title: A modified gambler's ruin model of polyethylene chains in the amorphous region.
abstract: Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).
authors.affiliation: Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA.
authors.forename: Z H
authors.initials: ZH
authors.lastname: Duan
authors.forename: L N
authors.initials: LN
authors.lastname: Howard