### Browsing by Subject "Monte Carlo simulation"

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Item Cross Median Crashes: Identification and Countermeasures(Minnesota Department of Transportation, 2008-06) Davis, Gary A.Show more The goals of this project were to first review the state-of-art with regard to identifying highway sections where median barriers would be most effective in preventing median-crossing crashes (MCC), and if necessary, develop remedies for any identified deficiencies. A statistical technique was developed for estimating the frequency and rate of MCCs on each of a set of highway sections, which required the analyst to review only a subset of hard-copy accident reports. This technique was applied to Minnesota’s freeways and rural expressways, and highway sections were ranked with respect to estimated frequency of MCCs. A first version of a simulation model was developed for comparing the cost-effectiveness of barrier projects on different highway sections. The model uses Monte Carlo simulation to estimate the probability that an encroaching vehicle crosses a median with a specific cross-section, and collides with another vehicle traveling in the opposite direction. The model is implemented as a pair of linked Excel spreadsheets, with a companion macro written in Visual Basic for Applications.Show more Item Equilibrium properties of DNA and other semiflexible polymers confined in nanochannels(2016-01) Muralidhar, AbhiramShow more Recent developments in next-generation sequencing (NGS) techniques have opened the door for low-cost, high-throughput sequencing of genomes. However, these developments have also exposed the inability of NGS to track large scale genomic information, which are extremely important to understand the relationship between genotype and phenotype. Genome mapping offers a reliable way to obtain information about large-scale structural variations in a given genome. A promising variant of genome mapping involves confining single DNA molecules in nanochannels whose cross-sectional dimensions are approximately 50 nm. Despite the development and commercialization of nanochannel-based genome mapping technology, the polymer physics of DNA in confinement is only beginning to be understood. Apart from its biological relevance, DNA is also used as a model polymer in experiments by polymer physicists. Indeed, the seminal experiments by Reisner et al. (2005) of DNA confined in nanochannels of different widths revealed discrepancies with the classical theories of Odijk and de Gennes for polymer confinement. Picking up from the conclusions of the dissertation of Tree (2014), this dissertation addresses a number of key outstanding problems in the area of nanoconfined DNA. Adopting a Monte Carlo chain growth technique known as the pruned-enriched Rosenbluth method, we examine the equilibrium and near-equilibrium properties of DNA and other semiflexible polymers in nanochannel confinement. We begin by analyzing the dependence of molecular weight on various thermodynamic properties of confined semiflexible polymers. This allows us to point out the finite size effects that can occur when using low molecular weight DNA in experiments. We then analyze the statistics of backfolding and hairpin formation in the context of existing theories and discuss how our results can be used to engineer better conditions for genome mapping. Finally, we elucidate the diffusion behavior of confined semiflexible polymers by comparing and contrasting our results for asymptotically long chains with other similar studies in the literature. We expect our findings to be not only beneficial to the design of better genome mapping devices, but also to the fundamental understanding of semiflexible polymers in confinement.Show more Item Molecular Simulations of Phase Behavior for Polymer Blends and Block Polymers(2018-05) Chen, QileShow more The wide variety of phase behavior associated with polymer mixtures and block polymers enables unprecedented opportunities in developing novel polymeric materials with desired properties. However, the molecular design space of multi-component polymer systems is now so vast that guidance from theory and modeling is essential. The greatest challenge of predictive materials design is the lack of accurate and precise simulation methods in computing the phase diagram of polymer systems, due primarily to difficulties in (i) transferring polymer molecules between condensed phases and (ii) the sensitivity of phase diagram with respect to the interaction parameters used in the simulations. The overarching goal of this thesis is to address the above two problems. In this thesis, advanced sampling techniques of Monte Carlo simulations and accurate molecular models were developed to allow for the accurate and precise calculation of the mixing thermodynamics for binary mixtures. Furthermore, a case study of predictive materials design is presented, where molecular dynamics simulations were employed to explore the phase diagram of block oligomers with various chain lengths, volume fractions, and chain architectures, and thus, to guide the experimental synthesis for molecules with desired microphase morphologies. The work in this thesis lays a solid foundation for predictive materials discoveries using molecular simulations.Show more Item A Monte Carlo Study of the Effects of Number of Clusters and Level-2 Residual Distributions on Multilevel Models(2021-11) Jia, HaoShow more Hierarchical Linear Modeling (HLM) has become an important approach to analyzing hierarchically structured data, which is common in educational research. But the accuracy of estimators and precision of statistical inference of HLM rely heavily on sufficiently large numbers of clusters, as well as the normality assumption of the residual distributions. The current study had two purposes. First, to synthesize the existing Monte Carlo research literature and identify gaps in the recommended number of clusters. This synthesis prompted two research questions with important implications for educational data analyses involving HLM: 1) What is the minimum required number of clusters for accurate estimation of level-2 parameters when assumptions are satisfied? 2) What is the minimum required number of clusters for accurate estimation of level-2 parameters when assumptions are violated? Much of the rationale for identifying minimum values of J for realistic data conditions is because clusters often require significant resources, leading to an interest in identifying a minimum J. To answer the research questions a Monte Carlo study was used to provide comprehensive recommendations for the minimum required sample size at level-2 of a two-level model for cross-sectional data. In order to fill the gaps of previous literature, the study adopted Latin Hypercube Sampling in the design of the simulation so that the sample sizes of both levels were randomly sampled from a wide range to mirror environments commonly found in educational research. A total of 40 combinations of J and n_j × 3 levels of ICC × 4 level-2 residual distributions × 4 covariate correlates = 1,920 combinations of conditions were studied. Bias in estimating fixed effects and variance components via ABs, ARBs, ln(RMSE)s, as well as Type I error rate and statistical power for corresponding statistical tests of those parameters, were investigated. The results showed that the fixed effects estimates were unbiased and were more accurately estimated when the number of clusters increased. A larger J was required for accurate Type I error rates of tests of fixed effects. In general, the fixed effects had sufficiently large statistical power. On the other hand, J > 75 was required for accurate variance components estimates and J > 100 was required for acceptable Type I error rates. Additionally, variance components were underpowered unless the sample sizes at both levels were large (J>100 and n_j>30) and ICC was bigger than .10. Finally, this current study provided guidance on minimum required sample size for future empirical research.Show more Item Supporting Data for "Effects of Electrolytes on Thermodynamics and Structure of Oligo(ethylene oxide)/Salt Solutions and Liquid–Liquid Equilibria of a Squalane/Tetraethylene Glycol Dimethyl Ether Blend"(2021-01-22) Shen, Zhengyuan; Chen, Qile P; Lodge, Timothy P; Siepmann, J Ilja; siepmann@umn.edu; Siepmann, J IljaShow more Data including input/output and restart files for all the systems, analysis codes (python, fortran, cpp), and figures in the paper "Effects of Electrolytes on Thermodynamics and Structure of Oligo(ethylene oxide)/Salt Solutions and Liquid–Liquid Equilibria of a Squalane/Tetraethylene Glycol Dimethyl Ether Blend". Sample movie files of the production trajectory are provided.Show more