CHAOTIC DYNAMICS IN AN ELASTIC MEDIUM WITH SURFACE DISORDER

We investigate the dynamics of an elastic medium described by a two-di mensional network of nodes of equal mass connected by springs whose fo rce constants are equal inside the network and chosen at random at its surface. The system can be considered a billiard in the sense that th e network is ordered all throughout its bulk. Being an eigenvalue prob lem its complexity is manifested in a frequency statistics which, in m ost of the spectrum, can be described by the Wigner-Dyson distribution . At low frequencies the dispersion relation is linear in the wave num ber and the network shows regular behavior (frequency statistics accor ding to Poisson distribution). We study the dynamical behavior of this model by investigating how the system escapes from a normal mode of t he ordered network, and calculate the Lyapunov exponent lambda in diff erent frequency regions.