In order to understand water quality in the coastal ocean and its effects on human health, the necessity arises to locate the sources of contaminants and track their transport throughout the ocean. Dynamical systems methods are applied to the study of transport of enterococci as an indicator of microbial concentration in the vicinity of Hobie Beach, an urban, subtropical beach in Miami, FL that is used for recreation and bathing on a daily basis. Previous studies on water quality have shown that Hobie Beach has high microbial levels despite having no known point source. To investigate the cause of these high microbial levels, a combination of measured surface drifter trajectories and numerically simulated flows in the vicinity of Hobie Beach is used. The numerically simulated flows are used to identify Lagrangian Coherent Structures (LCSs), which provide a template for transport in the study area. Surface drifter trajectories are shown to be consistent with the simulated flows and the LCS structure. LCSs are then used to explain the persistent water contamination and unusually high concentrations of microbes in the water off of this beach as compared with its neighboring beaches. From the drifter simulations, as well as field experiments, one can see that passive tracers are trapped in the area along the coastline by LCS. The Lagrangian circulation of Hobie Beach, influenced primarily by tide and land geometry causes a high retention rate of water near the shore, and can be used to explain the elevated levels of enterococci in the water.

A gauged SU(4) flavor symmetric hadronic Lagrangian with empirical hadron masses is constructed to study charmonium absorption and charmed hadron production in hadronic reactions. For the coupling constants, empirical values are used if available. Otherwise, they are determined from known coupling constants using the SU(4) relations. To take into account the finite sizes of hadrons, form factors are introduced at strong interaction vertices with empirical cutoff parameters. For J/ψabsorption by nucleons, we have included both two-and three-body final states and find that with a cutoff parameter of 1 GeV at interaction vertices involving charm hadrons, the cross section is at most 5 mb and is consistent with that extracted from J/ψproduction from both photo-and proton-nucleus reactions. We have also evaluated the cross sections for charmed hadron production from pion and rho meson interactions with nucleons. With the same cutoff parameter of 1 GeV at interaction vertices, we find that these cross sections have values of a few tenths of mb and are dominated bythe s-channel nucleon pole diagram. For charmed hadron production from proton-proton reactions, their cross sections including bothtwo-andthree-body final states are about 1 batcenter-of-mass energyof 11.5 GeV, which is comparable to the measured inclusive cross section in these reactions.Including photon as a U(1) gauge particle, we have extended the model to study charmed hadron production in photon-proton reactions with both two-and three-body final states included. For form factors, an overall one is introduced in each processin order to maintain the gauge invariance of the total amplitude. Fitting the cutoff parameter in the form factor to the measured total cross section for charmed hadron production in photon-proton reactions at a center-of-mass energy of 6 GeV, the ratio of the cross sections for two-body and three-body final states is consistent with available experimental data.This result is further compared with predictions from the leading-order perturbative QCD calculation. Knowledge of the cross sections for charmonium absorption byhadrons and for charmed hadron production in hadronic reactions is essential for understanding charm production in heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC), where a quark-gluon plasma is expected to be formed during the initial hot dense stage.

In this thesis we present a slight generalisation of the Pearl complex or relative quantum homology to some non monotone Lagrangian submanifolds. First we develop the theory for the so called almost monotone Lagrangian submanifolds, We apply it to uniruling problems as well as estimates for the relative Gromov width. In the second part we develop the theory for toric fiber in toric Fano manifolds, recovering previous computaional results of Floer homology .

The surface circulation of the northern South China Sea (NSCS) for the period of 1986-2006 is studied using the data of more than 505 satellite-tracked drifters from NOAA/AOML database and the data from ten drifters which were released by our lab in the Penghu channel and in the Luzon Strait in 2006. In this study, the spatial structure and the temporal variability of the surface currents, at mesoscale to seasonal cycle, are described in terms of Eulerian and Lagrangian statistics from the drifter velocities that have been processed. Maps of mean currents, velocity variance ellipses and mean kinetic energies were produced in domain of 0.5¢X¡Ñ0.5¢X. The mean flow map confirms that during the winter monsoon, there is a global cyclonic circulation in the NSCS and the southwestward current which passes Dongsha Island and is called the ¡§Dongsha Current¡¨. Its continuation is the southward coastal jet off Vietnam which is called the ¡§Vietnam Current¡¨. Maximum velocities in the Vietnam Current can exceed 100 cm/s. During the summer monsoon, the Dongsha Current became very weak and the drifters looped near Dongsha Island. The drifter data shows that part of Kuroshio water intrudes into South China Sea through Luzon Strait, Dongsha Current and Vietnam Current were coherent flows. Values of 5.12¡Ñ107 cm2/s, 2.56 days and 64.43 km were obtained for the diffusivity, Lagrangian time scale and spatial scale in the meridional direction in the NSCS, respectively. In the zonal direction, the statistics are half of the above values which show that the characteristic time and space scale are anisotropic. The mean velocity in the Dongsha Current is 0.33 m/s. The domain of Dongsha Current is subdivided into ten boxes of size 2¢X¡Ñ 2¢X in order to analyze the spatial structure of Lagrangian statistics. The result shows that the eddy kinetic energy is considerably higher than the mean kinetic energy in the region 113-121¢XE, indicating that the mesoscale motions are particularly frequent. The eddy kinetic energy gradually decreases toward the west and has a maximum value near the Luzon Strait. The drifters that flow southward along the east coast of Vietnam shows that the width of the Vietnam Current varies between 80 and 100 km and has a mean core speed of 60-150 cm/s. In winter, Maximum southward velocities could reach 130 cm/s at 38 km off the coast. In spring, a weaker maximum speed (around 100 cm/s) exists at about 18 km off the Vietnam coast. There were not enough drifter data in summer and fall.

We discuss a relativistic transport theory of condensed matter based on a microscopic system containing bosonic and fermionic degrees of freedom interacting via 3 - and 4-point interactions. We use the Dyson hierarchy as a solution to the underlying field theory and truncate this hierarchy by parametrizing the 2-particle-irreducible kernels of the 4- and 5-point vertex functions. We then perform a complete crossing-symmetric reduction of the 2-particle intermediate states of the theory. We obtain a reduction hierarchy and show how to explore the quality of our truncation scheme using this reduction hierarchy. Finally we discuss the problem of regularization of the theory in the case of hadronic matter by either putting form factors directly in the action or by using dispersion relations to introduce causal form factors into singular diagrams. / Graduation date: 1992

Currently, data size that we have to deal with is growing bigger and bigger. This fact implies that the computing time and computing power for dealing with the data is demanded. A way to circumvent the difficulty is as follows: Divide the data into several small blocks and then process these small blocks by several computers. Therefore, we need a tool for the decomposition-coordinated procedure. Alternating direction method of multipliers (ADMM) is a powerful algorithm for the mentioned purpose and has widely used in distributed optimizations. With ADMM algorithm, a big global optimization problem can be decomposed into several small local optimization problems. ADMM algorithm has been used in several recent distributed systems such as cloud systems and distributed antenna systems. In this thesis, we aim to apply the ADMM in a distributed antenna system. For the uplink setting, we develop a distributed demodulation algorithm, where multiple base stations collaborate with each other for data detection. On the other hand, for the downlink setting, we develop a distributed beamforming design algorithm, where multiple base stations collaborate to form a beamforming for mitigating the inter-cell interference. Finally, simulations are conducted to verify the efficiency of our designs.

Network-on-Chip (NoC) is emerging as a promising communication structure, which is scalable with respect to chip complexity. Meanwhile, latest chip designs are increasingly leveraging multiple voltage-frequency domains for energy-efficiency improvement. In this work, we propose a simultaneous task and voltage scheduling algorithm for energy minimization in NoC based designs. The energy-latency tradeoff is handled by Lagrangian relaxation. The core algorithm is a clustering based approach which not only assigns voltage levels and starting time to each task (or Processing Element) but also naturally finds voltage-frequency clusters. Compared to a recent previous work, which performs task scheduling and voltage assignment sequentially, our method leads to an average of 20 percent energy reduction.

In real-time, two way video communications, how to minimize the end-to-end delay for transmitting video data is very important. Since the delay produced by bits accumulated in the encoder buffer must be very small, we need an improved rate control to encode the video with high quality and maintain low buffer fullness. One approach to reduce the buffer fullness is to skip the encoding frames, but the frame-skipping will produce undesirable motion discontinuity in the encoded video sequence. In this thesis, we study the impact of low delay constraint in H.264 rate control and its improvements. The drawback of the H.264 rate control is it cannot handle the frame-skipping mechanism well. To modify this, we control the quantization parameter of each I-frame to avoid the buffer overflow and frame-skipping. Since encoding the I-frame by different quantization parameter will generate different rate and distortion for a group of pictures (GOP), we use Lagrangian optimization to find the tradeoff between rate and distortion for a GOP. By the estimation models of rate and distortion for a GOP, calculate the Lagrangian cost for each possible quantization parameter of I-frame, the quantization parameter with minimum Lagrangian cost will be our choice for I-frame. Simulation results show that our proposed rate control encode the video sequence with less skipped frames and with higher PSNR compared to H.264 rate control under low delay constraint.

In this study we consider an inventory routing problem in which a supplier distributes a single product to multiple retailers in a finite planning horizon. Retailers should satisfy the deterministic and dynamic demands of end customers in the planning horizon, but the retailers can backorder the demands of end customers considering the supply chain costs. In each period the supplier decides the retailers to be visited, and the amount of products to be supplied to each retailer by a fleet of vehicles. The decision problems of the supplier are about when, to whom and how much to deliver products, and in which order to visit retailers while minimizing system-wide costs. We propose a mixed integer programming model and a Lagrangian relaxation based solution approach in which both upper and lower bounds are computed. We test our solution approach with test instances taken from the literature and provide our computational results.

¡@¡@The main purpose of this paper is to analyze the surface progressive gravity waves propagating on a gentle sloping beach in two dimension. Instead of using the method of Eulerian system by the previous investigators, we introduce the governing equations completely in the Lagrangian system directly. All the characteristics of the wave system is expressed by a suitable perturbation expansion in the bottom slope under linearizing the problem in wave amplitude, then all the governing equations are systematically expanded to order. The solution of the wave system is to be solved to second order , even to high order could also be obtained. Based on the obtained results, the velocity potential, pressure and motion of the fluid particle in the wave system in time and space is therefore presented, and we can see that the bottom slope is a main factor to screw the wave field to deform to break. Finally, the experimental result is cited to compare and verify.