Geometry-Aware Merge Tree Comparisons for Time-Varying Data With Interleaving Distances
Not provided.
Computer Science↗
Engineering topics
Hotz, Ingrid
Publications and source records attributed to Hotz, Ingrid.
Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an essential role in capturing the shape of scalar field data. Herein we present a state–of–the–art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time–varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.
97 MATHEMATICS AND COMPUTING↗
High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded BeN 4 Polymorph
High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. In this paper, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material BeN 4 . A triclinic phase of beryllium tetranitride tr-BeN 4 was synthesized from elements at similar to 85 GPa. Upon decompression to ambient conditions, it transforms into a compound with atomic-thick BeN 4 layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated pi systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN 4 layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The BeN 4 layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions.
36 MATERIALS SCIENCE↗
State of the Art in Time‐Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties
Abstract We present a state‐of‐the‐art report on time‐dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time‐independent to time‐dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time‐dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.
Bujack, Roxana↗