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You searched for +publisher:"University of Notre Dame" +contributor:("Kathie E. Newman, Committee Co-Chair"). One record found.

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University of Notre Dame

1. Seng Kai Wong. A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model</h1>.

Degree: PhD, Physics, 2005, University of Notre Dame

The Ising model has been very successful in simulating ferromagnetic and antiferromagnetic materials. It is, in fact, the pedagogical explanation for the behavior of magnetic materials. Researchers have adapted the Ising model to simulate materials as disparate as foams, cell aggregates and metallic crystals. <pre><code>In this research, I used different modifications of Metropolis algorithms to simulate </code></pre> phase separation and Brownian motion in the Ising model. One of the algorithms (Algorithm Three in the text) is a choice popular with many researchers. My goal is to illuminate the differences in the dynamical and equilibrium properties of various algorithms and model parameters. <pre><code>I found that the most popular choice is not always the right choice. It produces a non-Boltzmann equilibrium and its simulated </code></pre> droplets diffuse much slower than other near-Boltzmann algorithms. In fact, the non-Boltzmann algorithm does not have a critical point, while the others do. <pre><code>In my phase separation simulations, I investigated a number of thermodynamical properties of the two-dimensional Ising model, </code></pre> including the surface energy, surface tension, partition function, free energy and entropy as a function of model parameters and algorithms. <pre><code>To obtain a functional form for analyzing phase-separation, I developed a second-nearest neighbor Solid-On-Solid (SOS) model. I found that the SOS model agrees well with the Ising model up to about one-half the critical temperature. I also used heuristic arguments to create a modified SOS model and compared it to simulation results for up to fourth-nearest-neighbor interactions. I discovered unexpected behavior when I used the model to simulate Brownian motion. For all the algorithms, droplets diffuse slower than </code></pre> predicted at low temperatures, which I explain by assuming that the underlying lattice is sticky. <pre><code>One could devise more tests to further distinguish and delineate the limitations of the algorithms, like simulating Stoke's flow. When one </code></pre> modifies or add more terms to the Ising Hamiltonian to simulate different phenomena, one needs to modify the algorithm’s acceptance probabilities accordingly in order to preserve detailed balance and Boltzmann equilibrium. I have presented a clear method to create algorithms that obey detailed balance and produce near-Boltzmann equilibria. Advisors/Committee Members: Kathie E. Newman, Committee Co-Chair, Jonathan R. Sapirstein, Committee Member, Jacek K. Furdyna, Committee Member, James A. Glazier, Committee Chair, Gerald L. Jones, Committee Member.

Subjects/Keywords: Thermodynamic; Monte Carlo; Phase Separation; Brownian Motion; Ising Model; Solid-On-Solid Model

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Wong, S. K. (2005). A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model</h1>. (Doctoral Dissertation). University of Notre Dame. Retrieved from https://curate.nd.edu/show/9z902z12z0s

Chicago Manual of Style (16th Edition):

Wong, Seng Kai. “A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model</h1>.” 2005. Doctoral Dissertation, University of Notre Dame. Accessed January 17, 2020. https://curate.nd.edu/show/9z902z12z0s.

MLA Handbook (7th Edition):

Wong, Seng Kai. “A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model</h1>.” 2005. Web. 17 Jan 2020.

Vancouver:

Wong SK. A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model</h1>. [Internet] [Doctoral dissertation]. University of Notre Dame; 2005. [cited 2020 Jan 17]. Available from: https://curate.nd.edu/show/9z902z12z0s.

Council of Science Editors:

Wong SK. A Cursory Study of the Thermodynamic and Mechanical Properties of Monte-Carlo Simulations of the Ising Model</h1>. [Doctoral Dissertation]. University of Notre Dame; 2005. Available from: https://curate.nd.edu/show/9z902z12z0s

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