GLEqPy
======
*Generalized Langevin Equation with Python*
This repo contains tools for the simulation of the generalized Langevin equation (GLE) and
the calculation of memory/friction kernels.
The GLE is a non-Markovian counterpart to the Langevin equation,
$$ \mathbf{p} = -\frac{d W}{d \mathbf{x}}(t) - \int_0^t \mathbf{K}(t-\tau) \mathbf{p}(\tau) d\tau + \mathbf{R}(t) $$
where $\mathbf{p}$ and $\mathbf{x}$ are the momenta and positions of your system, $W$ is
the potential of mean force, $\mathbf{K}$ is the memory kernel (generally a tensor),
and $\mathbf{R}$ is a correlated stochastic process.
<p align="center">
<img src="https://raw.githubusercontent.com/afarahva/gleqpy/main/examples/1D/memory.png" width="500">
</p>
The figure above compares memory kernels, one that was used as an input for a
simulation and others that were extracted by analyzing the data from that simulation.
Pedagogical examples of how to set up, run, and analyze GLE simulations are provided in the
**examples** directory. Examples include toy simulations, GLE for solid dynamics with ASE,
and GLE for solution phase dynamics with LAMMPS.
Getting Started
---------------
The easiest way to install GLEqPy is by using `pip`.
`pip install gleqpy`
The memory analysis tools only require `numpy` and `scipy`.
The ase module requires the [Atomic Simulation Environment](https://wiki.fysik.dtu.dk/ase/index.html)
to be installed.
The examples directory contains discusses how to use [LAMMPS](https://www.lammps.org/) to run GLE simulations.
Submodules
----------
**ase** - GLE integrators and helpful forcefields for Atomic Simulation Environment.
**examples** - Helpful examples.
**memory** - Functions for calculating memory kernels, and a database for memory kernels
calculated from prior simulations.
**md** - Python based MD code, useful for testing purposes and building toy simulations.
Citing glepy
------------
If you use glepy, please cite:
Farahvash A, Agrawal M, Peterson AA, Willard AP. Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach. J Chem Theory Comput. 2023 Sep 26;19(18):6452-6460. doi: [10.1021/acs.jctc.3c00473](10.1021/acs.jctc.3c00473).
Raw data
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