On the conformational structure of a stiff homopolymer

In this paper we complete the study of the phase diagram and conformational states of a stiff homopolymer. It is known that folding of a sufficiently stiff chain results in formation of a torus. We find that the phase diagram obtained from the Gaussian variational treatment actually contains not one, but several distinct toroidal states distinguished by the winding number. Such states are separated by first order transition curves terminating in critical points at low values of the stiffness. These findings are further supported by off-lattice Monte Carlo simulation. Moreover, the simulation shows that the kinetics of folding of a stiff chain passes through various metastable states corresponding to hairpin conformations with abrupt U-turns.Comment: 9 pages, 16 PS figures. Journal of Chemical Physics, in pres

Computation of periodic solution bifurcations in ODEs using bordered systems

We consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous ODEs, namely the fold, the period-doubling (or flip) bifurcation, and the torus (or Neimark–Sacker) bifurcation. In the fold and flip cases we append one scalar equation to the standard periodic BVP that defines the periodic solution; in the torus case four scalar equations are appended. Evaluation of these scalar equations and their derivatives requires the solution of linear BVPs, whose sparsity structure (after discretization) is identical to that of the linearization of the periodic BVP. Therefore the calculations can be done using existing numerical linear algebra techniques, such as those implemented in the software AUTO and COLSYS