The file faraday.py is a python script to integrate the equations of motion for inviscid Faraday waves in inhomogeneous domains with the finite element method. The files pendula.nb and plotfaraday.nb are Mathematica notebooks to plot results from simulations. The file accel.py is a python script for controlling an Arduino to collect data from an accelerometer in Faraday wave experiments. The folders contain data files from experiments and simulation output.
The python code has been run with anaconda 3.8, which can be downloaded here: https://www.anaconda.com/distribution/. The scripts require packages numpy, scipy, matplotlib, pyserial, fenics, and mshr, Create a new anaconda environment and install from the default channels with conda create -n faraday_env numpy scipy matplotlib pyserial. Activate the environment with conda activate faraday_env, then install fenics and mshr from the conda-forge channel with conda install -c conda-forge fenics mshr. NB the matplotlib package from the conda-forge channel has not worked well on mac systems.
The accelerometer script uses the arduino command line interface, which can be installed following the instructions here: https://arduino.github.io/arduino-cli/dev/installation/. It is written for an Arduino Uno; for initial configuration, see: https://create.arduino.cc/projecthub/B45i/getting-started-with-arduino-cli-7652a5.
Running the script ./faraday.py -h will produce the following usage message:
usage: faraday.py [-h] [--frequency FREQ] [--gravity G]
[--acceleration ACCELERATION] [--width WIDTH]
[--length LENGTH] [--height HEIGHT] [--radius RADIUS]
[--tension SIGMA] [--density RHO] [--time SIMTIME]
[--steps STEPS] [--output {0,1}] [--iseed ISEED]
[--iamp IAMP] [--imodes IMODES] [--sseed SSEED]
[--samp SAMP] [--smodes SMODES] [--rtol RTOL] [--atol ATOL]
[--damp1 DAMP1] [--damp3 DAMP2] [--xmesh XMESH]
[--ymesh YMESH] [--zmesh ZMESH] [--threshold THRS]
--filebase OUTPUT [--refinement REFINEMENT] [--bmesh {0,1}]
[--nonlinear {0,1}] [--geometry {rectangle,cylinder,box}]
[--contact {stick,slip,periodic}] [--nthreads NTHREADS]
Moving mesh simulation for inviscid Faraday waves with inhomogeneous
substrate.
optional arguments:
-h, --help show this help message and exit
--frequency FREQ Driving frequency in Hertz
--gravity G Gravitational acceleration in cm/s^2
--acceleration ACCELERATION
Driving acceleration in terms of gravitational
acceleration
--width WIDTH Width in cm
--length LENGTH Length in cm
--height HEIGHT Height in cm
--radius RADIUS Radius in cm
--tension SIGMA Surface tension in dyne/cm^2
--density RHO Fluid density in g/cm^3
--time SIMTIME Simulation time in driving cycles
--steps STEPS Output steps per cycle
--output {0,1} Flag to output full data or abbreviated data
--iseed ISEED Seed for random initial conditions
--iamp IAMP Amplitude for modes in random initial conditions
--imodes IMODES Number of modes to include in random initial
conditions
--sseed SSEED Seed for random substrate shape
--samp SAMP Amplitude for modes in random substrate shape
--smodes SMODES Number of modes to include in random substrate shape
--rtol RTOL Integration relative tolerance
--atol ATOL Integration absolute tolerance
--damp1 DAMP1 Constant damping coefficient
--damp3 DAMP2 Curvature damping coefficient
--xmesh XMESH Lateral mesh refinement
--ymesh YMESH Lateral mesh refinement
--zmesh ZMESH Vertical mesh refinement
--threshold THRS Threshold change in log norm magnitude to stop
integration
--filebase OUTPUT Base string for file output
--refinement REFINEMENT
Number of refinements for top
--bmesh {0,1} Flag to move boundary mesh in time stepping. This is
faster and tentatively more accurate than the
alternative mesh movement, but suffers numerical
instabilities for large deviations.
--nonlinear {0,1} Flag to include nonlinear terms
--geometry {rectangle,cylinder,box}
Mesh geometry. Options are rectangle, cylinder, and
box.
--contact {stick,slip,periodic}
Contact line boundary conditions. Options are stick,
slip, and periodic. periodic is not available for
cylinder geometry.
--nthreads NTHREADS Number of threads to allow parallel computations to
run over.
Running the script ./accel.py -h will produce the following usage message:
usage: accel.py [-h] --filebase FILEBASE [--directory DATA] [--Nt NT]
[--delay DELAY] [--xy {0,1}] [--run {0,1}] [--count COUNT]
[--port /DEV/CU.USBMODEM14101]
Upload an Arduino sketch and read output from the accelerometer.
optional arguments:
-h, --help show this help message and exit
--filebase FILEBASE Base string for file output.
--directory DATA Directory to save files. Default "data".
--Nt NT Number of buffer ints. Default 150.
--delay DELAY Delay between samples. Default 2.0.
--xy {0,1} Flag for x and y output. Default 1.
--run {0,1} Flag for running arduino and reading output; if 0,
data is read from previous runs if files exist.
Default 1.
--count COUNT Initial count. Default 0.
--port /DEV/CU.USBMODEM14101
Arduino port.
For faraday.py script, if the file filebasesubstrate.dat exists, the script reads a line containing an integer Nmodes giving the number of modes, followed by lines which each contain Nmodes numbers specifying the sine and cosine mode amplitudes for the substrate shape. For rectangle geometries, there is a single sine and a single cosine line. For the box geometries, there are Nmodes lines for sine-sine modes, followed by Nmodes lines for sine-cosine modes, followed by Nmodes lines for cosine-sine modes, followed by Nmodes lines for cosine-cosine modes. For the cylinder geometry, there are Nmodes lines for Bessel-sine modes, followed Nmodes lines for Bessel-cosine modes. If the file filebaseic.dat exists, the script will read a line of text which contains the surface potentials values and height, separated by spaces followed by a line containing the coordinates of the surface mesh points.
For faraday.py script, the script will always append to (or create) the file filebase.txt file a line of text containing the applied frequency, acceleration, measured frequency, measured growth rate, measured wave number, substrate inhomogeneity height, and random seed. If the output flag is set to 1, the script will list more information in filebase.txt in a readable format, a filebasefs.dat containing the final surface height, which can be used as an initial condition in other simulations by copying it to a filebaseic.dat, and also create binary files filebase.npy containing the mesh evolution in binary format and filebasenorms.npy containing the surface disturbance norms, which can be parsed with the Mathematica plot notebooks.
For the accel.py script, the script will append a line to filebase.txt each time data is saved which contains the measurement count, the measured acceleration amplitude, the measured frequency, the measured initial phase, the measured mean z acceleration, the measured mean x acceleration, and the measured mean y acceleration. It will also create files filebase{x,y,z}count.npy for each saved data which contain binary time series for each direction. Every time the data is plotted, a file filebasecount.pdf is also saved, and when the saved data is plotted, a file filebase.pdf is created.
The data folder contains various data files generated from the faraday.py script and the Mathematica notebooks, including the substrate geometries and instability boundaries plotted in plotfaraday.nb.
The experiments folder contains experimental data collected from our Faraday instability experiments. The subfolders flat2, periodic2, and random2 corresponding to the experiments performed with the flat, sinusoidal, and selected random substrate described in the manuscript. The *.txt files within each subfolder contain the recorded driving acceleration and frequency for each measurement, and the *.npy files contain the raw accelerometer data for each measurement.
The sweeps folder contains file output from batches of simulations used to determine stability boundaries. The subfolder random contains faraday.py output for the 500 randomly generated substrates that were used to generate the selected random substrate for the experiments. The subfolders periodic2acc, random2acc, and periodic2acc contain faraday.py simulation output corresponding to the substrates that were 3d printed in experiments, and the sharpamp subfolder contains simulations of the sharply peaked substrates. The subfolders finite1, finite2, and finite3 contain the final average swinging amplitude for the pendulum array subject to 1024 random finite-size perturbations.