title: Random walks on a ( 2+1)-dimensional deformable medium.
abstract: A model of random walks on a deformable medium is proposed in 2+1 dimensions. The behavior of the walk is characterized by the stability parameter beta and the stiffness exponent alpha. The average square end-to-end distance l<R2(t)> approximately equals (2nu) and the average number of visited sites <S(t)> approximately equals (k) are calculated. As beta increases, for each alpha there exists a critical transition point beta(c) from purely random walks ( nu = 1/2 and k approximate to 1) to compact growth ( nu = 1/3 and k = 2/3). The relationship between beta(c) and alpha can be expressed as beta(c) = e(alpha). The landscape generated by a walk is also investigated by means of the visit-number distribution N(n)(beta). There exists a scaling relationship of the form N(n)(beta)approximately n(-2)f(n/beta(z)).
authors.affiliation: Department of Physics, Wuhan University, Wuhan 430072, People's Republic of China.
authors.forename: Sheng-You
authors.initials: SY
authors.lastname: Huang
authors.forename: Xian-Wu
authors.initials: XW
authors.lastname: Zou
authors.forename: Wen-Bing
authors.initials: WB
authors.lastname: Zhang
authors.forename: Zhun-Zhi
authors.initials: ZZ
authors.lastname: Jin