arXiv subjects

Ingrid Hotz

Publications and source records attributed to Ingrid Hotz.

32 records · Page 2Linked to original sources

arXiv2021

Segmentation Driven Peeling for Visual Analysis of Electronic Transitions

Electronic transitions in molecules due to absorption or emission of light is a complex quantum mechanical process. Their study plays an important role in the design of novel materials. A common yet challenging task in the study is to determine the nature of those electronic transitions, i.e. which subgroups of the molecule are involved in the transition by donating or accepting electrons, followed by an investigation of the variation in the donor-acceptor behavior for different transitions or conformations of the molecules. In this paper, we present a novel approach towards the study of electronic transitions based on the visual analysis of a bivariate field, namely the electron density in the hole and particle Natural Transition Orbital (NTO). The visual analysis focuses on the continuous scatter plots (CSPs) of the bivariate field linked to their spatial domain. The method supports selections in the CSP visualized as fiber surfaces in the spatial domain, the grouping of atoms, and segmentation of the density fields to peel the CSP. This peeling operator is central to the visual analysis process and helps identify donors and acceptors. We study different molecular systems, identifying local excitation and charge transfer excitations to demonstrate the utility of the method.

physics.chem-ph↗

arXiv2021

Geometry-Aware Merge Tree Comparisons for Time-Varying Data with Interleaving Distances

Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First, they give compressed and topology-preserving representations of data instances. Second, their comparisons provide a basis for studying the relations among data instances, such as their distributions, clusters, outliers, and periodicities. A number of comparative measures have been developed for merge trees. However, these measures are often computationally expensive since they implicitly consider all possible correspondences between critical points of the merge trees. In this paper, we perform geometry-aware comparisons of merge trees using labeled interleaving distances. The main idea is to decouple the computation of a comparative measure into two steps: a labeling step that generates a correspondence between the critical points of two merge trees, and a comparison step that computes distances between a pair of labeled merge trees by encoding them as matrices. We show that our approach is general, computationally efficient, and practically useful. Our general framework makes it possible to integrate geometric information of the data domain in the labeling process. At the same time, it reduces the computational complexity since not all possible correspondences have to be considered. We demonstrate via experiments that such geometry-aware merge tree comparisons help to detect transitions, clusters, and periodicities of time-varying datasets, as well as to diagnose and highlight the topological changes between adjacent data instances.

cs.HC↗

arXiv2021

Visual Analysis of Electronic Densities and Transitions in Molecules

The study of electronic transitions within a molecule connected to the absorption or emission of light is a common task in the process of the design of new materials. The transitions are complex quantum mechanical processes and a detailed analysis requires a breakdown of these processes into components that can be interpreted via characteristic chemical properties. We approach these tasks by providing a detailed analysis of the electron density field. This entails methods to quantify and visualize electron localization and transfer from molecular subgroups combining spatial and abstract representations. The core of our method uses geometric segmentation of the electronic density field coupled with a graph-theoretic formulation of charge transfer between molecular subgroups. The design of the methods has been guided by the goal of providing a generic and objective analysis following fundamental concepts. We illustrate the proposed approach using several case studies involving the study of electronic transitions in different molecular systems.

cs.HC↗

arXiv2021

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. 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.

cs.HC↗

arXiv2021

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. Here we report the synthesis at ~90 GPa of novel beryllium polynitrides, monoclinic and triclinic BeN4. The triclinic phase, upon decompression to ambient conditions, transforms into a compound with atomic-thick BeN4 layers interconnected via weak van der Waals bonds consisting of polyacetylene-like nitrogen chains with conjugated π-systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN4 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 BeN4 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.

cond-mat.mtrl-sci↗

arXiv2020

Topology-Based Feature Design and Tracking for Multi-Center Cyclones

In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of different feature definitions for the same concept are used. Often, these definitions compete with each other and it is unclear which definition should be used in which context. A prominent example is the definition of cyclones in climate research. Despite the differences, frequently these feature definitions can be related to topological concepts. In our approach, we provide a cyclone tracking framework that supports interactive feature definition and comparison based on a precomputed tracking graph that stores all extremal points as well as their temporal correspondents. The framework combines a set of independent building blocks: critical point extraction, critical point tracking, feature definition, and track exploration. One of the major advantages of such an approach is the flexibility it provides, that is, each block is exchangeable. Moreover, it also enables us to perform the most expensive analysis, the construction of a full tracking graph, as a prepossessing step, while keeping the feature definition interactive. Different feature definitions can be explored and compared interactively based on this tracking graph. Features are specified by rules for grouping critical points, while feature tracking corresponds to filtering and querying the full tracking graph by specific requests. We demonstrate this method for cyclone identification and tracking in the context of climate research.

cs.LG↗

arXiv2020

Cinema Darkroom: A Deferred Rendering Framework for Large-Scale Datasets

This paper presents a framework that fully leverages the advantages of a deferred rendering approach for the interactive visualization of large-scale datasets. Geometry buffers (G-Buffers) are generated and stored in situ, and shading is performed post hoc in an interactive image-based rendering front end. This decoupled framework has two major advantages. First, the G-Buffers only need to be computed and stored once---which corresponds to the most expensive part of the rendering pipeline. Second, the stored G-Buffers can later be consumed in an image-based rendering front end that enables users to interactively adjust various visualization parameters---such as the applied color map or the strength of ambient occlusion---where suitable choices are often not known a priori. This paper demonstrates the use of Cinema Darkroom on several real-world datasets, highlighting CD's ability to effectively decouple the complexity and size of the dataset from its visualization.

cs.GR↗

arXiv2020

Structure of a collisionless pair jet in a magnetized electron-proton plasma: Flow-aligned magnetic field

We present the results from a particle-in-cell (PIC) simulation that models the interaction between a spatially localized electron-positron cloud and an electron-ion plasma. The latter is permeated by a magnetic field that is initially spatially uniform and aligned with the mean velocity vector of the pair cloud. The pair cloud expels the magnetic field and piles it up into an electromagnetic piston. Its electromagnetic field is strong enough to separate the pair cloud from the ambient plasma in the direction that is perpendicular to the cloud propagation direction. The piston propagates away from the spine of the injected pair cloud and it accelerates the protons to a high nonrelativistic speed. The accelerated protons form an outer cocoon that will eventually become separated from the unperturbed ambient plasma by a fast magnetosonic shock. No electromagnetic piston forms at the front of the cloud and a shock is mediated here by the filamentation instability. The final plasma distribution resembles that of a hydrodynamic jet. Collisionless plasma jets may form in the coronal plasma of accreting black holes and the interaction between the strong magnetic field of the piston and the hot pair cloud may contribute to radio emissions by such objects.

astro-ph.HE↗

arXiv2019

Continuous Histograms for Anisotropy of 2D Symmetric Piece-wise Linear Tensor Fields

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field analysis, such methods are also interesting for the analysis of derived scalar invariants. While there are standard algorithms to compute and analyze contours, they are not directly applicable to tensor invariants when using component-wise tensor interpolation. In this chapter we present an accurate derivation of the contour spectrum for invariants with quadratic behavior computed from two-dimensional piece-wise linear tensor fields. For this work, we are mostly motivated by a consistent treatment of the anisotropy field, which plays an important role as stability measure for tensor field topology. We show that it is possible to derive an analytical expression for the distribution of the invariant values in this setting, which is exemplary given for the anisotropy in all details. Our derivation is based on a topological sub-division of the mesh in triangles that exhibit a monotonic behavior. This triangulation can also directly be used to compute the accurate contour tree with standard algorithms. We compare the results to a naïve approach based on linear interpolation on the original mesh or the subdivision.

cs.GR↗

arXiv2019

Inviwo -- A Visualization System with Usage Abstraction Levels

The complexity of today's visualization applications demands specific visualization systems tailored for the development of these applications. Frequently, such systems utilize levels of abstraction to improve the application development process, for instance by providing a data flow network editor. Unfortunately, these abstractions result in several issues, which need to be circumvented through an abstraction-centered system design. Often, a high level of abstraction hides low level details, which makes it difficult to directly access the underlying computing platform, which would be important to achieve an optimal performance. Therefore, we propose a layer structure developed for modern and sustainable visualization systems allowing developers to interact with all contained abstraction levels. We refer to this interaction capabilities as usage abstraction levels, since we target application developers with various levels of experience. We formulate the requirements for such a system, derive the desired architecture, and present how the concepts have been exemplary realized within the Inviwo visualization system. Furthermore, we address several specific challenges that arise during the realization of such a layered architecture, such as communication between different computing platforms, performance centered encapsulation, as well as layer-independent development by supporting cross layer documentation and debugging capabilities.

cs.GR↗

arXiv2019

Mathematical Foundations in Visualization

Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to provide a taxonomy of the usage of mathematics in visualization, and to identify a fundamental set of mathematics that should be taught to students as part of an introduction to contemporary visualization research. Within the scope of this chapter, we are unable to provide a full review of all mathematical foundations of visualization; rather, we identify a number of concepts that are useful in visualization, explain their significance, and provide references for further reading.

cs.HC↗

arXiv2018

Binding Sites for Luminescent Amyloid Biomarkers from non-Biased Molecular Dynamics Simulations

A very stable binding site for the interaction between an pentameric oligothiophene and an amyloid-$β$(1-42) fibril has been identified by means of non-biased molecular dynamics simulations. In this site, the probe is locked in an all-trans conformation with a Coulombic binding energy of 1,200 kJ/mol due to the interactions between the anionic carboxyl groups of the probe and the cationic $ε$-amino groups in the lysine side chain. Upon binding, the conformationally restricted probes show a pronounced increase in molecular planarity. This is in-line with the observed changes in luminescence properties that serve as the foundation for their use as biomarkers.

physics.chem-ph↗

arXiv2014

Acceleration feature points of unsteady shear flows

In this paper, we propose a novel framework to extract features such as vortex cores and saddle points in two-dimensional unsteady flows. This feature extraction strategy generalizes critical points of snapshot topology in a Galilean-invariant manner, allows to prioritize features according to their strength and longevity, enables to track the temporal evolution of features, is robust against noise and has no subjective parameters. These characteristics are realized via several constitutive elements. First, acceleration is employed as a feature identifier following Goto and Vassilicos (2006), thus ensuring Galilean invariance. Second, the acceleration magnitude is used as basis for a mathematically well-developed scalar field topology. The minima of this field are called acceleration feature points, a superset of the acceleration zeros. These points are discriminated into vortices and saddle points depending the spectral properties of the velocity Jacobian. Third, all operations are based on discrete topology for the scalar field with combinatorial algorithms. This parameter-free foundation allows (1) to use persistence as a physically meaningful importance measure to prioritize feature points, (2) ensures robustness since no differentiation and interpolation need to be performed with the data, and (3) enables a natural and robust tracking algorithm for the temporal feature evolution. In particular, we can track vortex merging events in an unsupervised manner. Data based analyses are presented for an incompressible periodic cylinder wake, an incompressible planar mixing layer and a weakly compressible planar jet. They demonstrate the power of the tracking approach, which provides a spatiotemporal hierarchy of the minima.

physics.flu-dyn↗

arXiv2012

Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices

This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using basic ideas from probability theory and builds upon an algorithm from discrete Morse theory with a strong mathematical foundation. While a formal proof is only hinted at, we do provide a thorough numerical evaluation of our method and compare it to established algorithms.

cs.CV↗