  In this paper we demonstrate the use of multivariate topological algorithms
to analyse and interpret Lattice Quantum Chromodynamics (QCD) data. Lattice QCD
is a long established field of theoretical physics research in the pursuit of
understanding the strong nuclear force. Complex computer simulations model
interactions between quarks and gluons to test theories regarding the behaviour
of matter in a range of extreme environments. Data sets are typically generated
using Monte Carlo methods, providing an ensemble of configurations, from which
observable averages must be computed. This presents issues with regard to
visualisation and analysis of the data as a typical ensemble study can generate
hundreds or thousands of unique configurations. We show how multivariate
topological methods, such as the Joint Contour Net, can assist physicists in
the detection and tracking of important features within their data in a
temporal setting. This enables them to focus upon the structure and
distribution of the core observables by identifying them within the surrounding
data. These techniques also demonstrate how quantitative approaches can help
understand the lifetime of objects in a dynamic system.
