In the present study, a fully nonlinear 2-D finite difference scheme has been developed based on inviscid and incompressible flow in a rectangular tank. The rectangular tank is coupled to a linear elastic-supported structure made up by reinforced concrete. Wave breaking and run-up are not considered in the present numerical model due to the free surface is assumed as a single-value function. The main purpose of this study is to analyze interactions between sloshing forces generated by system vibrations and structure motions. The accuracy of present study is made by comparing to other reported numerical results and the consequence shows well agreement. The present study can be applied for designing various combinations of coupled structure systems for different necessity. The analyses of practical examples are also presented in this study. The present numerical model can provide a quick and accurate way on determining the natural frequencies of connecting fluid-structure system and this is hard to identify through experiment.

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This course project is made up of two parts. Part one is an investigation and implementation of pricing of financial derivatives using numerical methods for the solution of partial differential equations. Part two is an introduction of Monte Carlo methods in financial engineering. The name of course is MA573:Computational Methods in Financial Mathematics, spring 2009, given by Professor Marcel Blais.

A mathematical model considering ellipsoidal surface for the forming tube is proposed in this work to examine the plastic deformation behavior of a thin-walled tube during tube bulge hydroforming process in an open die. In the formulation of this mathematical model, nonuniform thinning in the free bulged region and sticking and sliding friction modes between the tube and die are considered. In the sticking friction mode, the elements in contact with the die do not move or slide after contact with the die. Whereas, in the sliding friction mode, the elements in contact with the die will continue to deform plastically in the subsequent forming process. The relationship between the internal pressure and the bulge height of the tube is examined. The effects of various forming parameters such as the die entry radius, the initial thickness, the length/diameter ratio, material property, etc., upon the forming pressure and the thickness distribution of products were discussed systematically.

In the present study, a two-dimensional numerical model based on a time-independent finite difference method was developed and the model is used to analysis the dynamic interaction among wave, sloshing fluid in tank and the floating tank. The free surface of wave and sloshing fluid in the tank are all assumed to be a single value function and the wave breaking is, therefore, not considered in the study. The numerical model is firstly validated by some bench make studies. Extensive simulation were made to discuss the effects of geometry of the floating tank, the ratio of depth to breadth of fluid in tank, the fundamental freq of floating tank ¡V structure system etc.

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This text describes different aspects of the design of a Doctor-on-a-Chip device. Doctor-on-a-Chip is a DNA analysis system integrated on a single chip, which should provide all of the advantages that stem from the system integration, such as small sample volume, fast and accurate analysis, and low cost. The text describes all of the steps of the on-chip sample analysis, including DNA extraction from the sample, purification, PCR amplification, novel dielectrophoretic sorting of the DNA molecules, and finally detection. The overview is given of the technologies which are available to make the integration on a single chip possible. The microfluidic technologies that are used to manipulate the sample and other chemical reagents are already known and in this text they are analyzed in terms of their feasibility in the on-chip system integration. These microfluidic technologies include, but are not limited to, microvalves, micromixers, micropumps, and chambers for PCR amplification. The novelty in the DNA analysis brought by Doctor-on-a-Chip is the way in which the different DNA molecules in the sample (for example, human and virus DNA) are sorted into different populations. This is done by means of dielectrophoresis – the force experienced by dielectric particles (such as DNA molecules) when subject to a non-uniform electric field. Different DNA molecules within a sample experience different dielectrophoretic forces within the same electric field, which makes their separation, and therefore detection, possible. In this text, the emphasis is put on numerical modelling of the dielectrophoretic effect on biological particles. The importance of numerical modelling lies in the fact that with the accurate model it is easier to design systems of microelectrodes for dielectrophoretic separation, and tune their sub-micrometre features to achieve the maximum separation efficacy. The numerical model described in this text is also experimentally verified with the novel microelectrodes design for dielectrophoretic separation, which is successfully used to separate the mixture of different particles in the micron and sub-micron range.

This work outlines the design and implementation of an algorithm to simulate two-polarisation bowed string motion, for the purpose of realistic sound synthesis. The algorithm is based on a physical model of a linear string, coupled with a bow, stopping fi ngers, and a rigid, distributed fingerboard. In one polarisation, the normal interaction forces are based on a nonlinear impact model. In the other polarisation, the tangential forces between the string and the bow, fingers, and fingerboard are based on a force-velocity friction curve model, also nonlinear. The linear string model includes accurate time-domain reproduction of frequency-dependent decay times. The equations of motion for the full system are discretised with an energy-balanced finite difference scheme, and integrated in the discrete time domain. Control parameters are dynamically updated, allowing for the simulation of a wide range of bowed string gestures. The playability range of the proposed algorithm is explored, and example synthesised gestures are demonstrated.

Recently the phenomena of Bose-Einstein condensates have been observed in laboratories, and the related problems are extensively studied. In this paper we consider the nonlinear Schrödinger equation in the laser beam rotating magnetic field and compute its corresponding energy functional under the mass conservative condition. By separating time and space variables, factoring real part and image part, and discretizing via finite difference method, the original equation can be transformed to a large scale parametrized polynomial systems. We use continuation method to find the solutions that satisfy the mass conservative condition. We will also explore bifurcation points on the curves and other solutions lying on bifurcation branches. The numerical results show that when the rotating angular momentum is small, we can find the solutions by continuation method along some particular curves and these curves are regular. As the angular momentum is increasing, there will be more bifurcation points on curves.