Acceleration waves on random fields with fractal and Hurst effects

In this study, we determine the effect of spatial randomness on the probability of shock formulation and the distance to form shocks from acceleration waves as a function of the initial amplitude. The noise is applied to the dissipation and elastic nonlinearity of the system for two different cases: (i) two variables with the same noise of varying intensity and (ii) four variables with the same noise of varying intensity. The random fields used here are unique as they can capture and decouple the field's fractal dimension and Hurst parameter. We focus on determining the driving parameter, either fractal or Hurst, which is significant in altering the response of the system.