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).
| 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 ) | |
