Fracture paths described by generalized random walks on curved spatiotemporal surfaces

Issue title: International Conference on Complexity and Frontiers in Strength and Fracture (ICS 2001), Sendai, Japan, 24–27 June 2001, Part II

Article type: Research Article

Authors: Hara, H. | Tsuzuki, Y. | Yokobori, Jr., A.T.^;

Affiliations: Department of Aeronautics and Space Engineering, Graduate School of Engineering, Tohoku University, Sendai 980‐8579, Japan | Department of Electrical Information Engineering, Faculty of Engineering, Aomori University, Aomori 030‐0943, Japan

Note: [] Corresponding author. E‐mail: yokobori@rift.mech.tohoku.ac.jp.

Abstract: An expression representing trajectories of fracture paths is obtained as a first arrival length. The first arrival length is a function representing a quantity generalized from the first passage time. The expression is the average value of the first arrival length found by solving a backward Fokker–Planck equation on a curved spatiotemporal surface. The backward FP equation is derived from generalized random walks (GRW). In the GRW, jump probabilities are specified by additional arbitrary functions. Furthermore, we propose a stochastic differential equation of random variables representing the fracture paths.

Keywords: Fracture paths, first arrival length, random walks, curved spatiotemporal surface

Journal: Strength, Fracture and Complexity, vol. 1, no. 2, pp. 59-67, 2003