No description available.

No description available.

No description available.

No description available.

Mathematical modeling provides a powerful framework for insight into current scientific theories as well as hypothesis generation for further research. Despite its undeniable potential to enrich scientific advancement, the application of mathematical modeling remains conspicuously scarce in the field of family science. The complexity inherent in family dynamics, coupled with the intricate interplay of emotions in the individual, underscores the necessity of a robust analytical approach. Addressing this critical gap in the literature, this thesis introduces a sophisticated mathematical model of family dynamics integrating essential elements from family systems theory, emotion dynamics, and appraisal theory. The model is implemented as a versatile computer program capable of simulating family interaction over time, and allows for customization to suit specific research needs. Noteworthy outcomes from the current model parameters include the emergence of both asymptotic and periodic emotion dynamics, the significant influence of family roles on behavior and rapport, and the ripple effect of a single individual's behavior on the system as a whole. Through the exploration of emergent behaviors, this model offers invaluable insights and paves the way for future mathematical modeling and advancements in family science research.

Intravenously delivered cancer drugs face transport limitations at the tumor site and cannot reach all parts of tumors at therapeutically effective concentrations. Transport limitations also prevent oxygen from distributing evenly in tumors resulting in hypoxia, which plays a critical role in cancer progression. In this dissertation, I present the development of micro-devices that mimic transport limitations of drugs and nutrients on three dimensional tumor tissues, enable visualization and quantification of the ensuing gradients, and enable simple analysis and mathematical modeling of obtained data. To measure the independent effects of oxygen gradients on tumor tissues, an oxygen delivery device that used microelectrodes to generate oxygen directly underneath three-dimensional tumor cylindroids was developed. Supplying oxygen for 60 hours eliminated the necrotic region typically found in the center of cylindroids. Dead cells were observed moving away from the location of oxygen delivery. These measurements show that oxygen gradients are an important determinant of cell viability and rearrangement. Another micro-device was developed to mimic the delivery and systemic clearance of therapeutic agents. This microfluidic device consisted of cuboidal tumor tissue subjected to continuous medium perfusion along one face. The device was used to measure the spatiotemporal dynamics of the accumulation of therapeutic bacteria in tumors. Suspensions of Salmonella typhimurium and Escherichia coli strains were delivered to tumor tissues for 1 hour. Bacterial motility strongly correlated (R2 = 99.3%) with the extent of tissue accumulation. Based on spatio-temporal profiles and a mathematical model of motility and growth, bacterial dispersion was found to be necessary for deep penetration into tissue. These results show that motility is critical for effective distribution of bacteria in tumors. The microfluidic device was further used to mimic the delivery and clearance of equal concentrations of doxorubicin and liposome-encapsulated doxorubicin (Doxil). A pharmacokinetic/pharmacodynamic model incorporating mechanisms of tissue-level diffusion and binding was developed and experimental data was fit to this model. Doxorubicin was found to have the optimal diffusivity and binding for maximizing therapeutic effect. Doxil was severely limited by low intratumor drug release. These results show that in-vitro models mimicking tissue-level transport limitations more accurately predict the therapeutic response of drugs.

This is one of the first time series studies of bacteria in soils supporting actively growing corn crops. Mathematically modeling bacteria population dynamics has the potential as a tool to more precisely assess the economic optimal nitrogen fertilizer rate for farmers. As a first step in this modeling effort, we examine the possibility that the bacteria population growth might be described by a dynamic model developed in the food sciences describing bacteria growth in food meant for human consumption. We make the assumption that air temperature above the soil can be used as an approximation for soil temperature. Also, because there were two rates of data collection (one for bacteria and one for weather), the weather data was averaged between bacteria samples to obtain the same number of samples per data set. It is under these assumptions that we demonstrate in this thesis that this model, developed by McMeekin and Chandler, fails to apply to bacteria in agricultural soils.

<p> The analysis of stepping motors using linear models has been simplified through identifications of the constants. Though the existing nonlinear models assuming a smooth air-gap machine may, in some cases, yield a fairly close prediction of the characteristics of a stepping motor, the models do not represent the actual motors which are essentially salient-pole motors. A new salient-pole nonlinear model is introduced. The analysis of permanent-magnet stepping motors using the nonlinear models has been simplified by assuming constant current sources. Dynamic behaviors of a permanent -magnet stepping motor are shown by phase-plane plots and step by step transient response plots.</p> <p> Computer control of stepping motors in both open-loop and closed-loop is discussed. The open-loop control has been demonstrated to be successful and a closed-loop control system using light-sensors as feedback has been designed.</p> / Thesis / Master of Engineering (MEngr)

Autonomous robots are employed in several important tasks, for example, from health care to military and defense applications involving operations in hazardous and inaccessible environments. Legged autonomous robots can be advantageous due to high adaptability and stability over any terrain, superior obstacle avoidance capability, and advantages through redundancy by utilizing multiple legs. Compared to rigid-legged robots, flexible-legged robots are highly compliant, suitable for non-destructive inspection applications, and possess enhanced gait control with improved energy efficiency. An approach to designing flexible-legged robots is to mimic desirable features evolved via natural selection in biological organisms. Conceptualizing new biologically inspired flexible-legged robots can expand the usability and improve the efficiency of robots in different applications. In this project, the inspiration for locomotion design is the mobility principle utilized by small-scale organisms in the form of beating protrusions referred to as cilia or flagella. Notably, the collective beating dynamics of ciliary arrays reveal essential characteristics such as synchronization, phase locking, and metachronal coordination suitable for terrestrial and aquatic robot locomotion. This thesis presents the formulation, simulation, and analysis of a planar bio-inspired flexible-legged robot for terrestrial locomotion. Each leg of the robot is modeled as a bundle of flexible filaments using constrained Euler elastica that is suitable to describe some of the characteristics of cilia or flagella. The legs/protrusions are mechanically coupled through the base, representing the robot's payload, via linear springs or elastic lumped elements, to produce certain desired collective beating patterns upon individual moment actuations. The locomotion mechanism is illustrated in simulation, wherein the results pave the ground for future work with refined modeling to account for hardware implementation constraints.

No description available.