Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis

Lagrangian coherent structures and trajectory similarity: two important tools for scientific visualization

This thesis studies the computation and visualization of Lagrangian coherent structures (LCS), an emerging technique for analyzing time-varying velocity fields (e.g. blood vessels and airflows), and the measure of similarity for trajectories (e.g. hurricane paths). LCS surfaces and trajectory-based techniques (e.g. trajectory clustering) are complementary to each other for visualization, while velocity fields and trajectories are two important types of scientific data, which are more and more accessible by virtue of the technology development for both data collection and numerical simulation. A key step for LCS computation is tracing the paths of collections of particles through a flow field. When a flow field is interpolated from the nodes of an unstructured mesh, the process of advecting a particle must first find which cell in the unstructured mesh contains the particle. Since the paths of nearby particles often diverge, the parallelization of particle advection quickly leads to incoherent memory accesses of the unstructured mesh. We have developed a new block advection GPU approach that reorganizes particles into spatially coherent bundles as they follow their advection paths, which greatly improves memory coherence and thus shared-memory GPU performance. This approach works best for flows that meet the CFL criterion on unstructured meshes of uniformly sized elements, small enough to fit at least two timesteps in GPU memory. LCS surfaces provide insight into unsteady fluid flow, but their construction has posed many challenges. These structures can be characterized as ridges of a field, but their local definition utilizes an ambiguous eigenvector direction that can point in one of two directions, and its ambiguity can lead to noise and other problems. We overcome these issues with an application of a global ridge definition, applied using the hierarchical watershed transformation. We show results on a mathematical flow model and a simulated vascular flow dataset indicating the watershed method produces less noisy structures. Trajectory similarity has been shown to be a powerful tool for visualizing and analyzing trajectories. In this paper we propose a novel measure of trajectory similarity using both spatial and directional information. The similarity is asymmetric, bounded within [0,1], affine-invariant, and efficiently computed. Asymmetric mappings between a pair of trajectories can be derived from this similarity. Experimental results demonstrate that the measure is better than existing measures in both similarity scores and trajectory mappings. The measure also inspires a simple similarity-based clustering method for effectivly visualizing a large number of trajectories, which outperforms the state-of-the-art model-based clustering method (VFKM)

Aeronautical engineering: A continuing bibliography with indexes (supplement 278)

This bibliography lists 414 reports, articles, and other documents introduced into the NASA scientific and technical information system in April 1992

NASA Thesaurus. Volume 2: Access vocabulary

The NASA Thesaurus -- Volume 2, Access Vocabulary -- contains an alphabetical listing of all Thesaurus terms (postable and nonpostable) and permutations of all multiword and pseudo-multiword terms. Also included are Other Words (non-Thesaurus terms) consisting of abbreviations, chemical symbols, etc. The permutations and Other Words provide 'access' to the appropriate postable entries in the Thesaurus

NASA Thesaurus. Volume 1: Hierarchical listing

There are 16,713 postable terms and 3,716 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary

Precise Tests of Fundamental Symmetries at Low Energies using a 3He-129Xe Comagnetometer

Effects of theories beyond the Standard Model would become directly apparent at high energies, which are probably out of reach for colliders. As an alternative, low-energy high-precision measurements of quantities are performed, looking for deviations from the Standard Model (SM) predictions. In this case: Firstly, a small amount of the large effects of quantum gravity at the Planck scale should remain at low energies, which is tested by looking for Lorentz invariance violation in the neutron sector. Secondly, new sources of CP-violation would cause permanent electric dipole moments (EDMs)of particles that are many orders of magnitude larger than the EDMs predicted by the SM. The experimental approach is to measure the free precession of nuclear spin polarized 3He and 129Xe atoms in a homogeneous magnetic guiding field of about 400 nT using LTC SQUIDs as low-noise magnetic flux detectors. This dissertation reports on the search for a CPT and Lorentz invariance violating coupling of the 3He and 129Xe nuclear spins to posited background fields. An upper limit on the equatorial component of the background field interacting with the spin of the bound neutron bn < 8.4 10^-34 GeV (68% C.L.) was obtained. Furthermore, the technical developments and preparations for measurements of the 129Xe EDM are described

NASA thesaurus. Volume 1: Hierarchical Listing

There are over 17,000 postable terms and nearly 4,000 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary and Volume 3 - Definitions