LDFrienT

LDFrienT was created within the scope of my master's project at the institute of applied physics at the University of Tübingen in 2020. This project, on the one hand, provides a general framework for lattice density functional theory (LDFT). This framework comes in the form of an abstract base class, the class LdftModel in the module ldft_model.py. It provides some general functions to LDFT (such as Picard iterations, calculation of surface properties, etc.) and, more importantly, a nice structure for your LDFT-project. To take advatage this framework, simply create a class for your LDFT-model, which inherits from LdftModel and implement the abstract methodes. Those are specific to your model (e.g. the calculation of the free energy). The purpose of this framework was to make the code clean and uniform for every project of this type.

On the other hand, LDFrienT comes with four readily implemented LDFT-models which make use of the LdftModel-framework. Those implemented models are the

• two-dimensional lattice gas in the mean field approximation (the class LG2dMf in the module lg_2d_mf.py)
• two-dimensional lattice gas in the highlander approximation (the class LG2dAOHighl in the module lg_2d_highl.py)
• three-dimensional lattice gas in the mean field approximation (the class LG3dMf in the module lg_3d_mf.py)
• three-dimensional lattice gas in the highlander approximation (the class LG3dAOHighl in the module lg_3d_highl.py)

Moreover, the generator.py-skript provides some usefull functions to generate series of density profiles (samples) of a certain LDFT-model. Some of these functions are customized to the above classes (LG2dMf, LG2dAOHighl, LG3dMf, LG3dAOHighl), though may easily be extended to your LDFT-model.

Requirements and dependencies

This project requires phython 3 and makes use of the following packages

• numpy
• matplotlib
• os
• picle
• functools
• abc
• scipy.optimize
• sys

If one wants to also take advantage of the notebooks, Jupyter notebook is required on your machine.

Documentation

The documentation-folder contains a detailed documentation about the LdftModel-interface and the classes LG2dAOHighl and LG2dMf. The three-dimensional cases (LG3dAOHighl and LG3dMf) have no seperate documentation, since they work prety much the same as in two dimensions.

Exaples and Tests

An easy example of how to use the LdftModel-framework properly is provided by the two classes LG2dMf and LG3dMf. A more complex example is given by LG2dAOHighl and LG3dAOHighl.

The notebooks LG2dAOHighl-testsheet.ipynb and LG2dMeanField-testsheed.ipynb were originaly intended for testing the classes LG2dAOHighl and LG2dMf. They might, however, also be used as a little tutorial to those classes.

The notebook generator-testsheet.ipynb was for testing the functions provided in generator.py, though serve as a tutorial to this module as well. Moreover, there is a notebook generator-interface.ipynb, which can be used, if one does not want to call the functions in generator.py from the terminal.

Content and file structure

This project has the following content

• code............................................................................. This folder holds all the code
  • ldft_classes_v2
    • ldft_model.py................................................. contains LdftModel-class (abstract class serving as LDFT framework)
    • lg_2d_highl.py................................................ contains LG2dAOHighl-class (two-dimensional lattice gas in Highlander approximation)
    • lg_2d_mf.py................................................... contains LG2dMf-class (two-dimensional lattice gas in mean field approximation)
    • lg_3d_higl.py................................................. contains LG3dAOHighl-class (three-dimensional lattice gas in Highlander approximation)
    • lg_3d_mf.py................................................... contains LG3dMf-class (three-dimensional lattice gas in mean field approximation)
  • LG2dAOHighl-testsheet.ipynb.............................. Test or tutorial for the LG2dAOHighl-class
  • LG2dMeanField-testsheet.ipynb........................... Test or tutorial for the LG2dMeanField-class
  • generator-interface.ipynb...................................... "Interface"-notebook for generator.py-modul
  • generator-testsheet.ipynb..................................... Test or tutorial for the generator.py-modul
  • generator.py.......................................................... contains functions to produce samples
• documentation........................................................... Here is the documentation for the code
  • LdftModel.rst......................................................... Documentation for LdftModel
  • LG2dAOHighl.rst................................................... Documentation for LG2dAOHighl
  • LG2dMf.rst............................................................. Documentation for LG2dMf
• samples...................................................................... some exemplary samples produce by the code
• .gitignore
• License
• README_GitHub......................................................... This read-me file