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On the Kratky-Porod model for semi-flexible polymers in an external force field

Kilanowski, Philip D.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1275421702

Abstract Details

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.
Mathematics
stochastic processes; polymers

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Citations

  • Kilanowski, P. D. (2010). On the Kratky-Porod model for semi-flexible polymers in an external force field [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1275421702

    APA Style (7th edition)

  • Kilanowski, Philip. On the Kratky-Porod model for semi-flexible polymers in an external force field. 2010. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1275421702.

    MLA Style (8th edition)

  • Kilanowski, Philip. "On the Kratky-Porod model for semi-flexible polymers in an external force field." Doctoral dissertation, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1275421702

    Chicago Manual of Style (17th edition)

osu1275421702
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This open access ETD is published by The Ohio State University and OhioLINK.