Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (April 26, 2007) Vita. Includes bibliographical references.

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2005. / Includes bibliographical references (p. 85-88).

Thesis (M.S.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains xv, 133 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 126-133).

Thesis (Ph. D.)--University of Idaho, 2006. / Abstract. "May 2006." Includes bibliographical references (leaves 100-106). Also available online in PDF format.

Asian options are an important family of derivative contracts with a wide variety of applications in commodity, currency, energy, interest rate, equity and insurance markets. In this master's thesis, we investigate methods for evaluating the price of the Asian call options with a fixed strike. One of them is the Monte Carlo method. The accurancy of this method can be observed through variance of the price. We will see that the variance with using Monte Carlo method has to be decreased. The Variance Reduction technique is useful for this aim. We will give evidence of the efficiency of one of the Variance Reduction thechniques - Control Variate method - in a mathematical context and a numerical comparison with the ordinary Monte Carlo method.

To compute the expectation of a function with respect to a multivariate distribution naive Monte Carlo is often not feasible. In such cases importance sampling leads to better estimates than the rejection method. A new importance sampling distribution, the product of one-dimensional table mountain distributions with exponential tails, turns out to be flexible and useful for Bayesian integration problems. To obtain a heavy-tailed importance sampling distribution a new radius transform for the above distribution is suggested. Together with a linear transform the new importance sampling distributions lead to simple and fast integration algorithms with reliable error bounds. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Monte Carlo (MC) methods are widely accepted as the most accurate technique for calculating dose distributions in radiation therapy physics. Simulating the particle transport through the treatment head of a linear accelerator utilizing a MC based code is both a widespread and practical approach to determining detailed clinical beam characteristics such as the energy, angular and spatial distribution of particles which are needed to properly quantify dose. One particular and versatile MC code, the Monte Carlo N-Particle (MCNP) radiation transport code, developed by Los Alamos National Laboratory, has been commonly used to model ionizing radiations for medical physics applications. In this thesis, a Varian 2100C linear accelerator (linac) is modeled and the electron and photon transport through the primary components of the treatment head are simulated using MCNP Version 5_1.3. The 6 MV photon spectra was characterized in a standard 10 x 10 cm2 field and subsequent dose calculations were made in a Virtual Water (VW) phantom. Energy fluence, percent depth dose and beam profile measurements were taken in a modeled VW phantom and the calculated data was compared to measured reference data. In addition, a human phantom was modeled for future dose calculations using the modeled linac. The linac model created can incorporate different beam energies for determining the dose distribution of multiple beam treatments in phantoms for standard 6 MV plans. The adaptability of this MCNP model allows for any number of geometries and sources encountered in medical physics to be computed and applied with relative ease. Future studies can involve adding complex multi-leaf collimator beam shaping and calculating the dose in human phantom models, which would serve as a basis for studies involving MCNP modeling for dose optimization in medical physics applications.

Current advancements in nuclear reactor core design are pushing reactor cores towards greater heterogeneity in an attempt to make nuclear power more sustainable in terms of fuel utilization and long-term disposal needs. These new designs are now being limited by the accuracy of the core simulators/methods. Increasing attention has been given to full core transport as the flux module in future core simulators. However, the current transport methods, due to their significant memory and computational time requirements, are not practical for whole core calculations. While most researchers are working on developing new acceleration and phase space parallelization techniques for the current fine mesh transport methods, this dissertation focuses on the development of a practical heterogeneous coarse mesh transport method. In this thesis, a heterogeneous coarse mesh transport method is extended from two to three dimensions in Cartesian geometry and new techniques are developed to reduce the strain on computational resources. The high efficiency of the method is achieved by decoupling the problem into a series of fixed source calculations in smaller sub-volume elements (e.g. coarse meshes). This decoupling lead to shifting the computation time to a priori calculations of response functions in unique sub-volumes in the system. Therefore, the method is well suited for large problems with repeated geometry such as those found in nuclear reactor cores. Even though the response functions can be generated with any available existing fine-mesh (deterministic or stochastic) code, a stochastic method was selected in this dissertation. Previous work in two dimensions used discrete polynomial expansions that are better suited for treating discrete variables found in pure deterministic transport methods. The amount of data needed to represent very heterogeneous problems accurately became quite large making the three dimensional extension impractical. The deterministic method was thus replaced by a stochastic response function generator making the transition to continuous variables fairly simple. This choice also improves the geometry handling capability of the coarse mesh method.

Polymer matrix composites reinforced by metal fibers are observed to present an onset of the insulator-to-conductor transition through previous experimental studies. Analytical studies revealed that the percolation threshold occurs when fiber volume fraction reaches the critical value. The numerical study based on Monte Carlo simulations are performed to investigate such a relation. In this work, the conductive fillers are modeled as a three dimensional (3D) network of identical units randomly distributed in the polymer matrix. For the simplest case, straight fibers are used in the simulation. The effects of the aspect ratio and fiber length on the critical volume fraction are also studied. Linearization is made to the logarithm of simulation results. Next, in order to study the effects of emulsion particles and the emulsion particle sizes on the percolation behavior, cubic particles are aligned in the sample model. The gap width to particle size ratio is fixed at 1/10. The calculated critical volume fraction is used in the power-law function to predict the electrical conductivity of the polymer composites. Due to the insensitivity of the thermal conductivity to the percolation threshold, a combination of two empirical equations is used to predict the range of overall thermal conductivity.

Rotorcraft transmission design is limited by empirical weight trends that are proportional to the power/torque raised to the two-thirds coupled with the relative inexperience industry has with the employment of variable speed transmission to heavy lift helicopters of the order of 100,000 lbs gross weight and 30,000 installed horsepower. The advanced rotorcraft transmission program objectives are to reduce transmission weight by at least 25%, reduce sound pressure levels by at least 10 dB, have a 5000 hr mean time between removal, and also incorporate the use of split torque technology in rotorcraft drivetrains of the future. The major obstacle that challenges rotorcraft drivetrain design is the selection, design, and optimization of a variable speed transmission in the goal of achieving a 50% reduction in rotor speed and its ability to handle high torque with light weight gears, as opposed to using a two-speed transmission which has inherent structural problems and is highly unreliable due to the embodiment of the traction type transmission, complex clutch and brake system. This thesis selects a nontraction pericyclic continuously variable transmission (P-CVT) as the best approach for a single main rotor heavy lift helicopter to target the above mentioned obstacle for drivetrain design and provides advancement in the state of the art of drivetrain design over existing planetary and split torque transmissions currently used in helicopters. The goal of the optimization process was to decrease weight, decrease noise, increase efficiency, and increase safety and reliability. The objective function utilized the minimization of the weight and the constraint is the tooth bending stress of the facegears. The most important parameters of the optimization process are weight, maintainability, and reliability which are cross-functionally related to each other, and these parameters are related to the torques and operating speeds. The analysis of the split torque type P-CVT achieved a weight reduction of 42.5% and 40.7% over planetary and split torque transmissions respectively. In addition, a 19.5 dB sound pressure level reduction was achieved using active gear struts, and also the use of fabricated steel truss like housing provided a higher maintainability and reliability, low cost, and low weight over cast magnesium housing currently employed in helicopters. The static finite element analysis of the split torque type P-CVT, both 2-D and 3-D, yielded stresses below the allowable bending stress of the material. The goal of the finite element analysis is to see if the designed product has met its functional requirements. The safety assessment of the split torque type P-CVT yielded a 99% probability of mission success based on a Monte Carlo simulation using stochastic- petri net analysis and a failure hazard analysis. This was followed by an FTA/RBD analysis which yielded an overall system failure rate of 140.35 failures per million hours, and a preliminary certification and time line of certification was performed. The use of spherical facegears and pericyclic kinematics has advanced the state of the art in drivetrain design primarily in the reduction of weight and noise coupled with high safety, reliability, and efficiency.