Dynamical renormalization of anharmonic lattices at the onset of fracture: Analytical results for scaling, noise, and memory

We present here results for dynamical renormalization of an anharmonic lattice. We investigate the dynamics of the lattice at the onset of fracture, and we show the existence of a map of this lattice into a transformed lattice with disorder (crack). By studying the properties of the transformed lattice we get exact analytical results for the decimalization of the noise, and approximate analtical results for the dynamical scaling of the lattice and dynamical memory for the crack. We discuss the existence of a nonhydrodynamical behavior and how it affects the correlation between motions of adjacent partiles. By drawing on the results of simulations and analytical methods, we are able to discuss how these concepts may be used to interpret more intensive simulations and experiments.