). Three models are evaluated under perfect foresight and fixed horizon which is subsequently extended to explore the impact of a longer foresight on market revenues. The results show that comparatively, the balancing mechanism represents the highest source of potential revenues followed by the wholesale power market and Firm Frequency Response respectively. Longer horizons show diminishing returns, with the 1 day horizon providing the vast majority of total revenues. However storage power capacity utilization benefits from such long horizons. These results could imply that short horizons are very effective in capturing revenues in both the wholesale market and balancing mechanism whereas sizing of a storage system should take into consideration horizon foresight and accuracy for greater benefit.

Output sustainability to exogenous and endogenous shocks: evidence from emerging economies

This paper studies the impact of exogenous and endogenous shocks (exogenous shock is used interchangeably with external shock; endogenous shock is used interchangeably with domestic shock) on output fluctuations in post-communist countries during the 2000s. The first part presents the analytical framework and formulates a research hypothesis. The second part presents vector autoregressive estimation and analysis model proposed by Pesaran (2004) and Pesaran and Smith (2006) that relates bank real lending, the cyclical component of output and spreads and accounts for cross-sectional dependence (CD) across the countries. Impulse response functions show that exogenous positive shock lead to a drop in output sustainability for 9 over 12 Central Eastern European countries and Russia, when the endogenous shock is mild and ambiguous. Moreover, the effect of exogenous shock is more significant during the crises. Variance decompositions show that exogenous shock in the aftermath of crisis had a substantial impact on economic activity of emerging economies.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Variability of the Atlantic thermohaline circulation described by three-dimensional empirical orthogonal functions

We describe the use of bivariate 3d empirical orthogonal functions (EOFs) in characterising low frequency variability of the Atlantic thermohaline circulation (THC) in the Hadley Centre global climate model, HadCM3. We find that the leading two modes are well correlated with an index of the meridional overturning circulation (MOC) on decadal timescales, with the leading mode alone accounting for 54% of the decadal variance. Episodes of coherent oscillations in the sub-space of the leading EOFs are identified; these episodes are of great interest for the predictability of the THC, and could indicate the existence of different regimes of natural variability. The mechanism identified for the multi-decadal variability is an internal ocean mode, dominated by changes in convection in the Nordic Seas, which lead the changes in the MOC by a few years. Variations in salinity transports from the Arctic and from the North Atlantic are the main feedbacks which control the oscillation. This mode has a weak feedback onto the atmosphere and hence a surface climatic influence. Interestingly, some of these climate impacts lead the changes in the overturning. There are also similarities to observed multi-decadal climate variability.

The response of a uniform horizontal temperature gradient to heating

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.