The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

2D hexagonal mesoporous platinum films exhibiting biaxial, in-plane pore alignment

The synthesis of 2D hexagonal mesoporous platinum films with biaxial, in-plane pore alignment is demonstrated by electrodeposition through an aligned lyotropic liquid crystal templating phase. Shear force is used to align a hexagonal lyotropic liquid crystalline templating phase of an inexpensive and a commercially available surfactant, C16EO10, at the surface of an electrode. Electrodeposition and subsequent characterisation of the films produced shows that the orientation and alignment of the phase is transferred to the deposited material. Transmission electron microscopy confirms the expected nanostructure of the films, whilst transmission and grazing incidence small angle X-ray scattering analysis confirms biaxial, in plane alignment of the pore structure. In addition further electrochemical studies in dilute sulfuric acid and methanol show that the pores are accessible to electrolyte solution as indicated by a large current flow; the modified electrode therefore has a high surface area, that catalyses methanol oxidation, and the pores have a very large aspect ratio (of theoretical maximum 2 × 105). Films with such aligned mesoporosity will advance the field of nanotechnology where the control of pore structure is paramount. The method reported is sufficiently generic to be used to control the structure and order of many materials, thus increasing the potential for the development of a wide range of novel electronic and optical devices.

Validation of three new measure-correlate-predict models for the long-term prospection of the wind resource

The estimation of the long-term wind resource at a prospective site based on a relatively short on-site measurement campaign is an indispensable task in the development of a commercial wind farm. The typical industry approach is based on the measure-correlate-predict �MCP� method where a relational model between the site wind velocity data and the data obtained from a suitable reference site is built from concurrent records. In a subsequent step, a long-term prediction for the prospective site is obtained from a combination of the relational model and the historic reference data. In the present paper, a systematic study is presented where three new MCP models, together with two published reference models �a simple linear regression and the variance ratio method�, have been evaluated based on concurrent synthetic wind speed time series for two sites, simulating the prospective and the reference site. The synthetic method has the advantage of generating time series with the desired statistical properties, including Weibull scale and shape factors, required to evaluate the five methods under all plausible conditions. In this work, first a systematic discussion of the statistical fundamentals behind MCP methods is provided and three new models, one based on a nonlinear regression and two �termed kernel methods� derived from the use of conditional probability density functions, are proposed. All models are evaluated by using five metrics under a wide range of values of the correlation coefficient, the Weibull scale, and the Weibull shape factor. Only one of all models, a kernel method based on bivariate Weibull probability functions, is capable of accurately predicting all performance metrics studied.

Effects of Thomson-scattering geometry on white-light imaging of an interplanetary shock: synthetic observations from forward magnetohydrodynamic modelling

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time–elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east–west asymmetry in its brightness and degree of polarisation. Therefore, measurement of the interplanetary polarised brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging.

The Limnology of Slapton Ley

Slapton Ley, a freshwater lake, located in south Devon (National Grid Reference SX 825 439), has been the focus of a wide range of research studies since the foundation of the Field Studies Council Centre in Slapton village in 1959, and the creation of the Slapton Ley Nature Reserve. Early concerns over eutrophication of the Lower Ley led to a range of studies focused on the impacts of land use change in the catchment, on nutrient delivery to the Ley, and on interpreting the impact of long-term nutrient enrichment of the Ley from palaeolimnological studies. What has been missing to date, however, is a focused study of the impacts of nutrient enrichment on the chemical and ecological structure and function of the combined Lower and Higher Ley systems. This paper attempts to draw together the various areas of study on the Ley to date in order to provide a review of current understanding of the limnology of Slapton Ley and to identify gaps in our knowledge. The past, present and future trophic status of the Ley is re-interpreted in the light of current understanding of the eutrophication process in the wider scientific community. Recommendations for future research are then made, with a view to the monitoring and management of Slapton Ley and its catchment.

Highly resolved observations of trace gases in the lowermost stratosphere and upper troposphere from the SPURT project: an overview

During SPURT (Spurenstofftransport in der Tropopausenregion, trace gas transport in the tropopause region) we performed measurements of a wide range of trace gases with different lifetimes and sink/source characteristics in the northern hemispheric upper troposphere (UT) and lowermost stratosphere (LMS). A large number of in-situ instruments were deployed on board a Learjet 35A, flying at altitudes up to 13.7 km, at times reaching to nearly 380 K potential temperature. Eight measurement campaigns (consisting of a total of 36 flights), distributed over all seasons and typically covering latitudes between 35° N and 75° N in the European longitude sector (10° W–20° E), were performed. Here we present an overview of the project, describing the instrumentation, the encountered meteorological situations during the campaigns and the data set available from SPURT. Measurements were obtained for N2O, CH4, CO, CO2, CFC12, H2, SF6, NO, NOy, O3 and H2O. We illustrate the strength of this new data set by showing mean distributions of the mixing ratios of selected trace gases, using a potential temperature-equivalent latitude coordinate system. The observations reveal that the LMS is most stratospheric in character during spring, with the highest mixing ratios of O3 and NOy and the lowest mixing ratios of N2O and SF6. The lowest mixing ratios of NOy and O3 are observed during autumn, together with the highest mixing ratios of N2O and SF6 indicating a strong tropospheric influence. For H2O, however, the maximum concentrations in the LMS are found during summer, suggesting unique (temperature- and convection-controlled) conditions for this molecule during transport across the tropopause. The SPURT data set is presently the most accurate and complete data set for many trace species in the LMS, and its main value is the simultaneous measurement of a suite of trace gases having different lifetimes and physical-chemical histories. It is thus very well suited for studies of atmospheric transport, for model validation, and for investigations of seasonal changes in the UT/LMS, as demonstrated in accompanying and elsewhere published studies.

A dynamic model of neurovascular coupling: Implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

Temperament, family environment and anxiety in preschool children

This research examines the relationship between behavioural inhibition (BI), family environment (overinvolved and negative parenting, parental anxiety and parent-child attachment) and anxiety in a sample of 202 preschool children. Participants were aged between 3 years 2 months and 4 years 5 months, 101 were male. A thorough methodology was used that incorporated data from multiple observations of behaviour, diagnostic interviews and questionnaire measures. The results showed that children categorised as behaviourally inhibited were significantly more likely to meet criteria for a range of anxiety diagnoses. Furthermore, a wide range of family environment factors, including maternal anxiety, parenting and attachment were significantly associated with BI, with inhibited children more likely to experience adverse family environment factors. No interactions between temperament and family environment were found for child anxiety. However, a significant relationship between current maternal anxiety and child anxiety was found consistently even after controlling for BI. Additionally, there was some evidence of a relationship between maternal negativity and child anxiety, after controlling for BI. The results may suggest that temperament and family environment operate as additive, rather than interactive risk factors for child anxiety. This is discussed in the context of theoretical models of child anxiety and directions for future research.

A self-calibrating electrometer for atmospheric charge measurements from a balloon platform

Charged aerosol particles and water droplets are abundant throughout the lower atmosphere, and may influence interactions between small cloud droplets. This note describes a small, disposable sensor for the measurement of charge in non-thunderstorm cloud, which is an improvement of an earlier sensor [K. A. Nicoll and R. G. Harrison, Rev. Sci. Instrum. 80, 014501 (2009)]. The sensor utilizes a self-calibrating current measurement method. It is designed for use on a free balloon platform alongside a standard meteorological radiosonde, measuring currents from 2 fA to 15 pA and is stable to within 5 fA over a temperature range of 5 °C to −60 °C. During a balloon flight with the charge sensor through a stratocumulus cloud, charge layers up to 40 pC m−3 were detected on the cloud edges.

A novel function of the proneural factor Ascl1 in progenitor proliferation identified by genome-wide characterization of its targets

Proneural genes such as Ascl1 are known to promote cell cycle exit and neuronal differentiation when expressed in neural progenitor cells. The mechanisms by which proneural genes activate neurogenesis--and, in particular, the genes that they regulate--however, are mostly unknown. We performed a genome-wide characterization of the transcriptional targets of Ascl1 in the embryonic brain and in neural stem cell cultures by location analysis and expression profiling of embryos overexpressing or mutant for Ascl1. The wide range of molecular and cellular functions represented among these targets suggests that Ascl1 directly controls the specification of neural progenitors as well as the later steps of neuronal differentiation and neurite outgrowth. Surprisingly, Ascl1 also regulates the expression of a large number of genes involved in cell cycle progression, including canonical cell cycle regulators and oncogenic transcription factors. Mutational analysis in the embryonic brain and manipulation of Ascl1 activity in neural stem cell cultures revealed that Ascl1 is indeed required for normal proliferation of neural progenitors. This study identified a novel and unexpected activity of the proneural gene Ascl1, and revealed a direct molecular link between the phase of expansion of neural progenitors and the subsequent phases of cell cycle exit and neuronal differentiation.

Does convective aggregation need to be represented in cumulus parameterizations?

Tropical deep convection exhibits a variety of levels of aggregation over a wide range of scales. Based on a multisatellite analysis, the present study shows at mesoscale that different levels of aggregation are statistically associated with differing large-scale atmospheric states, despite similar convective intensity and large-scale forcings. The more aggregated the convection, the dryer and less cloudy the atmosphere, the stronger the outgoing longwave radiation, and the lower the planetary albedo. This suggests that mesoscale convective aggregation has the potential to affect couplings between moisture and convection and between convection, radiation, and large-scale ascent. In so doing, aggregation may play a role in phenomena such as “hot spots” or the Madden-Julian Oscillation. These findings support the need for the representation of mesoscale organization in cumulus parameterizations; most parameterizations used in current climate models lack any such representation. The ability of a cloud system-resolving model to reproduce observed relationships suggests that such models may be useful to guide attempts at parameterizations of convective aggregation.

A low-cost wireless temperature sensor: evaluation for use in environmental applications

With a wide range of applications benefiting from dense network air temperature observations but with limitations of costs, existing siting guidelines and risk of damage to sensors, new methods are required to gain a high resolution understanding of the spatio-temporal patterns of urban meteorological phenomena such as the urban heat island or precision farming needs. With the launch of a new generation of low cost sensors it is possible to deploy a network to monitor air temperature at finer spatial resolutions. Here we investigate the Aginova Sentinel Micro (ASM) sensor with a bespoke radiation shield (together < US$150) which can provide secure near-real-time air temperature data to a server utilising existing (or user deployed) Wireless Fidelity (Wi-Fi) networks. This makes it ideally suited for deployment where wireless communications readily exist, notably urban areas. Assessment of the performance of the ASM relative to traceable standards in a water bath and atmospheric chamber show it to have good measurement accuracy with mean errors < ± 0.22 °C between -25 and 30 °C, with a time constant in ambient air of 110 ± 15 s. Subsequent field tests of it within the bespoke shield also had excellent performance (root-mean-square error = 0.13 °C) over a range of meteorological conditions relative to a traceable operational UK Met Office platinum resistance thermometer. These results indicate that the ASM and bespoke shield are more than fit-for-purpose for dense network deployment in urban areas at relatively low cost compared to existing observation techniques.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Seasonal intercomparison of observational rainfall datasets over India during the southwest monsoon season

The Indian monsoon is an important component of Earth's climate system, accurate forecasting of its mean rainfall being essential for regional food and water security. Accurate measurement of the rainfall is essential for various water-related applications, the evaluation of numerical models and detection and attribution of trends, but a variety of different gridded rainfall datasets are available for these purposes. In this study, six gridded rainfall datasets are compared against the India Meteorological Department (IMD) gridded rainfall dataset, chosen as the most representative of the observed system due to its high gauge density. The datasets comprise those based solely on rain gauge observations and those merging rain gauge data with satellite-derived products. Various skill scores and subjective comparisons are carried out for the Indian region during the south-west monsoon season (June to September). Relative biases and skill metrics are documented at all-India and sub-regional scales. In the gauge-based (land-only) category, Asian Precipitation-Highly-Resolved Observational Data Integration Towards Evaluation of water resources (APHRODITE) and Global Precipitation Climatology Center (GPCC) datasets perform better relative to the others in terms of a variety of skill metrics. In the merged category, the Global Precipitation Climatology Project (GPCP) dataset is shown to perform better than the Climate Prediction Center Merged Analysis of Precipitation (CMAP) for the Indian monsoon in terms of various metrics, when compared with the IMD gridded data. Most of the datasets have difficulty in representing rainfall over orographic regions including the Western Ghats mountains, in north-east India and the Himalayan foothills. The wide range of skill scores seen among the datasets and even the change of sign of bias found in some years are causes of concern. This uncertainty between datasets is largest in north-east India. These results will help those studying the Indian monsoon region to select an appropriate dataset depending on their application and focus of research.

On the relationship between decadal buoyancy anomalies and variability of the Atlantic meridional overturning circulation

Owing to the role of the Atlantic meridional overturning circulation (AMOC) in ocean heat transport, AMOC variability is thought to play a role in climate variability on a wide range of time scales. This paper focuses on the potential role of the AMOC in climate variability on decadal time scales. Coupled and ocean-only general circulation models run in idealized geometries are utilized to study the relationships between decadal AMOC and buoyancy variability and determine whether the AMOC plays an active role in setting sea surface temperature on decadal time scales.DecadalAMOC variability is related to changes in the buoyancy field along the western boundary according to the thermal wind relation. Buoyancy anomalies originate in the upper ocean of the subpolar gyre and travel westward as baroclinic Rossby waves. When the buoyancy anomalies strike the western boundary, they are advected southward by the deep western boundary current, leading to latitudinally coherent AMOC variability. The AMOC is observed to respond passively to decadal buoyancy anomalies: although variability of the AMOC leads to meridional ocean heat transport anomalies, these transports are not responsible for creating the buoyancy anomalies in the subpolar gyre that drive AMOC variability.