Python package for automatically superimposing data sets to create a master curve, using Gaussian process regression and maximum a posteriori estimation.

Publication of this work is forthcoming. For now, if you use this software, please cite it using the metadata in the citation file.

Check out the documentation to learn more about the package and how to use its API. A tutorial and explanation of the demos are coming soon!

mastercurves is in the PyPI! You can easily install it using pip:

pip install mastercurves

and likewise update it:

pip install mastercurves --upgrade

Once the package has been installed, you can simply import it's modules:

from mastercurves import MasterCurve
from mastercurves.transforms import Multiply, PowerLawAge

To begin creating a master curve, first define a MasterCurve object:

mc = MasterCurve()

and add data to the object:

mc.add_data(xs, ys, states)

Here, xs is a python list (of length n) of NumPy arrays. Each of these arrays contains the x-coordinates for a data set at a particular state. Similarly, ys is a list of length n of NumPy arrays, each containing the y-coordinates for a data set at corresponding states. states is a list of length n, with elements parameterizing the different states.

Coordinate transforms can be added to the mastercurve as follows:

mc.add_htransform(Multiply())

The above line tells the software to shift the data sets on the horizontal axis by a multiplicative factor. Note: by default, Multiply() assumes that the logarithm of the corresponding coordinate was taken before adding the data to the MasterCurve object. To override this, pass the argument Multiply(scale = "linear"). An analagous method, add_vtransform(), exists for transformations to the y-coordinate, which similarly assumes logarithmically scaled data.

When the data and transformations have been added to the MasterCurve, shifting the data is easy!

mc.superpose()

The results can be visualized in a single line as well:

mc.plot()

Multiple examples of the software's use can be found in the demos folder, which demonstrate much of the functionality of the software.

Inquiries and suggestions can be directed to krlennon[at]mit.edu. In particular, useful transformations can be directly added to the transforms directory, either in a local copy of the package or by raising an issue here!

GNU General Public License v3.0

The data used in the demos has been generously provided by authors of the following publications:

T. H. Larsen and E. M. Furst, Microrheology of the liquid-solid transition during gelation, Phys. Rev. Lett., vol. 100, p. 146001, Apr 2008.

S. M. Lalwani, P. Batys, M. Sammalkorpi, and J. L.Lutkenhaus, Relaxation Times of Solid-like Polyelectrolyte Complexes of Varying pH and Water Content, Macromolecules, vol. 54, pp. 7765-7776, Sep 2021.

The data in other examples was digitized from the following publications:

R. Gupta, B. Baldewa, and Y. M. Joshi, Time temperature superposition in soft glassy materials, Soft Matter, vol. 8, pp. 4171-4176, 2012.

R. I. Dekker, M. Dinkgreve, H. de Cagny, D. J. Koeze, B. P. Tighe, and D. Bonn, Scaling of flow curves: Comparison between experiments and simulations, Journal of Non-Newtonian Fluid Mechanics, vol. 261, pp. 33-37, 2018.

D. J. Plazek, Temperature dependence of the viscoelastic behavior of polystyrene, The Journal of Physical Chemistry, vol. 69, pp. 3480-3487, Oct 1965.