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Classical alternating direction (AD) methods for parabolic equations, based on some standard implicit time stepping procedure such as Crank-Nicolson, can have errors associated with the AD perturbations that are much larger than the errors associated with the underlying time stepping procedure . We plan to show that minor modifications in the AD procedures can virtually eliminate the perturbation errors at an minor additional computational cost. A mixed finite element method is applied in the spactial variables. Similar to the finite difference and finite element methods in spactial variables, we plan to have the same accuracy in time. A convergence analysis can also be shown .

A FORTRAN code was developed to numerically simulate the mixed convective flow over a three-dimensional horizontal backward-facing step. The momentum and energy equations under the assumption of the Boussinesq approximation were discretized by means of a finite volume technique. The SIMPLE algorithm scheme was applied to link the pressure and velocity fields inside the domain while an OpenMP parallel implementation was proposed to improve the numerical performance and to accelerate the numerical solution. The heating process corresponds to a channel heated from below at constant temperature keeping insulated all the other channel walls. In addition, the back-step was considered as a thermally conducting block and its influence in the heating process was explored by holding different solid to fluid thermal conductivity ratios. The effects over the velocity and temperature distribution of buoyancy forces, acting perpendicular to the mainstream flow, are studied for three different Richardson numbers Ri=3, 2, and 1 and the results are compared against those of pure forced convection Ri=0. In these simulations the Reynolds number is fixed at 200 while the bottom wall temperature is adjusted to fulfill the conditions for the different Ri. Under this assumption, as Ri increases the buoyancy effects are the dominant effects in the mixed convective process. The numerical results indicate that the velocity field and the temperature distribution for pure forced convection are highly distorted if compared with the mixed convective flow. If the Ri parameter is increased, then the primary re-circulation zone is reduced. Similarly, as the buoyancy forces become predominant in the flow, the convective rolls, in the form of spiral-flow structures, become curlier and then higher velocity components are found inside the domain. The temperature field distribution showed that as the Ri is increased a thicker layer of high temperature flow is located at the channel??s top wall as a result of the higher rates of low-density flow moving to the top wall. The flow is ascending by the channel sidewalls, while descending by the channel span-wise central plane. The parallel numerical strategy is presented and some results for the performance of the OpenMP implementation are included. In this sense, linear speedup was obtained when using 16 possessors in parallel.

The preparations of multinuclear supramolecules assembled from ethynylferrocene(s) redox-active subunit end-capping with [(£b5-C5H5)(dppe)Ru] metal centers are described. Electrochemical measurements indicate that ferrocenyl-ethynyl spacers appear to be promising spacers which can ensure fast and quantitative transfer of information between two Ru2+ metal centers.

Cheat, a kind of crime, happens in the classroom. This paper is purposed to find how to reduce the probability of cheating, how the policy can make an effect on teachers and students, and how to achieve the best interaction between them. The best interaction is that teachers put in high effort and students choose the strategy which is not to cheat. In the beginning, we assume the game is static. Under the mixed strategy equilibrium, the punishment to cheat has nothing to do with reducing the probability of cheating, but it has a trade-off relation with the probability of teachers to put in high effort. If we add peer pressure into the students¡¦ utility, it will take more probability of teachers to put in high effort to avoid cheating. However, if the policy which is to reward teachers who put in high effort brings into effect, it helps not only reduce the probability of cheating but also achieve the best interaction. After the mixed strategy equilibrium, I release two assumptions. One is to transform the game from static into dynamic, and the other is to make the effort function become continuous. Teachers then become first mover. At this moment, teachers have first-move advantage. When teachers put in some effort more than the level mentioned in the article, students do not have the incentive to cheat. In this case, it is easier to achieve the best reaction.

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The present study developes a mixed finite element formulation for the analysis of piezoelectric circular and annular plates. This formulation combines the conventional displacement-electric potential type variational principle and the piezoelectric Reissner`s principle with a weighting factor which represents ratio of weights imposed on the above two variational principles, and which can be adjusted by comparing with experiment results. With this formulation, stresses and electric displacements, like displacements and electric potential, are primary variables and are continuous across elements and element interfaces. Also, all displacement, stress, electric displacement, and electric potential boundary conditions can be easily and exactly imposed. Static deformations and vibration frequencies of some typical piezoelectric circular and annular plates are then obtained with the present approach and are compared with those by other methods. Based on experiment results in the literature, it is found that better results could be obtained in general by the present mixed finite element formulation than the others when 1 is chosen as the weighting factor.

Thesis (M.A.)--University of Hong Kong, 2001. / Includes bibliographical references.

Thesis (Honors)--University of South Florida, 2009. / Title from cover. "Semester completed: spring 2009." "This thesis is a continuation of my Engineering Capstone Design. ... The initial design was completed as a group (consisting of five people) under the fabricated engineering firm Lever Engineering, LLC and was completed as if it would be submitted to the County for actual approval"--Abstract. Includes bibliographical references (p. [2-3] of first group).

The purpose of this study was to compare 4 growth curve functions (Brody, Logistic, Gompertz, and Von Bertalanffy) in describing the weight change across age in Angus cow. A total of 1,705 weight-age records from birth to at least 3-year of age from 171 cows were collected. All the growth models were fitted as a nonlinear mixed model using NLMIXED procedure in SAS9.2 (REML Approach) and MCMC method through WinBUGS (Bayesian Approach). The goodness of fit of these four models was compared in terms of AIC, BIC, and DIC. The results show that the Gompertz model fitted the data best under REML Approach while the Brody model appeared to be the best model under Bayesian Approach. The Bayesian Approach provided more flexibility in setting up the mixed model and more reasonable estimates for all the growth models compared to the REML Approach. These results show some advantages of Bayesian nonlinear mixed modeling. / text