Contact Problems in Kirchhoff's Nonlinear Theory of Rods

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

The principal investigator will do research on non-linear problems in Kirchhoff's theory of elastic rods with the goals of (i) finding, for knotted and unknotted closed rods and open rods subject to terminal forces and torques, precise analytic representations of equilibrium configurations that show both isolated points and intervals of self-contact; (ii) deriving practical necessary and sufficient conditions for an equilibrium configuration to be stable in the sense that it gives a strict local minimum to elastic energy; (iii) obtaining insight into the dependence of bifurcation diagrams on knot type and the presence of intrinsic curvature; (iv) understanding the way in which the occurrence of plectonemic loops leads to hysteresis in torsion-stretching experiments for elastic rods and in single molecule manipulation experiments on DNA. The analytical representations of equilibrium configurations will be employed to develop a new Metropolis Monte Carlo procedure for evaluating partition functions for thermally fluctuating DNA molecules subject to specified constraints and end conditions. Graduate students will participate in this research which lies, as described below, at the interface between modern continuum mechanics and molecular biology. Each human cell has a meter of DNA in a nucleus that is less than 1 micron in diameter. Throughout the life of the cell, its compacted DNA is in a state of rapid, yet controlled, activity, because the regulation of life functions requires repeated transcription of appropriate portions of the genetic code into strands of RNA. The present research project addresses issues in theoretical mechanics that must be resolved before one can attain full understanding of the way in which highly compacted DNA is made available for the processes of transcription, replication, and recombination.