Consider a population of m-type individuals labelled by {1,2,...,m}. Let x=(x_1,x_2,...,x_m) denote the relative frequencies of all types with x_i denoting the relative frequency of type i for 1<i<m. For a random sample of size 2 from the population, the probability that the individuals of the sample are of the same type is given by H= sum of the squares of x_i's up to m. In this thesis, we focus on the case where x = (x_1,x_2,...x_m) is a random vector. The quantity H appears in various fields of study. For instance, it is associated with the Shannon entropy in communication, the Herfindahl-Hirschman index in economics and known as the homozygosity in population genetics. In Feng (2010), fluctuation theorems for the infinite dimensional case of H are considered. In this thesis we present, under a moment assumption, a Central Limit Theorem (CLT) associated with H and present as examples the Gamma subordinator case, which is a well known result by Griffiths (1979), and the generalized Gamma subordinator case. / Thesis / Master of Science (MSc)

A rapid coliphage detection assay (RCDA), based on the phage-induced release of b-galactosidase from cells of Escherichia coli (Ijzerman, M., J.O. Falkinham III and C. Hagedorn. (1993) [A liquid, colorimetric presence-absence coliphage detection method. J. Virol. Meth. 45:229-234] was modified to reduce the number of steps required to perform the assay, remove the need for specialized media and buffers, reduce the volumes required, and simplify growth and reaction conditions. Tolerances of the assay were defined at each step of the assay. The number of steps has been reduced from 12 to 7. The b-galactosidase reaction buffer was eliminated. Culture volumes were reduced from 25 ml to 5 ml and reaction volumes were reduced from 10 ml to 0.5 ml. Optimal growth conditions were 37 o C with orbital shaking at 200 rpm, a one hour subculture time and an incubation of subculture with water sample for two hours. Color development occurred at 37 o C in 30 minutes. The changes and modifications of the assay increased the ease of its performance without sacrificing the ability of the assay to detect as few as two phage particles per sample. By understanding the tolerances of the assay, technical support representatives of companies producing kits modeled after the assay will be prepared to answer questions from customers concerning possible kit failures or user error. / Master of Science

Three aspects in determining the first natural frequency of steel joist supported floors were studied. The aspects are: 1) determining which finite element model best predict the behavior of joist-slab tee-beams, 2) investigating the ability of proposed equations to calculate the effective moment of inertia of joist-slab tee-beams, and 3) developing a finite element model to predict the first natural frequency of steel joist supported floors. Several finite element models were tested to determine which one best predicted the experimental results of six joist-slab setups. The model which best predicted the experimental results was used. Next, a study was done to determine the ability of a proposed equation to predict the effective moment of inertia of joist-slab tee-beams. The study modeled and analyzed 130 joist-slab configurations and compared the results to those calculated using the proposed equations. Finally, a finite element modeling technique was developed to predict the first natural frequency of steel joist supported floors. Seven in-situ floors were experimentally tested, and those results were compared to the predicted values given by the models. / Master of Science

Our civilization is facing increased populations and scarcity of habitat for a variety of species. Encroaching on these landscapes while engaging in habitat fragmentation and destruction, has negatively impacted biodiversity and subsequently put thousands of species at risk of going extinct. With humans causing peril for various species via habitat losses and degradation due to our developing of landscapes, as Landscape Architects, we have a responsibility to minimize, negate, or rectify these losses and while still providing serviceable landscapes for our fellow humans. One possible avenue to pursue when motives for the well being of the collective are being considered is designing landscapes that serve both human and species in unison, with services being provided for humans and satisfying the needs of wildlife. This project is based on a desire to accommodate the needs of a growing community by providing a stormwater retainment system serving as a pedestrian artery to a historic river, while also accommodating the needs of wildlife by establishing a constructed meadow that satisfies habitat requirements for the Eastern Meadowlark. Through analysis of storm water volumes, building code setbacks regarding waterways, habitat requirements of the Eastern Meadowlark and land volume manipulation, a solution to many obstacles facing community and species has been posited in this project: the Dianna Dayle River Walk. / Master of Landscape Architecture

The intent of this thesis was to develop a component system derived from a desired form. Through analysis of the initial form, I gained an understanding of the underlying parameters, principles, and topologies the form exhibited that could then be interpreted into the development of a component system. Through the process of design, utilizing iterative attempts of creating a component system directly mimicking the original form, I began to realize the need to better understand the underlying principles and topologies of the original form. This understanding became the basis in my attempts to assemble components toward a direct copy of the original form. This experimentation led to the realization that direct copy was not achievable. However, the deeper understanding of the principles exhibited within the initial form provided the framework to develop a component system that would exhibit similar results while simultaneously allowing for greater control in the development of a member with a particular desired outcome. The conversation between Form and Method was a continuous dialogue throughout the project: from the form of the initial model and the method of developing a component system based on the principles it exhibited, to the formal expression of the component itself, and eventually to a final iteration that combines the principles of the original construct through the method of assembly based on the form of the component. / Master of Architecture

In my dissertation, I developed mixed hp-finite element methods for linear elasticity with weakly imposed symmetry, which is based on Arnold-Falk-Winther's stable mixed finite elements. I have proved the h-stability of my method for meshes with arbitrary variable orders. In order to show the h-stability, I need an upper limit of the highest order of meshes, which can be an arbitrary nonnegative integer. / text

In today’s world there are 2.6 billion people that lack basic sanitation (37% of world inhabitants). In August of 2012, Cranfield University was awarded by the Bill & Melinda Gates Foundation with $810,000 to produce a prototype of the Cranfield’s innovative Nano-membrane Toilet (NMT). Finally, the prototype is going to be exhibited at the “Reinvent the Toilet Fair” during 21st and 22nd of March 2014 in the Taj Palace Hotel, New Delhi (India). Cranfield’s NMT demands electricity for its daily performance. Nevertheless, it is targeted to off-grid communities. Consequently, a human-powered generator (HPG) was selected as a backup solution. The current MSc by Research aimed to design and test of a prototype of the aforesaid HPG. Moreover, to promote its usage, a portable power supply unit is designed to store energy and power small-loads like charging mobile phones and electric lighting. To select the most suitable design for our case study, a methodology using the Technique for Order of Preference by Similarity to the Ideal Solution has been developed. As a result the plugged-in bike HPG alternative was selected. Next, prototypes of this generator and the portable power supply unit were developed, tested and shipped for display. While testing of the plugged-in generator and portable power supply unit, 26 Watt-hours (Wh) were harvested over 15 minutes, with its corresponding average charging power of 105 Watts. Nevertheless, the present study concludes 96 Wh as a more accurate energy level to be harvested during one hour of pedalling. Considering 96 Wh of energy, a round-trip battery efficiency of 70% (lead-acid), and a NMT’s demand of 283 Wh; a 10 people household needs to pedal the HPG over 4 hours and 20 minutes. Nevertheless, if considering an 85% inverter efficiency, 57.12 Wh are available to fully charge one mobile phone (5.6 Wh) and provide 4.5 hours of room and desk lighting (11 Watts bulb).

Analysis of different types of fault is an important and complex task in a power system. Accurate fault analysis requires models that determine fault distances in a transmission line. The mathematical models accurately capture behavior of different types of faults and location in a timely manner, and prevents damaging power system from fault energy. The purpose of this thesis is to use two methods for determining fault locations and their distance to the reference end buses connected by the faulted transmission line. The two methods used in this investigation are referred to as impedance-based and traveling wave methods. To analyze both methods, various types of faults were modeled and simulated at various locations on a two-bus transmission system using EMTP program. Application and usefulness of each method is identified and presented in the thesis. It is found that Impedance-based methods are easier and more widely used than traveling-wave methods.

Numerical simulation of cell motility is one of the difficult problems in computational science. It belongs to a class of problems which involve moving interfaces between flowing or deforming media. Different numerical techniques are being developed for different application areas and in this work an attempt is made to apply two popular numerical techniques used in the field of computational multiphase flows to a cell motility problem. An unsteady cell motility problem is considered to simulate numerically based on a two-dimensional mathematical model. Two important numerical methods, the Level set method and the Front tracking methods are applied to the cell motility problem to study several cases and to verify the convergence of the solution. With the assumption of no mechanical or physical obstructions to the cell, the results of the numerical simulations show that the domain shapes converge to a circular shape as they reach the steady state condition. The final steady state velocities with which the domains move and the final steady state area to which they converge are observed to be independent of domain shapes. Moreover all shapes converge to exactly same radius of circle and move with same velocity after reaching steady state condition.

In this section, we will consider two methods for computing an eigenvector and in addition the associated eigenvalue of a matrix A.