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On the Kratky-Porod model for semi-flexible polymers in an external force field
Kilanowski, Philip D.

2010, Doctor of Philosophy, Ohio State University, Mathematics.
We prove, by means of matrix-valued stochastic processes, the convergence, in a suitable scaling limit, of the position vectors along a polymer in the discrete freely rotating chain model to that of the continuous Kratky-Porod model, building on an earlier result for the original model without a force, and showing that it holds when an external force field is added to the system. In doing so, we also prove that the process of tangent vectors satisfies a stochastic differential equation, showing that it is the sum of a spherical Brownian motion and a projective drift term, and we analyze this equation to prove statements about the polymer in the regimes of high and low values of the force parameter and persistence length. We augment these theoretical results with a numerical Monte Carlo simulation of the polymer and formulate a conjecture to describe how the correlation function between tangent vectors changes with the force.
Peter March, PhD (Advisor)
Yuan Lou, PhD (Committee Member)
Saleh Tanveer, PhD (Committee Member)
Harold Fisk, PhD (Committee Member)
238 p.

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Kilanowski, P. (2010). On the Kratky-Porod model for semi-flexible polymers in an external force field. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Kilanowski, Philip. "On the Kratky-Porod model for semi-flexible polymers in an external force field." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Kilanowski, Philip "On the Kratky-Porod model for semi-flexible polymers in an external force field." Electronic Thesis or Dissertation. Ohio State University, 2010. https://etd.ohiolink.edu/

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