3,503 research outputs found
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
Random copolymer: Gaussian variational approach
We study the phase transitions of a random copolymer chain with quenched
disorder. We apply a replica variational approach based on a Gaussian trial
Hamiltonian in terms of the correlation functions of monomer Fourier
coordinates. This allows us to study collapse, phase separation and freezing
transitions within the same mean field theory. The effective free energy of the
system is derived analytically and analysed numerically. Such quantities as the
radius of gyration or the average value of the overlap between different
replicas are treated as observables and evaluated by introducing appropriate
external fields to the Hamiltonian. We obtain the phase diagram and show that
this system exhibits a scale dependent freezing transition. The correlations
between replicas appear at different length scales as the temperature
decreases. This indicates the existence of the topological frustration.Comment: 15 pages, 4 Postscript figure
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
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