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No two species can indefinitely occupy the same ecological niche according to the competitive exclusion principle. When competing strains of the same pathogen invade a homogeneous population, the strain with the largest basic reproductive ratio R0 will force the other strains to extinction. However, over 51 pathogens are documented to have multiple strains [3] coexisting, contrary to the results from homogeneous models. In reality, the world is heterogeneous with the population varying in susceptibility. As such, the study of epidemiology, and hence the problem of pathogen coexistence should entail heterogeneity. Heterogeneous models tend to capture dynamics such as resistance to infection, giving more accurate results of the epidemics. This study will focus on the behavior of multi-pathogen heterogeneous models and will try to answer the question: what are the conditions on the model parameters that lead to pathogen coexistence? The goal is to understand the mechanisms in heterogeneous populations that mediate pathogen coexistence. Using the moment closure method, Fleming et. al. [22] used a two pathogen heterogeneous model (1.9) to show that pathogen coexistence was possible between strains of the baculovirus under certain conditions. In the first part of our study, we consider the same model using the hidden keystone variable (HKV) method. We show that under some conditions, the moment closure method and the HKV method give the same results. We also show that pathogen coexistence is possible for a much wider range of parameters, and give a complete analysis of the model (1.9), and give an explanation for the observed coexistence. The host population (gypsy moth) considered in the model (1.9) has a year life span, and hence, demography was introduced to the model using a discrete time model (1.12). In the second part of our study, we will consider a multi-pathogen compartmental heterogeneous model (3.1) with continuous time demography. We show using a Lyapunov function that pathogen coexistence is possible between multiple strains of the same pathogen. We provide analytical and numerical evidence that multiple strains of the same pathogen can coexist in a heterogeneous population.

Elliot Rodger, a 22-year-old student, carried out the Day of Retribution in Isla Vista, California, leaving six dead and fourteen wounded, before taking his own life. There here have been numerous attempts to explain his behavior including claims of him having features of autism spectrum disorder, traits of psychopathy and psychotic symptoms, narcissism, depression, fragile masculinity, and deviant sexual fantasies. This study examines the link between strain, coping and violence, based on General Strain Theory, using a qualitative content analysis of Elliot’s manifesto, My Twisted World: The Story of Elliot Rodger. The results indicate that Elliot experienced multiple sources of strain in his life and that he lacked adequate coping skills, which affected his perceptions of and interactions with the world. He experienced isolation, frustration and anger. These negative emotions together with his sense of entitlement intensified over the years, creating desire for revenge and justifying use of extreme violence as an attempt to eliminate strain and find relief.

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A stretchable silver ink was screen printed to TPU sheets, then tensile coupons of the TPU, both bare and laminated to cotton, Denim and spandex fabric, were subjected to 1000 cycles of 20% uniaxial strain. In-situ resistance measurements of printed traces were processed to generate datasets of maximum and minimum resistance per cycle. A mechanistic fit model was used to predict the resistance behavior of the ink across TPU/fabric levels. The results show that traces strained on TPU laminated to spandex (polyester) fibers had an average rate of increase in resistance significantly lower than that of traces strained on bare TPU. The variation in predicted resistance was significantly lower in the spandex group than in the TPU group. Trace width was not found to have a significant effect on the resistance behavior across TPU/fabric groups. More testing is required to understand the effect of lamination to high elasticity fabrics on resistance behavior as it relates to the viscoelastic properties of the fibers and weave structure.

Spinal ligaments may be a significant source of chronic back pain, yet they are often disregarded by the clinical community due to a lack of information with regards to their material response, and innervation characteristics. The purpose of this dissertation was to characterize the material response of spinal ligaments and to review their innervation characteristics. Review of relevant literature revealed that all of the major spinal ligaments are innervated. They cause painful sensations when irritated and provide reflexive control of the deep spinal musculature. As such, including the neurologic implications of iatrogenic ligament damage in the evaluation of surgical procedures aimed at relieving back pain will likely result in more effective long-term solutions. The material response of spinal ligaments has not previously been fully quantified due to limitations associated with standard soft tissue testing techniques. The present work presents and validates a novel testing methodology capable of overcoming these limitations. In particular, the anisotropic, inhomogeneous material constitutive properties of the human supraspinous ligament are quantified and methods for determining the response of the other spinal ligaments are presented. In addition, a method for determining the anisotropic, inhomogeneous pre-strain distribution of the spinal ligaments is presented. The multi-axial pre-strain distributions of the human anterior longitudinal ligament, ligamentum flavum and supraspinous ligament were determined using this methodology. Results from this work clearly demonstrate that spinal ligaments are not uniaxial structures, and that finite element models which account for pre-strain and incorporate ligament’s complex material properties may provide increased fidelity to the in vivo condition.

In order to design more efficient and reliable structures, axial load tests are performed on foundation piles. Traditionally, static tests with an average duration of approximately twenty-four hours have been performed on test piles to obtain their axial capacity. These static tests require multiple piles used as anchors in addition to the test pile. Static tests are both expensive and time consuming. An alternative to static testing is dynamic testing which requires sophisticated interpretation, can damage the pile and may not produce accurate results. There is a relatively new testing method called the Statnamic Testing Method which tests foundation piles at a very fast rate, but still slower than with dynamic tests. As the rate at which load is applied to a test pile increases, the axial capacity also increases, particularly in clay. Research suggests that shear strength of soil typically increases 10% per log cycle increase in strain rate. Strain rate effects can vary widely and may be influenced by many factors including plasticity index, structure, ageing, overconsolidation ratio, temperature, etc. Statnamic testing was performed for this work. Nine static tests were performed on six different piles identical to the Statnamic test pile and driven through the same soil profile. The static tests had times to failure ranging from ten seconds to eighteen hours. Failure load increased by 13.7% per log cycle increase in velocity. Statnamic tests need more careful analysis when performed in clay to avoid over predicting pile capacity. A factor of 0.55 should be applied to Statnamic capacity to predict static capacity.

Carbon fiber reinforced plastic (CFRP) composites have extensive value in the aerospace, defense, sporting goods, and high performance automobile industries. These composites have huge benefits including high strength to weight ratios and the ability to tailor their properties. A significant issue with carbon fiber composites is the potential for catastrophic fatigue failure. To better understand this fatigue, there is first a huge push to measure strain accurately and in-situ to monitor carbon fiber composites. In this paper, piezoresistive nickel nanostrand (NiNs) nanocomposites were embedded in between layers of carbon fiber composite for real time, in situ strain monitoring. Several different embedding methods have been investigated. These include the direct embedding of a patch of dry NiNs and the embedding of NiNs-polymer matrix nanocomposite patches which are insulated from the surrounding carbon fiber. Also, two different polymer matrix materials were used in the nanocomposite to compare the piezoresistive signal. These nanocomposites are shown to display repeatable piezoresistivity, thus becoming a strain sensor capable of accurately measuring strain real time and in-situ. This patch has compatible mechanical properties to existing advanced composites and shows good resolution to small strain. This method of strain sensing in carbon fiber composites is more easily implemented and used than other strain measurement methods including fiber Bragg grating and acoustic emissions. To show that these embedded strain gages can be used in a variety of carbon fiber components, two different applications were also pursued.

Due to their unique properties, carbon fiber reinforced polymers (CFRP) are becoming ever more prevalent in today's society. Unfortunately, CFRP suffer from a wide range of failure modes and structural health monitoring methods are currently insufficient to predict these failures. It is apparent that self-sensing structural health monitoring could be advantageous to protect consumers from catastrophic failure in CFRP structures. Previous research has shown that embedded nickel nanostrand nanocomposites can be used to instantaneously measure strain in carbon fiber composites, but these methods have been severely limited and can induce high stress concentrations that compromise the structural integrity of the carbon fiber structure. In this research the strain sensor material and the connective circuitry to the sensor are analyzed to improve the practicality of in situ strain sensing of carbon fiber structures. It has been found that the use of nickel nanostrands embedded directly onto carbon fiber as a strain sensor material has no advantages over a carbon fiber strain sensor alone. Additionally, it has been shown that the circuitry to the strain sensor plays a critical role in obtaining a strong, consistent piezoresistive signal that can be related to strain. The use of nickel coated carbon fiber in the circuitry has been evaluated and shown to reduce the noise in a piezoresistive signal while allowing for remote strain sensing from greater distances away from the strain location. The piezoresistive strain sensing utilized in the tested sensor designs relies on electrons tunneling through an insulting barrier between two conductors. This phenomenon is known as quantum tunneling. Two factors - tunneling barrier height and gap distance - affect the probability of quantum tunneling occurring. Thus, to accurately model and predict the piezoresistivity of nanocomposites these two parameters must be known. Through the use of dielectric spectroscopy the gap distance can be determined. Using nanoindenting, the barrier height for various polymers was also determined. The measured values can be used, in future work, to improve the modeling of nickel nanostrand nanocomposite.