README

2DChebClass is a code Andreas Nold and Ben Goddard developed as a project for classical density functional theory (DFT) and dynamic DFT (DDFT) computations at the group of Serafim Kalliadasis at Imperial College London. Since then, it evolved into a library of classes and functions to solve 1D and 2D DFT and DDFT problems. Its use is not restricted to DFT and DDFT - it can be used to solve a wide range of (integro)-PDE systems in various 1D and 2D geometries.

How do I run tests?

1. Please open "AddPaths.m" in the main folder. Define via "dirData" a folder where the computational results should be saved.
2. Run any file in the Computations folder.

Repositories and References

• Repository of the University of Edinburgh
• Bitbucket
• Private repository on Bitbucket for development
• Brief description of the Software by Co-developer Ben Goddard here.

Requirements (Matlab Versions)

The code was tested using Matlab2014a, Matlab2015a, Matlab2015b and Matlab2016a.

Publications

The code was used to compute results published in the following papers:

• Benjamin D. Goddard, Beth Gooding, Grigoris A. Pavliotis, Hannah Short ,2020, "Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions" ArXiv
• B. D. Goddard, R. D. Mills-Williams, Grigorios Pavliotis, 2020, "Well-Posedness and Equilibrium Behaviour of Overdamped Dynamic Density Functional Theory" ArXiv
• Goddard, Mills-Williams, Sun, 2020, "The singular hydrodynamic interactions between two spheres in Stokes flow", Phys. Fluids, 32, 062001 PoF
• Nold, A., MacDowell, L. G., Sibley, D. N., Goddard, B. D., Kalliadasis, S., 2018, “The vicinity of an equilibrium three-phase contact line using density-functional theory: density profiles normal to the fluid interface”, Mol. Phys. (5 pgs.) Links: core.ac.uk, Mol Phys
• Nold, A., Goddard, B. D., Yatsyshin, P., Savva, N., & Kalliadasis, S., 2017 ”Pseudospectral methods for density functional theory in bounded and unbounded domains." J. Comp. Phys. 334 639-664. Links: ArXiv, J Comp Phys
• Goddard, B. D., Nold, A., & Kalliadasis, S., 2016 “Dynamical density functional theory with hydrodynamic interactions in confined geometries” J. Chem. Phys. 145 Art. No. 214106 (19 pgs.). PubMed
• Nold, A., Sibley, D.N., Goddard, B.D. & Kalliadasis, S., 2015 “Nanoscale fluid structure of liquid-solid-vapour contact lines for a wide range of contact angles,” Math. Model. Nat. Phenom. 10 111–125. Links: ArXiv, MMNP

Contact

Andreas Nold, andreasnold@me.com

Ben Goddard, b.goddard@ed.ac.uk