DNA, the genetic molecule deoxyribonucleic acid, exists as a twisted pair of polymer molecules, each with N~ monomer units. The two polymer molecules are cross-linked by N~ ``base pairs.'' It requires energy ε to unlink each base pair, and a base pair can be unlinked only if it has a neighboring base pair that is already unlinked (or if it is at the end of the molecule). Find the probability that n pairs are unlinked at temperature T if
a) one end of the molecule is prevented from unlinking, so that the molecule ``unwinds'' from one end only.
b) the molecule can unwind from both ends.
Reference: C. Kittel, Amer. J. Phys. 37, 917 (1969).