published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

No description available.

No description available.

No description available.

The concept of inclusive fitness plays a key role in much of sociobiology. Yet most theoretical studies concerning the evolution of social behavior circumvent inclusive fitness by mobilizing the concept of frequency dependent individual fitness. Given certain assumptions, it is shown that models based on these two different concepts are dynamically equivalent. The models do differ, however, in bookkeeping methods which are advantageous under different circumstances. A knowledge of these circumstances should prove of value to students of social behavior. It is then shown that evolution acts according to an adaptive landscape based on Hamilton's inclusive fitness in the absence of strong selection and inbreeding. This yields an inclusive fitness analogue to much of traditional population genetics. For example, heterozygote superiority in inclusive fitness yields stable polymorphisms, while intermediate dominance results in fixation of one of the alleles. When individuals do not affect one another's fitnesses, the inclusive fitness topography collapses to one based on individual fitness. A general rule for the evolution of social behavior under intermediate dominance is shown to yield Hamilton's Rule as a special case. Next, a general model for examining the evolution of social behavior is developed which, unlike inclusive fitness models, does not require that benefits received be linear functions of the number of social donors encountered. The subsocial route for the evolution of eusociality in haplodiploid organisms is then examined within the context of this model. Nonlinearities render conditions for frequency independent fixation or loss of sister-helping alleles more stringent than expected from models based on the assumption of linear benefits. In particular, both stable polymorphisms and frequency dependent selective thresholds for sister-helping behavior may commonly obtain.

Stable channel design is a very important element in many water resources projects. Both bed and bank stability are necessary design criteria. The channel is designed for some critical flow rate and sediment load, where the bank erodibility, sediment size distribution, and channel resistance to flow are imposed conditions. For these conditions the stable channel width, depth, and slope are predicted. Earlier studies by Lacey, Blench, and others related the channel dimensions to the flow rate as a power function. In Blench's study the coefficient of the function was dependent on the nature and charge of the bed material, and the erodibility of the sides, while the exponent was a constant. This study extends the power function equation relationship. The width, depth, and width/depth ratio were considered functions of the flow rate, and the coefficients and exponents were both found to be dependent on the sediment concentration and the bank erodibility. The tractive force method was used in this analysis. A set of design graphs were determined from simultaneous solutions of the Manning and Laursen equations. From the graphs design equations were formulated. Some simple example problems were solved using this method. In the analysis the bank erodibility (maximum permissible bank shear) needed to be quantified. Experiments were performed with a Preston tube to determine the shear distributions in channels with various roughness patterns. From the results the maximum bank shear could be determined as a coefficient times the maximum bed shear. When the smooth channel and rough channel were tested, the results compared well with the values used by Lane (coefficient approximately 0.76). When the banks were smooth and the bed was rough, or vice versa, the coefficient was found to be different than 0.76. More testing is considered necessary to determine if the difference is significant.

Numerous studies of the behavior of speculative prices have shown that the empirical distribution of such returns is consistently more peaked and fat-tailed than a Gaussian, and often positively skewed. Strong evidence is presented indicating hat such returns are better modeled by two-and three-component normal mixtures. By varying the means, variances, and probability weights of the component normals, a wide variety of peaked, fat-tailed, and symmetric or skewed distributions may be represented with very tractable mathematical expressions. Examination of the returns of 116 CBOE firms over three two-year periods indicates a high percentage of good fits for such normal mixtures, based on the chi-square statistic. Further, inspection of the parameters estimated for the two-component normal mixture reveals that the larger variance is quite frequently not associated with the lower probability weight as hypothesized by Mandelbrot and others. A new method of selecting class-boundaries is proposed to improve the reliability of the chi-square goodness-of-fit test. Using simulation, this method is found to be superior to the traditional Mann-Wald equiprobable approach, particularly for low priced securities. Using the assumption of risk-neutrality and a mixture of normals density for the underlying security returns, the mixture call option pricing model is derived. Call option prices are shown to be weighted sums of Black-Scholes prices, with solutions to the mixture model converging to Black-Scholes prices, with solutions to the mixture model converging to Black-Scholes solutions as the number of periods to expiration becomes large. Using the parameters obtained from typical mixture densities of actual CBOE firms, mixture model prices are generated and compared with Black-Scholes prices. It is found that out of the money, near term options are underpriced by Black-Scholes relative to the mixture model. The closer to expiration and the farther out of the money the option, the more Black-Scholes under-prices relative to the mixture model. Additionally, the fatter tailed and more positively skewed the underlying security returns distribution, the greater the differences between the two call option pricing models.

No description available.

No description available.