Feedback methods for inverse simulation of dynamic models for engineering systems applications

Inverse simulation is a form of inverse modelling in which computer simulation methods are used to find the time histories of input variables that, for a given model, match a set of required output responses. Conventional inverse simulation methods for dynamic models are computationally intensive and can present difficulties for high-speed applications. This paper includes a review of established methods of inverse simulation,giving some emphasis to iterative techniques that were first developed for aeronautical applications. It goes on to discuss the application of a different approach which is based on feedback principles. This feedback method is suitable for a wide range of linear and nonlinear dynamic models and involves two distinct stages. The first stage involves design of a feedback loop around the given simulation model and, in the second stage, that closed-loop system is used for inversion of the model. Issues of robustness within closed-loop systems used in inverse simulation are not significant as there are no plant uncertainties or external disturbances. Thus the process is simpler than that required for the development of a control system of equivalent complexity. Engineering applications of this feedback approach to inverse simulation are described through case studies that put particular emphasis on nonlinear and multi-input multi-output models

Path integral ground state approaches for the study of weakly bound clusters and confined molecules

This thesis presents the study of weakly bound clusters in the ground state (or the zero-temperature limit) using path integral molecular dynamics. Specifically, we look individually at the quantum properties of small clusters of hydrogen and water molecules and confined hydrogen within water cages, known as clathrate hydrates, which serves as a more practical application. Clathrate hydrates have been extensively studied as a clean storage container for molecular hydrogen and there have been discrepancies on the hydrogen occupancy number between various theoretical and experimental studies. It has been shown that the occupancy number is sensitive to the potential energy surfaces and models of the hydrogen and water systems. A preliminary study of hydrogen contained in clathrates is performed using a traditional hydrogen pair potential and water-hydrogen interaction potential. Hydrogen occupancy and structural distributions are compared to literature values. Small clusters of the individual molecules themselves are then focused on. The molecular hydrogen pair potentials are evaluated by calculating the Raman vibrational shift, a property that is very sensitive to the interaction potential, and comparing to experimental measurements. These shifts are calculated using first order perturbation theory based on pair distribution functions generated from Langevin equation path integral ground state (LePIGS) simulations for all bosonic isotopologues. It is determined that the shifts calculated using the Hinde pair potential give better agreement to experimental results than the traditional hydrogen potentials that we have been using in the past. The perturbation theory approach is then compared with two exact methods to calculate the shifts. For the application of hydrogen clusters, it is determined that perturbation theory is the best choice when balancing accuracy and precision. In the literature, there has been a discrepancy in the shape of the chemical potential at low temperature and in the ground state. We calculate the ground state chemical potential using LePIGS and find agreement with other PIGS results. We then extend our LePIGS code to simulate flexible molecules by investigating the water dimer. Ground state energies, dissociation energies, and structural properties are calculated using two empirically based interaction potentials and one ab initio potential, MB-pol, that includes polarizability and many-body effects which has been shown to reproduce experimental dissociation energies. We further demonstrate that imaginary time correlation functions generated from LePIGS can be used to calculate accurate vibrational transition energies. This work serves as a demonstration of the effectiveness of the LePIGS method towards calculating ground state properties of small clusters and provides useful information on the interaction potentials that should be used for systems containing hydrogen or water, specifically hydrogen contained in a flexible clathrate hydrate. An analytic form of the 1-D Hinde pair potential for molecular hydrogen is also contained for general use

Developing a Method to Study Ground State Properties of Hydrogen Clusters

This thesis presents the benchmarking and development of a method to study ground state properties of hydrogen clusters using molecular dynamics. Benchmark studies are performed on our Path Integral Molecular Dynamics code using the Langevin equation for finite temperature studies and our Langevin equation Path Integral Ground State code to study systems in the zero-temperature limit when all particles occupy their nuclear ground state. A simulation is run on the first 'real' system using this method, a parahydrogen molecule interacting with a fixed water molecule using a trivial unity trial wavefunction. We further develop a systematic method of optimizing the necessary parameters required for our ground state simulations and introduce more complex trial wavefunctions to study parahydrogen clusters and their isotopologues orthodeuterium and paratritium. The effect of energy convergence with parameters is observed using the trivial unity trial wavefunction, a Jastrow-type wavefunction that represents a liquid-like system, and a normal mode wavefunction that represents a solid-like system. Using a unity wavefunction gives slower energy convergence and is inefficient compared to the other two. Using the Lindemann criterion, the normal mode wavefunction acting on floppy systems introduces an ergodicity problem in our simulation, while the Jastrow does not. However, even for the most solid-like clusters, the Jastrow and the normal mode wavefunctions are equally efficient, therefore we choose the Jastrow trial wavefunction to look at properties of a range of cluster sizes. The energetic and structural properties obtained for parahydrogen and orthodeuterium clusters are consistent with previous studies, but to our knowledge, we may be the first to predict these properties for neutral paratritium clusters. The results of our ground state simulations of parahydrogen clusters, namely the distribution of pair distances, are used to calculate Raman vibrational shifts and compare to experiment. We investigate the accuracy of four interaction potentials over a range of cluster sizes and determine that, for the most part, the ab initio derived interaction potentials predict shifts more accurately than the empirically based potentials for cluster sizes smaller than the first solvation shell and the trend is reversed as the cluster size increases. This work can serve as a guide to simulate any system in the nuclear ground state using any trial wavefunction, in addition to providing several applications in using this ground state method.4 month

Characterization of clean and fouled ultrafiltration membranes

Much research into the fundamentals of membrane formation and separation has been performed in order to improve the efficiency of the manufacture of ultrafiltration membranes. Determination of the membrane characteristics is a key problem in these investigations. In this paper, we report on a study of membrane morphology by fractional rejection measurements, using low molecular weight saccharides as the test solute, and by electron microscopy. Using a simple model for solute/solvent transport through cylindrical pores, a “characteristic pore size” was derived from saccharide rejection data. This pore size of a hypothetical isoporous membrane, interpreting the measured separation characteristics, provides a promising means of describing differences between membranes with respect to pore size and pore size changes caused by solute adsorption. From high resolution electron micrographs, information was obtained on the skin layer morphologies and, for some membranes the sizes of the larger pores could be estimated

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Break-Junction Tunneling on MgB_2

Tunneling data on magnesium diboride, MgB_2, are reviewed with a particular focus on superconductor-insulator-superconductor (SIS) junctions formed by a break-junction method. The collective tunneling literature reveals two distinct energy scales, a large gap, Delta_L~7.2 meV, close to the expected BCS value, and a small gap, Delta_S~2.4 meV. The SIS break junctions show clearly that the small gap closes near the bulk critical temperature, T_c=39 K. The SIS spectra allow proximity effects to be ruled out as the cause for the small gap and therefore make a strong case that MgB_2 is a coupled, two-band superconductor. While the break junctions sometimes reveal parallel contributions to the conductance from both bands, it is more often found that Delta_S dominates the spectra. In these cases, a subtle feature is observed near Delta_S+Delta_L that is reminiscent of strong-coupling effects. This feature is consistent with quasiparticle scattering contributions to the interband coupling which provides an important insight into the nature of two-band superconductivity in MgB_2.Comment: 9 pages, 10 pictures, accepted for publication in a special issue of Physica C on MgB2, minor change

Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations

The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important model system for the high-$T_c$ superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.Comment: 16 pages, 26 figure

Evaluation of community level interventions to address social and structural determinants of health: a cluster randomised controlled trial

<p>Abstract</p> <p>Background</p> <p>In London and the rest of the UK, diseases associated with poor diet, inadequate physical activity and mental illness account for a large proportion of area based health inequality. There is a lack of evidence on interventions promoting healthier behaviours especially in marginalised populations, at a structural or ecological level and utilising a community development approach.</p> <p>The Well London project financed by the Big Lottery 'Wellbeing' Fund and implemented by a consortium of London based agencies led by the Greater London Authority and the London Health Commission is implementing a set of complex interventions across 20 deprived areas of London. The interventions focus on healthy eating, healthy physical activity and mental health and wellbeing and are designed and executed with community participation complementing existing facilities and services.</p> <p>Methods/Design</p> <p>The programme will be evaluated through a cluster randomised controlled trial. Forty areas across London were chosen based on deprivation scores. Areas were characterised by high proportion of Black and Minority Ethnic residents, worklessness, ill-health and poor physical environments. Twenty areas were randomly assigned to the intervention arm of Well London project and twenty 'matched' areas assigned as controls. Measures of physical activity, diet and mental health are collected at start and end of the project and compared to assess impact.</p> <p>The quantitative element will be complemented by a longitudinal qualitative study elucidating pathways of influence between intervention activities and health outcomes. A related element of the study investigates the health-related aspects of the structural and ecological characteristics of the project areas. The project 'process' will also be evaluated.</p> <p>Discussion</p> <p>The size of the project and the fact that the interventions are 'complex' in the sense that firstly, there are a number of interacting components with a wide range of groups and organisational levels targeted by the intervention, and secondly, a degree of flexibility or tailoring of the intervention, makes this trial potentially very useful in providing evidence of the types of activities that can be used to address chronic health problems in communities suffering from multiple deprivation.</p> <p>Trial Registration</p> <p>Current Controlled Trials ISRCTN68175121</p

Retention of Two-Band Superconductivity in Highly Carbon-Doped MgB2

Tunneling data on MgB_{1.8}C_{0.2} show a reduction in the energy gap of the pi-bands by a factor of two from undoped MgB2 that is consistent with the Tc reduction, but inconsistent with the expectations of the dirty limit. Dirty-limit theory for undoped MgB2 predicts a single gap about three times larger than measured and a reduced Tc comparable to that measured. Our heavily-doped samples exhibit a uniform dispersion of C suggestive of significantly enhanced scattering, and we conclude that the retention of two-band superconductivity in these samples is caused by a selective suppression of interband scattering.Comment: 4 pages, 4 figures; added one figure, added one reference, minor changes to the text, manuscript accepted for publication as a Phys. Rev. B Rapid Communicatio