Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems

Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of the so-called local quadratic support is proved. The results concerning strong convexity are used to derive sufficient conditions for attainable sets of continuous-time nonlinear systems to be strongly convex. An application of these conditions is a novel method to over-approximate attainable sets when strong convexity is present.Comment: 20 pages, 3 figure

On the Computation of Integral Curves in Adaptive Mesh Refinement Vector Fields

Integral curves, such as streamlines, streaklines, pathlines, and timelines, are an essential tool in the analysis of vector field structures, offering straightforward and intuitive interpretation of visualization results. While such curves have a long-standing tradition in vector field visualization, their application to Adaptive Mesh Refinement (AMR) simulation results poses unique problems. AMR is a highly effective discretization method for a variety of physical simulation problems and has recently been applied to the study of vector fields in flow and magnetohydrodynamic applications. The cell-centered nature of AMR data and discontinuities in the vector field representation arising from AMR level boundaries complicate the application of numerical integration methods to compute integral curves. In this paper, we propose a novel approach to alleviate these problems and show its application to streamline visualization in an AMR model of the magnetic field of the solar system as well as to a simulation of two incompressible viscous vortex rings merging

Rational Strain Engineering in Delafossite Oxides for Highly Efficient Hydrogen Evolution Catalysis in Acidic Media

The rational design of hydrogen evolution reaction (HER) electrocatalysts which are competitive with platinum is an outstanding challenge to make power-to-gas technologies economically viable. Here, we introduce the delafossites PdCrO$_2$, PdCoO$_2$ and PtCoO$_2$ as a new family of electrocatalysts for the HER in acidic media. We show that in PdCoO$_2$ the inherently strained Pd metal sublattice acts as a pseudomorphic template for the growth of a strained (by +2.3%) Pd rich capping layer under reductive conditions. The surface modification continuously improves the electrocatalytic activity by simultaneously increasing the exchange current density j$_0$ from 2 to 5 mA/cm$^2_{geo}$ and by reducing the Tafel slope down to 38 mV/decade, leading to overpotentials $\eta_{10}$ < 15 mV for 10 mA/cm$^2_{geo}$, superior to bulk platinum. The greatly improved activity is attributed to the in-situ stabilization of a $\beta$-palladium hydride phase with drastically enhanced surface catalytic properties with respect to pure or nanostructured palladium. These findings illustrate how operando induced electrodissolution can be used as a top-down design concept for rational surface and property engineering through the strain-stabilized formation of catalytically active phases

Local characterization of strongly convex sets

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0} \delta_\Omega(\epsilon)/\epsilon^2 exists whenever \Omega is closed and convex

In situ and in-transit analysis of cosmological simulations

Modern cosmological simulations have reached the trillion-element scale, rendering data storage and subsequent analysis formidable tasks. To address this circumstance, we present a new MPI-parallel approach for analysis of simulation data while the simulation runs, as an alternative to the traditional workflow consisting of periodically saving large data sets to disk for subsequent 'offline' analysis. We demonstrate this approach in the compressible gasdynamics/N-body code Nyx, a hybrid MPI + OpenMP code based on the BoxLib framework, used for large-scale cosmological simulations. We have enabled on-the-fly workflows in two different ways: one is a straightforward approach consisting of all MPI processes periodically halting the main simulation and analyzing each component of data that they own ('in situ'). The other consists of partitioning processes into disjoint MPI groups, with one performing the simulation and periodically sending data to the other 'sidecar' group, which post-processes it while the simulation continues ('in-transit'). The two groups execute their tasks asynchronously, stopping only to synchronize when a new set of simulation data needs to be analyzed. For both the in situ and in-transit approaches, we experiment with two different analysis suites with distinct performance behavior: one which finds dark matter halos in the simulation using merge trees to calculate the mass contained within iso-density contours, and another which calculates probability distribution functions and power spectra of various fields in the simulation. Both are common analysis tasks for cosmology, and both result in summary statistics significantly smaller than the original data set. We study the behavior of each type of analysis in each workflow in order to determine the optimal configuration for the different data analysis algorithms

Topological Galleries: A High Level User Interface for Topology Controlled Volume Rendering

Existing topological interfaces to volume rendering are limited by their reliance on sophisticated knowledge of topology by the user. We extend previous work by describing topological galleries, an interface for novice users that is based on the design galleries approach. We report three contributions: an interface based on hierarchical thumbnail galleries to display the containment relationships between topologically identifiable features, the use of the pruning hierarchy instead of branch decomposition for contour tree simplification, and drag-and-drop transfer function assignment for individual components. Initial results suggest that this approach suffers from limitations due to rapid drop-off of feature size in the pruning hierarchy. We explore these limitations by providing statistics of feature size as function of depth in the pruning hierarchy of the contour tree

Preface IEEE LDAV 2023

Join us for the 13th IEEE Symposium on Large Data Analysis and Visualization (IEEE LDAV) on Monday, October 23rd 2023 collocated with IEEE VIS 2023 in Melbourne, Victoria, Australia.<br/