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Spectral energy transfers in domain growth problems
Pradeep Kumar Yadav1, Mahendra Kumar Verma2, Sanjay Puri1
1School of Physical Sciences, <a href="https://ror.org/0567v8t28">Jawaharlal Nehru University</a>, New Delhi-110067, India.
Physical Review. E
|November 20, 2024
Summary
Domain growth models like Cahn-Hilliard and time-dependent Ginzburg-Landau show how small structures disappear. Spectral energy transfer differs between conserved and nonconserved dynamics, impacting how systems reach uniform states.
Area of Science:
- Physics
- Materials Science
- Computational Science
Background:
- Domain growth is a fundamental process where small structures disappear, leaving larger ones.
- Understanding this process is crucial in various scientific fields, including materials science and statistical physics.
- Spectral energy transfer plays a key role in the dynamics of these systems.
Purpose of the Study:
- To investigate spectral energy transfers in two standard domain growth models.
- To compare the dynamics of the Cahn-Hilliard (CH) equation with conserved dynamics and the time-dependent Ginzburg-Landau (TDGL) equation with nonconserved dynamics.
- To analyze how nonlinear terms facilitate energy transfers among Fourier modes.
Main Methods:
- Analysis of spectral energy transfers.
- Numerical simulations of the Cahn-Hilliard (CH) equation.
- Numerical simulations of the time-dependent Ginzburg-Landau (TDGL) equation.
Main Results:
- Nonlinear terms in both equations dissipate fluctuations and drive energy transfer among Fourier modes.
- In the TDGL equation, only the zero-wavevector mode (k=0) survives, leading to a uniform state.
- The CH equation, due to its conserved dynamics, exhibits different behavior for the k=0 mode, highlighting distinct dynamics.
Conclusions:
- The Cahn-Hilliard and TDGL equations exhibit fundamentally different dynamics in their domain growth processes.
- Conservation laws significantly influence the long-term behavior and spectral energy transfer in these models.
- The study provides insights into the mechanisms governing pattern formation and coarsening in physical systems.
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