modified_ch

This repository contains code that solves:

1. The Ohta-Kawasaki / modified Cahn-Hilliard equation used in Density Functional Theory (DFT) and
2. the modified diffusion / Fokker-Planck equation used in Self-Consistent Field Theory (SCFT).

The chapters below refer to where the results appear in my Master's thesis (available upon request).

---

---

• DFT numerics (Chapter 4, 7):

  1. 1D_Lie_SSP_RK2.ipynb - 1D DFT scheme based on Lie-splitting involving a Fourier pseudospectral method, and strong-stability preserving 2nd-order accurate Runge-Kutta (SSP-RK3) time-stepping with a 2nd-order accurate central difference scheme.
  2. 2D_Strang_SSP_RK3.ipynb - 2D DFT scheme based on a Strang-splitting involving two Fourier-PS methods, a 3rd-order SSP-RK3, and a 4th-order accurate central difference scheme.

• SCFT numerics (Chapters 6, 7):

  1. 1D_SCFT - 1D SCFT scheme based on the paper published by Rasmussen and Kalosakas (2002).
  2. 2D_SCFT - 2D SCFT scheme.

• Benchmarking (Appendix F):

  1. GPU_test.ipynb - Compares computational costs of CPU- and GPU-based methods. Used alongside EOC.ipynb for calculating the order of convergence for the 2D DFT scheme in Chapter 4, Section 4.3.

• Misc:

  1. lsa.nb - Mathematica code for calculating the theoretical DFT order-disorder curves.
  2. Pts1.csv, Pts2.csv - Data points of the theoretical DFT curves.
  3. SCFT_Us_XN_10-15_V_1-9 and DFT_Us_delta_0.40-0.64_V_1.0-23.8 - Output of the data arrays used to plot the scatter plots of figure 7.5 (comparison of DFT and SCFT equilibrium homogeneous lamellar periodicity).
  4. detect_peaks.py - Peak counter from here.
  5. uArrs - Various output arrays used in determining the order of convergence of the 2D DFT numerical scheme in chapter 4, section 4.3.
  6. ETDRK4 - Archived code. An attempt at the 1D exponential time-differencing 4th-order accurate Runge-Kutta method. See Kassam and Trefethen (2005) for more details. The method works for small enough time steps.
  7. Lie_Adam-Bashforth - My first attempt at the DFT numerical scheme. It works in 1D, 2D, and 3D. However, the stability analysis of this scheme is not easy.