In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented. / Singapore-MIT Alliance (SMA)

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: Leonard J. Cimini, Jr., Electrical and Computer Engineering. Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

The modeling of Sand Asphalt and experiments to measure their rheological properties are of vital concern to many industrial processes especially highway and roadway pavement construction industry. A variety of hot mix asphalt mixtures are used in highway and runway pavement construction, with each mixture catering to a specific need. These mixtures vary in type and percentage of aggregates and asphalt used and consequently exhibit marked differences in their response. The main thrust of this research is to provide experimental data which would be helpful in determining the efficacy of the constitutive models that have been developed for these hot mix asphalt mixtures. Here we attempt to provide experimental data in the raw form for Sand Asphalt mixtures that would be helpful in the theoretical modeling efforts involving asphalt materials using a continuum point of view. For example the data obtained can be of immense help to evaluate the constitutive model developed by Murali Krishnan and Rajagopal. The Sand Asphalt mixture in their model is modeled as `homogenized' single constituent due to the peculiarity of its makeup. The constitutive model of Murali Krishnan and Rajagopal is based on a thermodynamical framework for materials possessing multiple natural configurations (multiple stress free states) to derive the constitutive equations. Recently an Orthogonal Rheometer was built to characterize the granular solids by Gupta and Rajagopal which was later used by Baek in the torsional mode. In this work we have used the same Torsional Rheometer with some minor modifications in the design to measure some general properties of Sand Asphalt mixtures. Sand Asphalt mixtures, due to their non-linear viscoelastic character, exhibit `normal stress effects' and `stress relaxation'. The Rheometer that we used was able to capture these responses with high precision. We have laid out proper procedures for the further testing of asphalt related mixtures. A typical sand asphalt mixture sample in cylindrical shape was used as the test specimen. From this work some interesting data was obtained. A remarkable observation was that as the shear rate is increased, the normal force and torque generated initially decrease, but beyond a certain shear rate they attain a constant value.

In this thesis, we present algorithms for local and global minimization of some Procrustes type problems. Typically, these problems are about rotating and scaling a known set of data to fit another set with applications related to determination of rigid body movements, factor analysis and multidimensional scaling. The known sets of data are usually represented as matrices, and the rotation to be determined is commonly a matrix Q with orthonormal columns. The algorithms presented use Newton and Gauss-Newton search directions with optimal step lengths, which in most cases result in a fast computation of a solution. Some of these problems are known to have several minima, e.g., the weighted orthogonal Procrustes problem (WOPP). A study on the maximal amount of minima has been done for this problem. Theoretical results and empirical observations gives strong indications that there are not more than 2n minimizers, where n is the number of columns in Q. A global optimization method to compute all 2n minima is presented. Also considered in this thesis is a cubically convergent iteration method for solving nonlinear equations. The iteration method presented uses second order information (derivatives) when computing a search direction. Normally this is a computational heavy task, but if the second order derivatives are constant, which is the case for quadratic equations, a performance gain can be obtained. This is confirmed by a small numerical study. Finally, regularization of ill-posed nonlinear least squares problems is considered. The quite well known L-curve for linear least squares problems is put in context for nonlinear problems.

A method is developed for solving the two dimensional Helmholtz equation in a ductwith varying cross-section region bounded by a curved top and flat bottom, having oneregion inside. To compute the propagation of sound waves in a curved duct with a curvedinternal interface is difficult problem. One method is to transform the wave equation intoa solvable form and making the curved interface plane. To this end a local orthogonaltransformation is developed for the varying cross-sectional duct having one medium inside.This transformation is first used to make the curved top of the waveguide flat andto transform the Helmholtz equation into an initial value problem. Later on the local orthogonaltransformation is developed for a waveguide having two media inside with flattop, a flat bottom and a curved interface. This local orthogonal transformation is used toflatten the interface and also to transform the Helmholtz equation into a simple, solvableordinary differential equation. In this paper we present operator formulation for the partwith flat bottom and curved top including a curved interface. In the ordinary differentialequation with operators in coefficients, obtained after the transformation, all the operationsrelated to the transverse variable are treated as operators while the derivative withrespect to the range variable is kept.

This thesis examines the transient performance of packed bed heat regenerators when very large temperature differences are involved. The effects of gas temperature on the key gas physical properties of velocity, density and heat capacity were studied via simulation. Three models were developed and compared. The first model (HRKDV) considers heat balances for both solid and gas phases, the second (HRVDV) considers mass balances in addition to the heat balances set up in the first model and the third one (HRASO) considers that the only significant rate of accumulation term is that of the energy of the solid phase. The governing partial differential equations were solved by the method of lines with the spatial discretization accomplished by the method of orthogonal collocation. The findings of this work reveal that whereas the effects of large temperature changes on the gas velocity and density are completely negligible, the effects of temperature on the gas heat capacity must be considered "continuously" when large temperature swings occur. Considering the heat capacity as a constant, even at an average value, leads to significant errors in temperature profiles. / Graduation date: 1992

Vehicular Ad hoc Networks (VANET) consist of radio-equipped vehicles and roadside units (RSU) and support many safety and commercial applications. Multi-hop forwarding can extend the communication range of both RSUs and vehicular broadcasts. Recently, the use of Positive Orthogonal Codes (POC) as transmission patterns of repetition-based broadcast medium access control (MAC) for safety messages has been proposed. This thesis proposes a cooperative forwarding protocol in which multiple relays at each forwarding hop form a virtual relay and coordinate their transmission times to correspond to a POC codeword. The protocol thereby exploits spatial diversity while conforming to the POC-based MAC, resulting in fewer collisions and mitigating the effect of hidden terminals. The design is validated through NS2 simulations, which show comparable performance with other forwarding schemes while producing significantly less performance degradation for safety message broadcasts on the same channel.

Vehicular Ad hoc Networks (VANET) consist of radio-equipped vehicles and roadside units (RSU) and support many safety and commercial applications. Multi-hop forwarding can extend the communication range of both RSUs and vehicular broadcasts. Recently, the use of Positive Orthogonal Codes (POC) as transmission patterns of repetition-based broadcast medium access control (MAC) for safety messages has been proposed. This thesis proposes a cooperative forwarding protocol in which multiple relays at each forwarding hop form a virtual relay and coordinate their transmission times to correspond to a POC codeword. The protocol thereby exploits spatial diversity while conforming to the POC-based MAC, resulting in fewer collisions and mitigating the effect of hidden terminals. The design is validated through NS2 simulations, which show comparable performance with other forwarding schemes while producing significantly less performance degradation for safety message broadcasts on the same channel.

University of Macau / Faculty of Science and Technology / Department of Mathematics