Tracking scalar features in unstructured datasets
Proceedings of the conference on Visualization '98
Collapsing flow topology using area metrics
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
A topology simplification method for 2D vector fields
Proceedings of the conference on Visualization '00
Exploring scalar fields using critical isovalues
Proceedings of the conference on Visualization '02
Tracking and Visualizing Turbulent 3D Features
IEEE Transactions on Visualization and Computer Graphics
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Time-varying reeb graphs for continuous space-time data
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets
VIS '04 Proceedings of the conference on Visualization '04
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines
IEEE Transactions on Visualization and Computer Graphics
Volume Tracking Using Higher Dimensional Isosurfacing
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Large Mesh Simplification using Processing Sequences
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Subdomain Aware Contour Trees and Contour Evolution in Time-Dependent Scalar Fields
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
IEEE Transactions on Visualization and Computer Graphics
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Efficient isosurface tracking using precomputed correspondence table
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Visual Verification and Analysis of Cluster Detection for Molecular Dynamics
IEEE Transactions on Visualization and Computer Graphics
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
A Quantized Boundary Representation of 2D Flows
Computer Graphics Forum
Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
Combining in-situ and in-transit processing to enable extreme-scale scientific analysis
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Visualization for the Physical Sciences
Computer Graphics Forum
Energy-scale aware feature extraction for flow visualization
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
Exploring power behaviors and trade-offs of in-situ data analytics
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes known as Rayleigh-Taylor instability. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion. We present a new approach to analyze Rayleigh-Taylor instabilities in which we extract a hierarchical segmentation of the mixing envelope surface to identify bubbles and analyze analogous segmentations of fields on the original interface plane. We compute meaningful statistical information that reveals the evolution of topological features and corroborates the observations made by scientists. We also use geometric tracking to follow the evolution of single bubbles and highlight merge/split events leading to the formation of the large and complex structures characteristic of the later stages. In particular we (i) Provide a formal definition of a bubble; (ii) Segment the envelope surface to identify bubbles; (iii) Provide a multi-scale analysis technique to produce statistical measures of bubble growth; (iv) Correlate bubble measurements with analysis of fields on the interface plane; (v) Track the evolution of individual bubbles over time. Our approach is based on the rigorous mathematical foundations of Morse theory and can be applied to a more general class of applications.