HIGH ORDER SHOCK CAPTURING SCHEMES FOR HYPERBOLIC CONSERVATION LAWS AND THE APPLICATION IN OPEN CHANNEL FLOWS

Many applications in engineering practice can be described by thehyperbolic partial differential equations (PDEs). Numerical modeling of this typeof equations often involves large gradients or shocks, which makes it achallenging task for conventional numerical methods to accurately simulate suchsystems. Thus developing accurate and efficient shock capturing numericalschemes becomes important for the study of hyperbolic equations.In this dissertation, a detailed study of the numerical methods for linearand nonlinear unsteady hyperbolic equations was carried out. A new finitedifference shock capturing scheme of finite volume style was developed. Thisscheme is based on the high order Pad?? type compact central finite differencemethod with the weighted essentially non-oscillatory (WENO) reconstruction toeliminate non-physical oscillations near the discontinuities while maintain stablesolution in the smooth areas. The unconditionally stable semi-implicit Crank-Nicolson (CN) scheme is used for time integration.The theoretical development was conducted based on one-dimensionalhomogeneous scalar equation and system equations. Discussions were alsoextended to include source terms and to deal with problems of higher dimension.For the treatment of source terms, Strang splitting was used. For multidimensionalequations, the ?? -form Douglas-Gunn alternating direction implicit(ADI) method was employed. To compare the performance of the scheme withENO type interpolation, the current numerical framework was also applied usingENO reconstruction.The numerical schemes were tested on 1-D and 2-D benchmark problems,as well as published experimental results. The simulated results show thecapability of the proposed scheme to resolve discontinuities while maintainingaccuracy in smooth regions. Comparisons with the experimental results validatethe method for dam break problems. It is concluded that the proposed scheme isa useful tool for solving hyperbolic equations in general, and from engineeringapplication perspective it provides a new way of modeling open channel flows

Physical Activity, Daily Step Counts and Functional Ability in Older Adults: Using NHANES Database

Maintaining functional ability and independence are essential in the healthcare of older adults. Physical activity(PA) has been acknowledged as effective and economical health promotion strategies in older population. However, the amount of PA needed to maintain functional ability in older adults remains unclear. This investigation used PRISM Dose-response Curves Stimulation Variable slope model to explore the relationships between the amount of PA and functional ability in community-dwelling young-old, middle-old and old-old age group adults. ANOVA analysis was used to examine the relationship between functional ability and self-perceived active level changes compared to 10 years ago. NHANES 2005-2006 older participants datasets were used. The study found positive dose-response curve relationship in middle-old female adults. Older women aged 75-84 years benefit from every minute spent on PA, an amount of 150 minutes per week is necessary to obtain the most functional benefits. Older adults who are 65 years old and above need to walk 5,400 -6,500 steps per day or spend 1,500- 4,500kcal energy, or 150-450 minutes per week on PA to maintain their functional abilities in later ages. Older adults who perceive themselves less active compared to 10 years ago have more difficulties in doing daily activities than those who considered themselves the same active levels

Calculations of random fixed point index

AbstractIn this paper, we prove an important inequality and investigate some new calculating problems of random fixed point index, and generalize famous theorem by means of the theory of random fixed point index

Non-adiabatic holonomic quantum computation in linear system-bath coupling

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of $\frac{N-2}{N}$. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.Comment: 2 figures; accepted by Sci. Re

The PBDE-209 Exposure during Pregnancy and Lactation Impairs Immune Function in Rats

In the present study, we assessed the treatment effects of PBDE-209 administration on the immune function in rats during pregnancy and lactation. We harvested the blood and organs for flow cytometry, viability assay, enzyme-linked immunosorbent assay, and histological evaluation. The results of this study were the PBDE-209 exposure during pregnancy and lactation impairs immune function in rats. The results may contribute to understanding the mechanism of PBDE-209 in immune function

Synthesis and Antiproliferative Activity of Some Steroidal Lactams

Using cholesterol as starting material, a series of 6-substituted-3-aza-A-homo-3-oxycholestanes and 6-substituted-4-aza-A-homo-3-oxycholestanes were synthesized by the oxidation, reduction, oximation, Beckman rearrangement and condensation reaction. These synthesized compounds displayed a distinct cytotoxicity against MGC 7901, HeLa and SMMC 7404 cancer cells. Our results revealed that the structures of functional groups at position-6 on the steroidal ring are crucial for the IC50 value of antiproliferative activities of these compounds and the cytotoxic activity against MGC 7901 and SMMC 7404 cells was not significantly different between 4-N-lactams and 3-N-lactams when its 6-substituted group was a carbonyl or a hydroximino, but all 3-N-lactams showed a higher cytotoxicity against HeLa cells than 4-N-lactams. In particular, compounds 6, 8, 9 (IC506: 6.5 μmol/L; 8: 7.7 μmol/L; 9: 5.6 μmol/L) were even more cytotoxic than cisplatin to HeLa cells (positive contrast, 10.1 μmol/L). The information obtained from the studies may be useful for the design of novel chemotherapeutic drugs