Control of spatial discretisation in coastal oil spill modelling

Spatial discretisation plays an important role in many numerical environmental models. This paper studies the control of spatial discretisation in coastal oil spill modelling with a view to assure the quality of modelling outputs for given spatial data inputs. Spatial data analysis techniques are effective for investigating and improving the spatial discretisation in different phases of the modelling. Proposed methods are implemented and tested with experimental models. A new “Automatic Search” method based on GIS zone design principles is shown to significantly improve discretisation of bathymetric data and hydrodynamic modelling outputs. The concepts and methods developed in the study are expected to have general relevance for a range of applications in numerical environmental modelling

Model-Based Experimental Investigation of Hydrogenase-Like Electrocatalytic Inactivation and Activation Mechanisms

This thesis describes an experimental design framework study which is focused on the investigation of highly complex electrocatalytic mechanisms. Fully model-based approaches combined with the Butler-Volmer model is employed from a pure theoretical model to a validation of practical chemical reactions. The initial chapters introduce the fundamentals and applications of the electrochemistry. Chapter 1 provides an overview of the electrode processes and the governing physical factors which may limit an electrolysis reaction. In Chapter 2, detailed simulation techniques are introduced to interpret an abstractive system into a mathematic problem then to find an accurate, efficient and stable path to the solution. The results begin in Chapter 3, in which a novel high-order operator-splitting (OS) scheme, with fully implicit finite difference (FIFD) method is first time proposed to numerically solve the stiff nonlinear problems in electrochemistry, particularly in electrocatalysis. The developed algorithm is tested through a series of validations for different electrochemical reactions on large planar electrodes. The model predictions employing this method were verified against a classic two-point time evolution implicit finite difference method for typical electrochemical systems. In Chapter 4, the numerical methods are applied to explore a complex redox system, a recently observed hydrogenase-like reaction. Subtle kinetic and mechanistic information is extracted from the voltammetric behaviour and quantitative mechanistic insights obtained. In Chapter 5, an alternative chronoamperometric voltammetry is introduced to explore the same electrocatalytic system described in Chapter 4 in order to explore some unusual current features observed in the redox chemistry. These stepwise studies support a mechanism for glucose oxidation that proceeds most likely through a complex electrocatalytic (EC’CE) scheme with catalytic steps similar to the ones reported for [NiFe] hydrogenases. The overall mechanism of the molecular inactivation and activation process (IAP) was detailed on the basis of our experimentally validated models and compared to [NiFe] hydrogenase IAP. Our findings offer novel perspectives to design finely optimised catalysts by eliminating the inactivation phenomena

Towards understanding the electrogram: theaoretical & experimental multiscale modelling of factors affecting action potential propagation in cardiac tissue

Conduction of electrical excitation in cardiac tissue is mediated by multiple physiological factors. Abnormal conduction may lead to onset of arrhythmia, and is correlated experimentally and clinically with electrogram fractionation. In-silico modelling studies seek to characterise and predict the biophysical phenomena underlying electrical excitation and conduction, and thus inform experiment design, and diagnostic and treatment strategies. Existing models assume syncytial or continuum behaviour, which may not be an accurate assumption in the disease setting. The aim of this thesis is to correlate simple theoretical and experimental models of abnormal cardiac conduction, and investigate the limits of validity of the theoretical models under critical parameter choices. An experimental model of 1D continuum conduction is established in guinea pig pap- illary muscle to examine the relationship between mean tissue resistivity and electrical conduction velocity (CV). The relationship is compared with a monodomain tissue model coupled with the Luo Rudy I (LR1) guinea pig ventricular action potential, which obeys classical cable theory of conduction under pharmacological modulation. An experimental model of 1D discrete conduction is created via development of a micro-patterned culture model of the HL-1 atrial myocyte cell line on micro-electrode arrays, which has a lower baseline conduction velocity compared to conventional cardiomyocyte models. A novel 1D bidomain model of conduction of discrete cells coupled by gap junctions is proposed and validated, based on existing analytical and numerical studies, and coupled to the LR1 model. Simulation of slow conduction under modulation of physiological parameters reveal difference in the excitation conduction between continuum and discrete models. Electro- gram fractionation is observed in the discrete model, which may be a more realistic model of conduction in diseased myocardium. This work highlights possibilities and challenges in comparing and validating theoretical models with data from experiments, and the im- portance of choosing the appropriate modelling assumptions for the specific physiological question.Open Acces

Numerical modelling of electrical stimulation for cartilage tissue engineering

In this thesis, the design and validity of numerical models of electrical stimulation for cartilage tissue engineering are critically assessed at different scales. In sum, the results of this thesis pave the way for experimentally validated numerical models of electrical stimulation devices for cartilage tissue engineering. Furthermore, models of tissue samples can be developed down to the cellular scale and will contribute to the development of patient-specific stimulation approaches

Spiral pinballs, cardiac tissue and deforming capacitors.

‘Spiral pinballs’ are resonantly drifting spiral waves in excitable media that reflect from boundaries. Instead of reflecting at an angle equal to the one at which they approach the boundary—like a ray of light reflecting from a mirror—they reflect in a preferred direction. This invites comparison with a number of other complex systems that behave as nonspecular billiards, including bouncing droplets on a vibrated bath, swimming microorganisms and segments of chemical waves. In the first part of this thesis, we study the trajectories of spiral pinball reflections. A catalogue of interesting behaviours is discovered in both the small- and large-core rotation regimes and the long-term billiard dynamics is briefly considered. By using an asymptotic theory, we examine the reflection process in detail and thereby explain many of the observed phenomena. The second part of this thesis concerns itself with modelling spiral wave activity in a deforming medium. Our motivation stems from cardiac tissue, in which spiral waves and mechanical deformation are reciprocally coupled. We describe a simple modelling approach for this system and discuss its implementation. Various different results are presented using this model. Finally we consider a problem from the engineering world. Dielectric elastomers are flexible capacitors that undergo nonlinear elastic deformations in response to forces arising from electric surface charges. We propose a novel modelling approach that decomposes these forces into a compressive stress and a tangential shear. The tangential component corresponds to a fringing effect that is usually considered to be negligible. Via numerical simulations and comparison with experimental data we show that it nonetheless has an important role to play in selecting the deformed shapes that these systems adopt. In some cases, we are able to compute multiple equilibrium configurations and it is shown that doing so is necessary to obtain the most physically relevant states