Dynamics of thin liquid films over a spinning disk

Thin film dynamics over spinning disks is of central importance to a number of scientific research and industrial applications, such as heat/mass transfer, chemical reactions and chip devices. Although they have received a lot of attention in different applications, the key un- derlying dynamics governing the flow are not thoroughly understood, especially in terms of highly non-linear behaviour in free surface flows, in the presence of other physical forces or chemical reactions. The elucidation of the underlying mechanisms driving the flow is of utmost importance to both scientific research and industrial applications. In this research the dynamics of a thin film flowing over a rapidly spinning, horizontal disk, in presence of first-order chemical reactions is considered. A set of non-axisymmetric evolution equations for the film thickness, radial and azimuthal flow rates is derived using a boundary- layer (IBL) approximation in conjunction with the Karman-Polhausen approximation for the velocity distribution in the film. Numerical solutions of these highly nonlinear partial dif- ferential equations are obtained from finite difference scheme which reveals the formation of large-amplitude waves that travel from the disk inlet to its periphery. The equations with non- axisymmetric condition were investigated where elimination of azimuthal dependence presents different wave regimes across the disk radius, and three dimensional wave structures over the entire disk. Apart from hydrodynamics, the influence of these waves on the concentration and temperature profiles is analysed for a wide range of system parameters. It is shown that these waves lead to significant enhancement of the rates of heat and mass transfer, as well as chemical reaction due to the mixing associated with the flow. Additionally, due to the time-consuming implementation of the IBL model, the Neural Network (NN) technique is applied based on existing Finite Difference (FD) results, in order to predict the wave dynamics after initial times.The NN is trained on a dataset from various data points in space and time from IBL model, and then used to simulate the evolution of any wave characteristics of interest. Overall, the resulting NN model predicts the evolution of waves reasonably well when compared with the time-consuming finite difference scheme, and reduces the computation time significantly.Open Acces

Proceedings of the 2011 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory

This book is a collection of 15 reviewed technical reports summarizing the presentations at the 2011 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory. The covered topics include image processing, optical signal processing, visual inspection, pattern recognition and classification, human-machine interaction, world and situation modeling, autonomous system localization and mapping, information fusion, and trust propagation in sensor networks

Weak equilibria for time-inconsistent control: with applications to investment-withdrawal decisions

This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under general multi-dimensional controlled diffusion model and propose a formal definition of their equilibria. We show that an admissible pair $(\hat{u},C)$ of controlstopping policy is equilibrium if and only if the auxiliary function associated with it solves the extended HJB system, providing a methodology to verify or exclude equilibrium solutions. We provide several examples to illustrate applications to mathematical finance and control theory. For a problem whose reward function endogenously depends on the current wealth, the equilibrium is explicitly obtained. For another model with a non-exponential discount, we prove that any constant proportion strategy can not be equilibrium. We further show that general non-constant equilibrium exists and is described by singular boundary value problems. This example shows that considering our combined problems is essentially different from investigating them separately. In the end, we also provide a two-dimensional example with a hyperbolic discount

Thermal-optoacoustic model for cardiac radiofrequency ablation

The global objective of this thesis is to develop and validate a thermal model to predict the temperature of the tissue from an OA signal during thermal heating by radiofrequency ablation. In this way, we expect to demonstrate capabilities of OA imaging in temperature monitoring during RF ablation so that temperature maps of the tissue can be obtained during future ablation experiments. To get to the long term goal of developing a thermal-optoacoustic model, we will first aim to develop and validate a thermal model based on transient heat transfer theory. We aim to compare different analytical and numerical approaches to model the temperature in order to be able to choose the most accurate method. We further intend to validate the developed model in phantoms experiments and check whether it can be accurate for higher temperatures.Ingeniería IndustrialIndustria Ingeniaritz