Identifying and analyzing power-law scaling in two-dimensional image datasets.

Power-law distributions provide a general description of diverse natural phenomena in which events with a logarithmically increasing size occur with logarithmically decreasing probability. However, experimentally derived correlated two-dimensional information is often difficult to cleanly interpret as discrete events of defined size. Moreover, physical limitation of techniques such as those based on scanning probe microscopy, which can ideally be used to observe power-law behavior, reduce event number and thus render straightforward power-law fits even more challenging. Here we develop and compare different techniques to analyze event distributions from two-dimensional images. We show that tracking interface position allows the associated scaling parameters to be accurately extracted from both experimental and synthetic image-based datasets. We also show how these techniques can differentiate between power-law and non-power-law behavior by comparison of Hill, moments, and kernel estimators of this scaling parameter. We thus present computational tools to analyze power-law fits in two-dimensional datasets and identify the scaling parameters that best describe these distributions.

Hystorian: A processing tool for scanning probe microscopy and other n-dimensional datasets.

Research in materials science increasingly depends on the correlation of information from multiple characterisation techniques, acquired in ever larger datasets. Efficient methods of processing and storing these complex datasets are therefore crucial. Reliably keeping track of data processing is also essential to conform with the goals of open science. Here, we introduce Hystorian, a generic materials science data analysis Python package built at its core to improve the traceability, reproducibility, and archival ability of data processing. Proprietary data formats are converted into open hierarchical data format (HDF5) files, with both datasets and subsequent workflows automatically stored into a single location, thus allowing easy management of multiple data types. At present, Hystorian provides a basic scanning probe microscopy and x-ray diffraction analysis toolkit, and is readily extensible to suit user needs. It is also able to wrap over any existing processing functions, making it easy to append in an extant workflow.