Discrete Modeling of a String and Analysis of a Loop Soliton

[+] Author and Article Information
K. Nishinari

Department of Mechanical Engineering, School of Engineering, Yamagata University, Yonezawa, Yamagata 992, Japan

J. Appl. Mech 65(3), 737-747 (Sep 01, 1998) (11 pages) doi:10.1115/1.2789118 History: Received February 12, 1997; Revised March 02, 1998; Online October 25, 2007


A discrete model for an extensible string is proposed and analyzed by a discrete soliton theory and computer simulations. The relation between tension of the string and the size of a loop propagating on the string is obtained analytically by using the soliton theory. We use this relation to investigate dynamics and stability of loops, and it is found that one loop is stable against various kinds of perturbation. It is confirmed numerically that the loop can be formed by moving a boundary along a semicircle. If the moment of the string is introduced, behaviors of the formation are drastically changed and there is a critical value of stiffness of the string beyond which the loop cannot be formed. As for collision of two loops, we, found that two loops do not break after collision if the two are similar. This result of collision can be well explained by our former analysis of a continuous string theory (Nishinari, 1997).

Copyright © 1998 by The American Society of Mechanical Engineers
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