Reducing the number of templates for aligned-spin compact binary coalescence gravitational wave searches using metric-agnostic template nudging

Efficient multi-dimensional template placement is crucial in computationally intensive matched-filtering searches for Gravitational Waves (GWs). Here, we implement the Neighboring Cell Algorithm (NCA) to improve the detection volume of an existing Compact Binary Coalescence (CBC) template bank. This algorithm has already been successfully applied for a binary millisecond pulsar search in data from the Fermi satellite. It repositions templates from over-dense regions to under-dense regions and reduces the number of templates that would have been required by a stochastic method to achieve the same detection volume. Our method is readily generalizable to other CBC parameter spaces. Here we apply this method to the aligned--single-spin neutron-star--black-hole binary coalescence inspiral-merger-ringdown gravitational wave parameter space. We show that the template nudging algorithm can attain the equivalent effectualness of the stochastic method with 12% fewer templates

Ordering dynamics of blue phases entails kinetic stabilization of amorphous networks

The cubic blue phases of liquid crystals are fascinating and technologically promising examples of hierarchically structured soft materials, comprising ordered networks of defect lines (disclinations) within a liquid crystalline matrix. We present the first large-scale simulations of their domain growth, starting from a blue phase nucleus within a supercooled isotropic or cholesteric background. The nucleated phase is thermodynamically stable; one expects its slow orderly growth, creating a bulk cubic. Instead, we find that the strong propensity to form disclinations drives the rapid disorderly growth of a metastable amorphous defect network. During this process the original nucleus is destroyed; re-emergence of the stable phase may therefore require a second nucleation step. Our findings suggest that blue phases exhibit hierarchical behavior in their ordering dynamics, to match that in their structure.Comment: 11 pages, 5 figures, 2 supplementary figures, 2 supplementary tables, accepted by PNA

Designing Volumetric Truss Structures

We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself

Variational Level-Set Detection of Local Isosurfaces from Unstructured Point-based Volume Data

A standard approach for visualizing scalar volume data is the extraction of isosurfaces. The most efficient methods for surface extraction operate on regular grids. When data is given on unstructured point-based samples, regularization can be applied but may introduce interpolation errors. We propose a method for smooth isosurface visualization that operates directly on unstructured point-based volume data avoiding any resampling. We derive a variational formulation for smooth local isosurface extraction using an implicit surface representation in form of a level-set approach, deploying Moving Least Squares (MLS) approximation, and operating on a kd-tree. The locality of our approach has two aspects: first, our algorithm extracts only those components of the isosurface, which intersect a subdomain of interest; second, the action of the main term in the governing equation is concentrated near the current isosurface position. Both aspects reduce the computation times per level-set iteration. As for most level-set methods a reinitialization procedure is needed, but we also consider a modified algorithm where this step is eliminated. The final isosurface is extracted in form of a point cloud representation. We present a novel point completion scheme that allows us to handle highly adaptive point sample distributions. Subsequently, splat-based or mere (shaded) point rendering is applied. We apply our method to several synthetic and real-world data sets to demonstrate its validity and efficiency

Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Wavelet representation of contour sets

Journal ArticleWe present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contours and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields