Direct numerical simulation of turbulent flow and mass transfer around a rotating circular cylinder

Turbulent flow around a rotating circular cylinder has numerous applications including wall shear stress and mass-transfer measurement related to the corrosion studies. It is also of interest in the context of flow over convex surfaces where standard turbulence models perform poorly. The main purpose of this paper is to elucidate the basic turbulence mechanism around a rotating cylinder at low Reynolds numbers to provide a better understanding of flow fundamentals. Direct numerical simulation (DNS) has been performed in a reference frame rotating at constant angular velocity with the cylinder. The governing equations are discretized by using a finite-volume method. As for fully developed channel, pipe, and boundary layer flows, a laminar sublayer, buffer layer, and logarithmic outer region were observed. The level of mean velocity is lower in the buffer and outer regions but the logarithmic region still has a slope equal to the inverse of the von Karman constant. Instantaneous flow visualization revealed that the turbulence length scale typically decreases as the Reynolds number increases. Wavelet analysis provided some insight into the dependence of structural characteristics on wave number. The budget of the turbulent kinetic energy was computed and found to be similar to that in plane channel flow as well as in pipe and zero pressure gradient boundary layer flows. Coriolis effects show as an equivalent production for the azimuthal and radial velocity fluctuations leading to their ratio being lowered relative to similar nonrotating boundary layer flows.

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

A circular Malmquist-type index for measuring productivity

This paper develops two new indices for measuring productivity in multi-input multi-output situations. One index enables the measure of productivity change of a unit over time while the second index makes it possible to compare two units on productivity at the same or different points in time. Productivity in a single input single output context is defined as the ratio of output to input. In multi-input multi-output contexts this ratio is not defined. Instead, one of the methods traditionally used is the Malmquist Index of productivity change over time. This is computed by reference to the distances of the input-output bundles of a production unit at two different points in time from the efficient boundaries corresponding to those two points in time. The indices developed in this paper depart form the use of two different reference boundaries and instead they use a single reference boundary which in a sense is the most efficient boundary observed over two or more successive time periods. We discuss the assumptions which make possible the definition of such a single reference boundary and proceed to develop the two Malmquist-type indices for measuring productivity. One key advantage of using a single reference boundary is that the resulting index values are circular. That is it is possible to use the index values of successive time periods to derive an index value of productivity change over a time period of any length covered by successive index values or vice versa. Further, the use of a single reference boundary makes it possible to construct an index for comparing the productivities of two units either at the same or at two different points in time. This was not possible with the traditional Malmquist Index. We decompose both new indices into components which isolate production unit from industry or comparator unit effects. The components themselves like the indices developed are also circular. The components of the indices drill down to reveal more clearly the performance of each unit over time relative either to itself or to other units. The indices developed and their components are aimed at managers of production units to enable them to diagnose the performance of their units with a view to guiding them to improved performance.

Resistance heating of steel conductors of circular cross-section

The object of this thesis is to develop a method for calculating the losses developed in steel conductors of circular cross-section and at temperatures below 100oC, by the direct passage of a sinusoidally alternating current. Three cases are considered. 1. Isolated solid or tubular conductor. 2. Concentric arrangement of tube and solid return conductor. 3. Concentric arrangement of two tubes. These cases find applications in process temperature maintenance of pipelines, resistance heating of bars and design of bus-bars. The problems associated with the non-linearity of steel are examined. Resistance heating of bars and methods of surface heating of pipelines are briefly described. Magnetic-linear solutions based on Maxwell's equations are critically examined and conditions under which various formulae apply investigated. The conditions under which a tube is electrically equivalent to a solid conductor and to a semi-infinite plate are derived. Existing solutions for the calculation of losses in isolated steel conductors of circular cross-section are reviewed, evaluated and compared. Two methods of solution are developed for the three cases considered. The first is based on the magnetic-linear solutions and offers an alternative to the available methods which are not universal. The second solution extends the existing B/H step-function approximation method to small diameter conductors and to tubes in isolation or in a concentric arrangement. A comprehensive experimental investigation is presented for cases 1 and 2 above which confirms the validity of the proposed methods of solution. These are further supported by experimental results reported in the literature. Good agreement is obtained between measured and calculated loss values for surface field strengths beyond the linear part of the d.c. magnetisation characteristic. It is also shown that there is a difference in the electrical behaviour of a small diameter conductor or thin tube under resistance or induction heating conditions.