% % Taken from PIGLE downloaded from GITHUB repo https://zenodo.org/record/2025809#.YS6ciHySlPY % Copyright (c) 2018, Nadav Avidor (NA). % All rights reserved. % This file is part of the PIGLE - Particles Interacting in Generalized Langevin Equation simulator, subject to the % GNU/GPL-3.0-or-later.

PIGLE - Particles Interacting in Generalized Langevin Equation simulator Release: 1.0rc1 (a - alpha , b - beta, rc - release candidate)

PIGLE simulator solves the Generalized Langevin Equation for interacting particles, in a 4D potential energy surface. The potential has up to 3 spatial dimensions, and a rigid-body like rotation. Particles doesn't neceseraly share the same properties (such as mass or friction).

Here, I (KG) consider specifically the motion line-shape in the intermediate scattering function (ISF), supervised by Dr David Ward. I particularly focus on the ballistic region (i.e. over timescales shorter than the friction timescale), for the Li/ Cu (111) system. The simulink framework is adapted to include a noise filter, initially implemented as a low pass filter.

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Basic Usage:

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Installation:

• Install Matlab (tested with 2017b).
• Edit prep_environment.m

Execution of jobs:

• Create a potential of your choise and save it as 'mat' file, or create a function which generates the potential. One can use the functions and scripts in the subfolder generatePES - I have configured a potential for the Copper (111) surface.
• Configure the parameters in m-files under the subfolder UI.
• Run 'run_pigle.m'

Visualization:

The 'make_movie' file will help you to visuallize the dynamics.

Parallel Computing:

PIGLE support parallel computing (via matlab/Simulink support).

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List of PIGLE Files (NA):

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PIGLE: aux_files config_model.m generatePES make_movie.m pigle_sim prep_environment.m run_pigle.m sweepParams UI benchmark f_interaction.m LICENSE.txt pigle_data.mat prepare_configuration.m README.txt surface_params.m TODO.txt

./aux_files: calc_kinetic_energy.m calculate_sim_params.m generate_A_from_function.m make_data_path.m resample_data.m timeinput.m calculate_average_isf.m generate_A_from_frequencies_multiple_gamma.m hlp_f.m prepFuncs.m sim_gle_nd.m

./benchmark: analytic_gle.m analytic_le.m benchmark_biexp_gle.m biexp_gle_isf.m incoh_brownian_rot.m incoh_langevin_rot.m plot_diffusion_models.m

./generatePES: loadPES.m params_for_function_prepare_potential.m PES_library prepare_potential.m

./generatePES/PES_library: hexagonal6interp.m hexagonal.m

./pigle_sim: create_model.m delete_unconnected_lines.m sl_interactions.slx sl_pigle_Population.slx

./sweepParams: config_job.m config_job_params.m pigle_run_single_task.m pigle_shell_params.m run_job.m

./UI: pigle_ui.m pigle_ui_surface_params.m pigle_wrapper_params.m

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List of Analysis Files (KG):

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./analysis_code:

alpha_against_deltak - Plots fitting parameter alpha (ballistic exponential decay constant) over different incoming wavevectors - Able to plot comparison with experimental data (kindly provided by Dr David Ward)

noise_histogram - Extracts the noise in real and fourier space from the simulink framework, and characterises noise attributes

plotting_tau_range - Comparison of simulated and analytic ISF plots for a range of cut-off frequencies in the low-pass noise filter

potential_map - Plots trajectory of single particle in real space, superimposed over periodic potential surface

./figures: Contains high resolution versions of all figures used in the report, as well as pdf copies of the complete and shortened reports.