Systematic visualisation methods for material sciences

Abstract

Scientific visualisation of computational or observational data sets in material sciences is essential for studying data sets of ever increasing complexity. Rather than just using and implementing self-contained solutions to address particular problems, a systematic approach for modelling data sets opens the gateway to sharing data sets with other applications and general purpose visualisation frameworks. The fibre bundle data model is a mathematical description encompassing many diverse data types, ranging from molecular dynamics via continuum mechanics describing solid and fluids to finite elements. It fits well to be mapped to the Hierarchical Data Format file format as a widely used data storage container. Still various choices remain on such a data mapping and are reviewed in this article. The fibre bundle data model provides a classification scheme for data sets on an abstract level, disregarding implementation details and therefore eases selecting visualisation methods appropriate for the underlying data. Data are hereby studied via properties of their so called base space and fibre space. The base space is describing properties of the numerical discretion scheme, the fibre space is describing physical quantities. Visual data analysis of both spaces is important, but can be considered widely independent, depending on the need to either study computational or physical aspects of the data. Methods to study the topological structure of the base space complement methods to study scalar, vector and tensor fields and provide a highly systematic approach for scientific visualisation in material sciences.

Keywords:

• Scientific visualisation
• Differential Geometry
• Big data
• Data classification
• Molecular visualisation

Acknowledgements

We thank A. Kaiser, University of Innsbruck, for providing screenshots in HyperChem. The barium titanate (BaTiO₃) data set used for demonstrating the Vector Speckles technique was provided as part of the 2012 IEEE Visualization Challenge Contest. The data sets for the trajectories of silicon atoms were provided by B. Karki, Louisiana State University, supported in part by a grant from the National Science Foundation (grant no. EAR 1118869).