DNA Partition function and Graphene Fermi energy level Document Preview: Consider the following simplified model of a DNA molecule resembling a molecular zipper: a long chain consisting of two separate parallel strands, each strand being a linear chain of four basic molecular units, namely, bases called A, T, G and C. A base in each strand is pairwise connected with a base in the other by a hydrogen bond, there being two possible pairings A-T and G-C with binding energies W1 and W2 respectively. Each bond can exist in two states- broken and unbroken independently of all others. The chain consists of N base pairs, the fraction of A-T and G-C pairs being f1 and f2 (assumed uniform throughout the chain) with f1 +f2=1.What is the probability of a bond being in broken state at temperature T?Write down the canonical partition function of the system.Derive an expression for the entropy per DNA molecule S.Many of the novel properties of graphene, a newly discovered single-atom thick form of carbon, are attributed to the fact that the behavior of the electronic excitations (quasiparticles) in its hexagonal lattice formally resembles that of massless relativistic fermions in two dimensions. However, these quasiparticles move with constant speed vF (the Fermi velocity) instead of the speed of light c. Their energy-momentum relationship has the form (p)=vF*p, where p=|p| is the magnitude of the momentum vector but since vF