Breakdown of linear dynamics in phase-ordering kinetics

Simulations and experiments have shown that the linear theory in phase-ordering dynamics fails first on short length scales rather than long length scales as suggested previously. By following the example of a simple coupled nonlinear system, we show that the linear theory breaks down first at the largest wave numbers due to the nonlinear slaving of the most stable Fourier modes to the larger amplitude unstable modes. The range of wave numbers in which the dynamics is nonlinear expands toward smaller wave numbers with time. We present numerical results verifying the mode slaving hypothesis and determine ${\mathit{t}}_{\mathrm{br}}$(k), the time at which the linear theory breaks down as a function of wave number k. (c) 1995 The American Physical Society