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Post Doctoral Research Associate
Rutgers, the State University of New Jersey (732) 445-4619
Wright-Rieman Labs, Busch Campus
610 Taylor Road — Piscataway, NJ 08854-8066 Room A211 |
This thesis concerns the mechanics of elastic rods in case of configurations
with self-contacts. In this context we present two different studies: the
first one presents a mechanical model for DNA supercoiling in single molecule
experiments and the second study deals with the elasticity of knotted rods.
The first part of the thesis presents the elastic rod theory based on the
Kirchhoff equations, which addresses the mechanical equilibrium of elastic
rods considered as one dimensional bodies. These equations are completed with
constitutive relations for an isotropic and inextensible rod in the case of a
hookean material.
Single molecule experiments allow to exert mechanical stresses onto DNA
molecules and we focus on extension-rotation measurements. In such experiments
the DNA molecule supercoils and forms plectonemes. We present an analytical
model based on a variational formulation which takes into account DNA-DNA
interactions and thermal fluctuations. Our model allows to calculate the
mechanical response of the DNA molecule and also to predict the main
experimental results. We compare our predictions with experimental data and
find a good agreement.
The last part presents an analytical model which addresses the mechanical
response of a knotted rod when subjected to both a tensile force and a
torsional moment. Our model uses a matched asymptotic expansions method and
takes into account the impenetrability constraint. We then provide a general
method for building a solution of the Kirchhoff equations in the case of a
knotted rod. Our main result is the prediction of the contact set without
formulating hypothesis on its structure. We also predict an instability
related to the applied torsional moment.