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Finally, we prove a blow up criterion for the full compressible Navier-Stokes equations just in terms of the gradient of the velocity. / In this thesis, the author study the blowup of solutions for strong and classical solutions to the compressible Navier-Stokes equations. In the first part, we prove a blow up criterion for strong solutions to the compressible Navier-Stokes equations, similar to the Beal-Kato-Majda criterion for the ideal incompressible flows. / The same criterion for classical solutions to the compressible Navier-Stokes equations is established in the second part of this thesis. In addition, initial vacuum is allowed in both cases. / Huang, Xiangdi. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-09(E), Section: B. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 90-96). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

For the finite element (FE) simulation of relatively thin organs under complex dynamic loadings that are relevant in the biomedical engineering field, shell elements, compared to volume elements, have the potential to capture the whole thickness of the organ at once. Shell elements, are also known to feature efficiently large critical time steps, ensuring competitive computational times in dynamic structural analysis projects. As an improvement to the tools available for modelling and analysis, a new general nonlinear thick continuum-based (CB) shell FE embedded in an updated Lagrangian formulation and an explicit time integration scheme was recently developed. It can account for irregular and complex geometries, and hyper-elastic, large, nearly incompressible anisotropic 3D deformations characteristic of soft tissues. The original proof of concept was developed in MATLAB, which despite known advantages, is very slow. As a result, computational times, even for simple problems, have not been competitive. Therefore, the present work focused on re-writing the code in an efficient programming language with execution speed in mind in order to compete with the available elements which, in spite of having inferior capabilities, have better running times. In addition, a programming algorithm was needed to improve running time. Once it was implemented, the running time was reduced in half on a benchmark problem. Optimization was then exploited to introduce workarounds and design improvements that reduced running time further to 95% of its original value. The new version of the code was implemented in C++ and reached the goal of reducing running time while maintaining the expected functionality.

The Maketu Estuary is a shallow intertidal estuary (2.3 km2) located in the Bay of Plenty, North Island, New Zealand. The Kaituna River contributes the largest freshwater flow into the estuary through control gates. Lake Rotoiti and indirectly Lake Rotorua supply the base flow to the Kaituna River, with tributaries along the 50 km reach also significantly contributing to the flow. Water quality within the river is affected by elevated nutrients, faecal coliforms, high oxygen demand and algae concentrations derived from the lakes as well as contributions from tributaries and industrial and urban discharge. Through the use of a coupled hydrodynamic-biogeochemical numerical model ELCOM-CAEDYM, this study aims to examine the nutrient, phytoplankton and hydrodynamics of the Maketu Estuary and lower Kaituna River. Water quality and hydrodynamic measurements were sourced from Environment Bay of Plenty's data archives as well as a number of instrument deployments to collect water velocity, tidal elevation and salinity and temperature measurements during the course of this study. Included in the field work was a survey of the lower river and estuary bathymetry. Model simulations predicted that the maximum residence time in the Maketu Estuary is 1.5 days, occurring in the inner western region. Residence time in the lower river (mouth to 8.5 km upstream) is in the order of hours although some variations were predicted near the river mouth. Growth rates of four phytoplankton groups where assessed over a 15 day period in January 2004. In the Kaituna River ELCOM-CAEDYM predicted that the community growth rates were small with the exception of a slight increase in biomass of the two freshwater groups in a semi-detached river bend. The increase in the loop was correlated with an increase of residence time. In the estuary, marine diatoms showed the highest growth rates in the western region which is expected to relate to retention time and available nutrients. Dinoflagellates showed the smallest variation in predicted growth rates, most likely due to their broad salinity tolerance. The two freshwater species showed a reduction in abundance when mixed with marine water. A principle limiting factor to phytoplankton growth in both the river and estuary is the low residence time. A number of scenarios were simulated in the river and estuary by altering the forcing conditions in the model. A simulation of the increased nutrient load associated with the Rotoiti diversion wall revealed that phytoplankton growth in the river and estuary will not be significantly affected. Because of the close proximity of the control gates to the river mouth, a proportion of water drawn through the structure can be marine. By opening the old river channel, model simulations predicted that a reduction in salinity would be possible, however the outcome of complete freshwater is probably not achievable. Increasing the discharge volume from the river into the estuary was also simulated. The results indicated that increasing the freshwater inflow at Fords Cut would reduce the salinity in the estuary while increasing the net (residual) flow towards the estuary mouth. Increasing the flow would also result in a greater range of salinity in regions of the estuary. Changing the inflow location to the historic Papahikahawai Channel also affected the salinity in the estuary. The most significant effect of an inflow at this location was a reduction of the residual currents in the western region of the estuary.

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Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part fo the edge detection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus we consider this part of edge detection as a problem in numerical differentiation. We show that numerical differentiation of images is an ill-posed problem in the sense of Hadamard. Differentiation needs to be regularized by a regularizing filtering operation before differentiation. This shows that his part of edge detection consists of two steps, a filtering step and differentiation step.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 107-112).

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This study investigated Floating Production Storage and Offloading (FPSO) responses under wave and current interactions. A higher order boundary element method (HOBEM) was adopted to probe the behavior of an FPSO. Forces and moment of an FPSO were studied under wave and current interactions. The simulations of diffracted and radiated waves were performed in a time domain. Time marching schemes were used for this time domain calculation. The predictor-corrector(P-C) method was used. Boundary integral equations were used to solve each problem with Rankine sources and distributed over the entire calculation domain. For the far-field boundary condition, Orlanski’s truncated open boundary condition was used for an open truncated boundary condition to prevent reflected waves. The current effect was considered an explicit term due to being a moving coordinate. Various current heading angles were also studied. Truncated open boundary, maximum likelihood method, proper element size and shape, modulation function, and Chebyshev filtering were studied to avoid diverged solutions. From our findings, higher order elements fitted a complicated model such as an FPSO. We found that this method required considerably fewer elements than the constant panel method in order to obtain reasonable outcomes. Using our developed numerical method, we calculated wave forces and moment, mean drift forces, added mass, and damping coefficients. Conclusively, HOBEM was found to be more effective and more reliable in calculating and predicting wave and current influence on an FPSO. Future studies are needed to develop finer simulation tools for FPSO’s large horizontal behavior.

This paper present three kinds of nonlinear numerical methods to search for perfect complementary codes, include Newtonian Methods¡BLevenberg-Marquardt Algorithm and Trust-Regions. By searching for the solution of theses nonlinear equations, we can get complementary codes when setting for the length of element codes and the flock size. These search results is very generous. Complete complementary codes¡Bsuper complementary code and poly-phase complementary code are subsets of these searching results¡C These nonlinear equations are set to have ideal auto-correlation and cross-correlation properties, so the searching results of these nonlinear equations are still have perfect orthogonal complementary properties. Because the orthogonal complementary code is obtained via these nonlinear equations, the results are the most generous. So nonlinear numerical method is a good choice to search for another complementary code we don¡¦t know.