Spectral energy transfers in domain growth problems

In the domain growth process, small structures gradually vanish, leaving behind larger ones. We investigate spectral energy transfers in two standard models for domain growth: (a) the Cahn-Hilliard (CH) equation with conserved dynamics and (b) the time-dependent Ginzburg-Landau (TDGL) equation with nonconserved dynamics. The nonlinear terms in these equations dissipate fluctuations and facilitate energy transfers among Fourier modes. In the TDGL equation, only the ϕ(k=0,t) mode survives, and the order parameter ϕ(r,t) approaches a uniform state with ϕ=+1 or -1. On the other hand, there is no dynamics of the ϕ(k=0,t) mode in the CH equation due to the conservation law, highlighting the different dynamics of these equations.