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Statistical mechanics of some constrained systems :
DNA topology and electrostatics simulations

Defended on december 2nd, 2002
by Vincent Rossetto-Giaccherino


We study the geometry of an open single DNA molecule in micromanipulation device under supercoiling constraints. We derive the Călugăreanu-White theoerem, which relates this global constraint to the local torsional constraint. The rod-like chain model uses Fuller's formula for the writhe and leaves to a divergence. This model requires a cut-off to be regularised. With numerical computations we are able to demonstrate how to correct this pathological effect. Then, we use an statistics analogy between a light ray geometry and a semi-flexible polymer geometry to apply our results with polarisation in multiple light scattering, and interpret experiments in geometrical terms.

In the second part, we study numerical simulations for electrostatics. We construct from Maxwell equations a local algorithm, which has many advantages compared to usual simulations. We add a transverse field with a Monte-Carlo scheme. With this new method, we are able to take into account subtle effects like dielectric inhomogeneities in complexity O(N).

To read the PhD (in french only)

I   Étude de la mécanique statistique de l'ADN à l'aide de la notion de vrille
1. La molécule d'ADN PDF (135  kb ) PS (326  kb )
2. De la double chaîne à la notion de vrille PDF (211  kb ) PS (300  kb )
3. Modèles pour l'ADN PDF (151  kb ) PS (253  kb )
4. Simulations numériques PDF (161  kb ) PS (273  kb )
5. La vrille des chaînes nouées PDF (205  kb ) PS (297  kb )
6. Diffusion multiple de la lumière polarisée PDF (179  kb ) PS (913  kb )
II Simulations locales d'interactions coulombiennes
1. Simulations de systèmes chargés PDF (104  kb ) PS (240  kb )
2. Algorithmes locaux pour l'électrostatique PDF (96  kb ) PS (236  kb )
Bibliographie PDF (45  kb ) PS (230  kb )
Tables PDF (42  kb ) PS (227  kb )

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