- Modelling, analysis and numerical computations in complex systems
- Interdisciplinary collaborations
- Multi-scale, discrete and continuum, approach in mechanics
- Asymptotic and homogenization methods
- Statistical and classical physics of interacting rigid bodies
The thesis has been entitled On the statistical physics of chains and rods, with application to multi-scale sequence dependent DNA modelling and is available here.
The first part discusses the mechanics of heterogeneous single stranded, and double stranded, objects in the context of both classical statics and of equilibrium statistical physics, and in both discrete and continuum modeling framework. It is furthermore shown how these different length scale descriptions constitute, introducing the appropriate Cauchy-Born rules, a multi-scale approach to describe and understand the physics of general filamentary structure. In particular:
- Balance equations and variational principles are presented for single, and double, discrete rigid body chains and continuum rods
- Configurational correlations and persistences, in both discrete chain and continuum rod models, are discussed and the existence of a persistence matrix factorization is emphasised.
The second part presents the application of the proposed multi-scale framework to sequence dependent DNA mechanics modelling.
Precisely, we discuss
- The computation of sequence dependent equilibrium configurations under prescribed end force and couple using a continuum description, which leads to numerically efficient approximation of the original discrete equilibria.
- The computation of sequence dependent configurational correlations using a continuum description, which also leads to numerically efficient approximation of the original discrete problem.
List of Publications
- A solver for constrained chain equilibrium configurations , A. E. Grandchamp, J. H. Maddocks, in prep.
- Hamiltonian formulation of birod equilibrium , A. E. Grandchamp, J. H. Maddocks, in prep.
- Unscrambling shape and stiffness in heteropolymer statistical persistence , A. E. Grandchamp, J. H. Maddocks, submitted.
- Sequence-dependent persistence lengths of DNA, J. S. Mitchell, J. Glowacki., A. E. Grandchamp, R.S. Manning, J. H. Maddocks, Journal of chemical theory and computation, 13(4), 1539-1555.