Abstract
We present an analysis of multilayer Markov chains and apply the results to a model of a tethered polymer chain in shear flow. We find that the stationary probability measure in the direction of the flow is nonmonotonic, and has several maxima and minima for sufficiently high shear rates. This is in agreement with the experimental observation of cyclic dynamics for such polymer systems. Estimates for the stationary variance and expectation value were obtained and showed to be in accordance with our numerical results.
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P. S. Doyle, B. Ladoux, and J. -L. Viovy, Dynamics of a tethered polymer in shear flow. Phys. Rev. Lett. 84: 4769 (2000).
P. G. de Gennes, Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients. J. Chem. Phys. 60: 5030 (1974).
B. Ladoux and P. S. Doyle, Stretching tethered DNA Chains in shear flow. Europhys. Lett. 52: 511 (2000).
R. G. Larson, T. T. Perkins, D. E. Smith, and S. Chu, Hydrodynamics of a DNA molecule in a flow field. Phys. Rev. E 55: 1794 (1997).
J. F. Marko and E. D. Siggia, Stretching DNA. Macromolecules 28: 875 (1995).
P. Grassberger, Simulations of grafted polymers in a good solvent. J. Phys. A: Math. Gen. 38: 323 (2005).
J. W. Hatfield and S. R. Quake, Dynamic properties of an extended polymer in solution. Phys. Rev. Lett. 82: 3548 (1999).
A. Buguin, and F. Brochard-Wyart, Unwinding of globular polymers under strong flows. Macromolecules 29: 4937 (1996).
T. T. Perkins, D. E. Smith, and S. Chu, Single polymer dynamics of an elongational flow. Science 276: 2016 (1997).
T. T. Perkins, S. R. Quake, D. E. Smith, and S. Chu, Relaxation of a single DNA molecule observed by optical microscopy. Science 264: 819 (1994).
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Dubbeldam, J., Redig, F. Multilayer Markov Chains with Applications to Polymers in Shear Flow. J Stat Phys 125, 225–243 (2006). https://doi.org/10.1007/s10955-006-9166-z
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DOI: https://doi.org/10.1007/s10955-006-9166-z