Theses and Dissertations at Montana State University (MSU)

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    The emergence of collective behavior on social and biological networks
    (Montana State University - Bozeman, College of Letters & Science, 2018) Wilander, Adam Troy Charles; Chairperson, Graduate Committee: Scott McCallla; Dissertation contains an article of which Adam Troy Charles Wilander is not the main author.
    In this thesis, we broadly examine collective behaviors in various social and biological contexts. Aggregation, for instance, is a natural phenomenon that occurs in a variety of contexts; it is observed in schools of fish, flocks of birds, and colonies of bacteria, among others. This behavior can be found in some agent-based models, where it is typically assumed every pair of individuals interact according to a simple set of rules. In the first half of this thesis, we study a particular, well-understood aggregation model upon relaxation of the assumption that every individual interacts with every other. We review prior results on this topic -- when the underlying structure of interactions is an Erdos-Renyi graph. Seeking to incorporate community structure into the network, we establish the analogous problem under a class of networks called stochastic block graphs; a particular aspect of the system's metastable dynamics is explored upon varying the graph's connection densities. Finally, we evaluate the potential to leverage this system's dynamics in order to recover community structure (given a known graph as input). In the second half of this thesis, we similarly explore the aggregate behaviors of synchronization and desynchronization, appearing in diverse settings such as the study of metabolic oscillations and cell behaviors over time, respectively. Previous studies have leveraged a model in which repressilator entities are connected by a diffusive quorum sensing mechanism; these have shown (numerically) that the complex composition of observable behaviors depends upon the insertion point of the upregulating protein in the feedback loop. We rigorously prove a version of this; for negative feedback, negative signaling (Nf-Ns) systems we find only a unique stable equilibrium or a stable oscillation is possible. Additionally, we observe (numerically) the complex multistable dynamics that arise when a positive signal is included in the feedback loop and characterize this shift as a saddle node bifurcation of a cubic curve.
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    Effects of manufacturing conditions, stresses, temperature and humidity on the performance of an innovative fractional order control device
    (Montana State University - Bozeman, College of Engineering, 2005) Kulkarni, Nachiket Ashok; Chairperson, Graduate Committee: Aleksandra Vinogradov
    An innovative fractional order control device (Fractor) has been developed. The principal characteristic of the Fractor is a non-integer order power law relationship between the impedance and frequency. The exponent or the order in this power law is the Constant Phase Element (CPE). Warburg impedance is the ideal goal for the optimal performance of the Fractor which is intended for applications in feedback control systems. The Fractor is based on a specially developed material system which involves a synthesized polymer gel interfaced with metal electrodes. The roughness of the electrode is inversely correlated to the CPE. The main objective of this study is to determine the effectiveness of the Fractor depending on the manufacturing, loading and environmental conditions over a wide range of frequencies from 20 Hz to 500 kHz. A consistent experimental study has been performed to investigate the performance and response characteristics of the Fractor. Various material compositions of the Fractor have been investigated. The study has been performed for a wide range of parameters, including pressure, temperature, and humidity. The results of this investigation provide important information and guidelines for optimizing the performance and properties of the Fractor for feedback control of mechanical and electrical systems.
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