Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
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Item Effect of spatial variability of soil and soil-cement ground reinforcement on behavior of soil and overlying structures under static and dynamic loadings(Montana State University - Bozeman, College of Engineering, 2022) Zaregarizi, Shahabeddin; Chairperson, Graduate Committee: Mohammad Khosravi; This is a manuscript style paper that includes co-authored chapters.This study presents the results of spatial variability effect of soil and soil-cement (SC) ground reinforcement on behavior of soil and overlying structures under static and dynamic loadings. The objective is to evaluate the improvement/merit of employing stochastic modeling approaches, such as spatially correlated random fields, relative to deterministic analysis with uniform properties for the soil and SC walls. The results of studies are used to provide a representative SC shear strength for use in practical applications to account for spatial variability in soil-cement strength properties.Item Mathematical modeling for transcription of DNA with pausing : stochastic model with torque, and diffusive transport model(Montana State University - Bozeman, College of Letters & Science, 2016) Heberling, Tamra Lindsey; Chairperson, Graduate Committee: Lisa DavisIn fast-transcribing prokaryotic genes, like an rrn gene in Escherichia coli, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs is often interrupted by pauses, which has been observed to cause RNAP traffic jams; yet some studies indicate that elongation seems to be faster in the presence of multiple RNAPs than elongation by a single RNAP. We propose that an interaction between RNAPs via the torque produced by RNAP on helically twisted DNA can explain this apparent paradox. We have incorporated the torque mechanism into a stochastic model and simulated transcription both with and without torque. Simulation results illustrate that the torque causes shorter pause durations and fewer collisions between polymerases. Our results suggest that the torsional interaction of RNAPs is an important mechanism in maintaining fast transcription times, and that transcription should be viewed as a cooperative group effort by multiple polymerases. In an effort to further understand transcription, we investigate the Brownian ratchet model for nucleotide translocation. We model elongation as diffusive particle transport in a tilted periodic potential. To incorporate the RNAP pauses, a second periodic potential is added to the first. We present a formula for the mean escape time from a tilted, periodic potential composed of multiple periodic functions as the product of the mean escape time from each individual periodic function. This formula is extended to an arbitrary finite number of periodic functions. Two examples using truncated Fourier series are presented and analyzed.