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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.19747 |
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Table of Contents:
- 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 {\it Cahn-Hilliard} (CH) equation with conserved dynamics, and (b) the {\it time-dependent Ginzburg-Landau} (TDGL) equation with non-conserved dynamics. The nonlinear terms in these equations dissipate fluctuations and facilitate energy transfers among Fourier modes. In the TDGL equation, only the $ϕ(\mathbf{k} = 0, t)$ mode survives, and the order parameter $ϕ(\mathbf{r},t)$ approaches a uniform state with $ϕ= +1$ or $-1$. On the other hand, there is no dynamics of the $ϕ(\mathbf{k} = 0, t)$ mode in the CH equation due to the conservation law, highlighting the different dynamics of these equations.