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Results for “differential geometry”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Nonperturbative negative geometries: amplitudes at strong coupling and the amplituhedron

The amplituhedron determines scattering amplitudes in planar N = 4 super Yang-Mills by a single “positive geometry” in the space of kinematic and loop variables. We study a closely related definition of the amplituhedron for the simplest case of four-particle scattering, given as a sum over complementary “negative geometries”, which provides a natural geometric understanding of the exponentiation of infrared (IR) divergences, as well as a new geometric definition of an IR finite observable F(g, z) — dually interpreted as the expectation value of the null polygonal Wilson loop with a single Lagrangian insertion — which is directly determined by these negative geometries. This provides a long-sought direct link between canonical forms for positive (negative) geometries, and a completely IR finite post-loop-integration observable depending on a single kinematical variable z, from which the cusp anomalous dimension Γ cusp (g) can also be straightforwardly obtained. We study an especially simple class of negative geometries at all loop orders, associated with a “tree” structure in the negativity conditions, for which the contributions to F(g, z) and Γ cusp can easily be determined by an interesting non-linear differential equation immediately following from the combinatorics of negative geometries. This lets us compute these “tree” contributions to F(g, z) and Γ cusp for all values of the ‘t Hooft coupling. The result for Γ cusp remarkably shares all main qualitative characteristics of the known exact results obtained using integrability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Can we detect the stellar differential rotation of WASP-7 through the Rossiter–McLaughlin observations?

ABSTRACT The Rossiter–McLaughlin (RM) effect is the radial velocity signal generated when an object transits a rotating star. Stars rotate differentially and this affects the shape and amplitude of this signal, on a level that can no longer be ignored with precise spectrographs. Highly misaligned planets provide a unique opportunity to probe stellar differential rotation via the RM effect, as they cross several stellar latitudes. In this sense, WASP-7, and its hot Jupiter with a projected misalignment of ∼90°, is one of the most promising targets. The aim of this work is to understand if the stellar differential rotation is measurable through the RM signal for systems with a geometry similar to WASP-7. In this sense, we use a modified version of soap3.0 to explore the main hurdles that prevented the precise determination of the differential rotation of WASP-7. We also investigate whether the adoption of the next generation spectrographs, like ESPRESSO, would solve these issues. Additionally, we assess how instrumental and stellar noise influence this effect and the derived geometry of the system. We found that, for WASP-7, the white noise represents an important hurdle in the detection of the stellar differential rotation, and that a precision of at least 2 m s−1 or better is essential.

Serrano, L. M.↗
NASA NTRS1973

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

Gyekenyesi, J. P.↗
NASA NTRS1972

On the dependence of information display quality requirements upon human characteristics and pilot/automatics relations

Present information display concepts for pilot landing guidance are outlined considering manual control as well as substitution of man by fully competent automatics. Display improvements are achieved by compressing the distributed indicators into an accumulative display and thus reducing information scanning. Complete integration of quantitative indications, outer loop information, and real world display in a pictorial information channel geometry constitutes an interface with human ability to differentiate and integrate for optimal manual control of the aircraft.

Wilckens, V.↗
NASA NTRS1975

Fluid manifold design for a solar energy storage tank

A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

Humphries, W. R.↗
NASA NTRS1980

Flow Induced Spring Coefficients of Labyrinth Seals for Application in Rotor Dynamics

Flow induced aerodynamic spring coefficients of labyrinth seals are discussed and the restoring force in the deflection plane of the rotor and the lateral force acting perpendicularly to it are also considered. The effects of operational conditions on the spring characteristics of these components are examined, such as differential pressure, speed, inlet flow conditions, and the geometry of the labyrinth seals. Estimation formulas for the lateral forces due to shaft rotation and inlet swirl, which are developed through experiments, are presented. The utilization of the investigations is explained and results of stability calculations, especially for high pressure centrifugal compressors, are added. Suggestions are made concerning the avoidance of exciting forces in labyrinths.

Benckert, H.↗
NASA NTRS2000

X-Ray Line Spectroscopy of Massive X-Ray Binaries

Spectra from ASCA have provided the most, detailed view to date of the X-ray spectral properties of stellar winds in massive X-ray binaries. Using detailed atomic models that account for recombination cascade kinetics, we have reexamined archival data from Vela X-1 and Cen X-3 in the context of simple models of their wind geometries and velocity distributions. Our approach emphasizes apparent differential emission measure (DEM) distributions, and their dependence on orbital phase and wind parameters. A grid of theoretical DEM distributions is used to generate model spectra, which are compared to the data. We obtain good fits, and derive constraints oil the stellar wind parameters. We provide a summary of the method, and show that, even though the companion stars in Vela X-1 and Cen X-3 have comparable mass-loss rates, the winds in these two systems are dramatically different, in character.

Liedahl, D. A.↗
DOE OSTI2020

Logarithmic forms and differential equations for Feynman integrals

We describe in detail how a d log representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov [1] that reappeared in the context of Feynman integrals in [2–4]. The d log representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Bootstrapping closed string field theory

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of n zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1986

Observations of far-infrared line profiles in the Orion-KL region

Measurements of several far-infrared emission line profiles in the Orion-KL region are reported. The emission from the CO, OH, and forbidden O I emission lines toward the BN-KL and H2 peak 1 positions probably comes from dense, hot molecular gas in the Orion-KL shock. The CO and forbidden O I lines have similar profiles, suggesting that the high-velocity forbidden O I emission also arises in magnetohydrodynamic 'cloud' shocks. The velocity centroids of the lines are somewhat blueshifted. The far-infrared data thus support the interpretation that the blue asymmetry of the H2 2 micron lines is not mainly due to differential dust extinction, but rather to the kinematics and geometry of the shocked gas in the Orion-KL outflow. The forbidden O I and CO lines, however, have significantly less extreme blueshifted emission than the H2 lines. Both the forbidden O I 63 micron and forbidden C II 158 micron lines have features strongly supporting a common origin near the surface of the Orion molecular cloud.

Crawford, M. K.↗
DOE OSTI2022

Tailoring Corrosion Resistance of Additively Manufactured Metals with Atomic Layer Deposition

The goal of this work is to develop a scalable post-manufacturing capability at LANL that utilizes atomic layer deposition (ALD) for corrosion-resistant coatings onto additively manufactured (AM) metals. This will provide fundamentally new and essential capabilities towards the interchangeability of AM metals with traditionally wrought or machined material. This will be accomplished by (1) formulating novel ALD precursor doses and film thicknesses onto as-printed coupons of AM metals and (2) providing electrochemical characterization of corrosion susceptibility as a function of deposited film thickness. While ALD is well-established, the unique aspect (risk) of this work is application to rough AM surfaces. This risk is mitigated by repeating ALD deposition cycles, where thicker coatings laterally branch, resulting in a uniform coating. This risk will be assessed in the phase 1 feasibility study, wherein the application of ALD coatings to small AM coupon surfaces will be demonstrated using existing hardware and characterization tools at Sigma. This study alone will provide ground-breaking insight on the compatibility of ALD coating techniques with AM metals. Going beyond the phase 1 study, a standalone deposition chamber will be built, so full AM components can be coated and tested. While this MFR investment is focused on corrosion mitigation, it is critical to highlight external benefits of this technique outside the scope of this proposed study. ALD has extraordinary universality, whereby almost any material can be given almost any coating or graded density coating with atomic precision; and, the only limiting factors to scalability is the size of the dosing chamber. The self-limiting reactions intrinsic to ALD offers high conformity to part geometry and tolerance, even for internal surfaces where electroplating or conventional chemical vapor deposition falls short due to differential diffusion. This uniquely positions ALD at the forefront of post-manufacturing strategies for AM components, especially for those with complex geometry and internal surfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.

1D2V↗
DOE OSTI2021

CARDINAL

Cardinal is a code that automates the workflow for iteratively solving neutral particle transport via the OpenMC code and computational fluid dynamics via the NekRS code within the Multiphysics Object Oriented Simulation Environment (MOOSE), a finite element framework for solving general partial differential equations. Cardinal establishes a mapping between the Monte Carlo geometry representation used in OpenMC and the spectral element mesh used in NekRS to other physics applications built upon the MOOSE framework, allowing high-resolution particle transport and fluid dynamics physics feedback to the MOOSE application ecosystem. Heat generation rates as solved by OpenMC are used as heat sources in MOOSE, while the temperature and density fields from NekRS are used as conjugate heat transfer boundary conditions and/or source fields in MOOSE. OpenMC, Nek5000, and MOOSE are open source, community-developed simulation codes.

NOVAK, APRILJEAN RODGERS↗
DOE OSTI2025

Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials: Part II Resveratrol Exemplar

This SAND report summarizes work supported by an Engineering Sciences Research Foundation (ESRF) Lab Directed Research and Development (LDRD) project entitled “Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials.” This SAND report is written in two parts with Part 1 discusses recrystallization of our explosive exemplar and Part 2 summarizing our work with recrystallization of resveratrol. We have studied resveratrol recrystallization with a multiscale approach combining experiments, modeling and simulation. At the single crystal scale, microscopy experiments illuminate crystal time-dependent growth rates using advanced image analysis. Bench scale experiments were carried out to look at growth of multiple particles in a small reactor creating thousands of particles and analyzing the results with microscopy and μCT. For the modeling we combine kinetic Monte Carlo (kMC) models with subscale information from density functional theory (DFT) or molecular dynamics. This work is discussed in Part 1 and can also be found in a paper from the project discussing a coarse-grained kMC model specifically developed for resveratrol. For well-mixed systems, we have population balance equations (PBE) linked with species mass conservation forming a set of ordinary differential equations that can be solved quickly. For more complicated geometries, such as the vat crystallization used throughout the complex, a coupled computational fluid dynamic (CFD)/PBE method was developed to account for gradients in temperature and concentration and differences in crystallization rates throughout the domain. These simulations are more complex and require high performance computing. We present results for two cases: 5% seed fast cool with parameters fit to the well-mixed case and 5% seed slow cool using the same parameters. We show reasonable agreement with experiments though are particles are significantly larger than the experiments.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Dynamics of Diffusion Flames in von Karman Swirling Flows Studied

Von Karman swirling flow is generated by the viscous pumping action of a solid disk spinning in a quiescent fluid media. When this spinning disk is ignited in an oxidizing environment, a flat diffusion flame is established adjacent to the disk, embedded in the boundary layer (see the preceding illustration). For this geometry, the conservation equations reduce to a system of ordinary differential equations, enabling researchers to carry out detailed theoretical models to study the effects of varying strain on the dynamics of diffusion flames. Experimentally, the spinning disk burner provides an ideal configuration to precisely control the strain rates over a wide range. Our original motivation at the NASA Glenn Research Center to study these flames arose from a need to understand the flammability characteristics of solid fuels in microgravity where slow, subbuoyant flows can exist, producing very small strain rates. In a recent work (ref. 1), we showed that the flammability boundaries are wider and the minimum oxygen index (below which flames cannot be sustained) is lower for the von Karman flow configuration in comparison to a stagnation-point flow. Adding a small forced convection to the swirling flow pushes the flame into regions of higher strain and, thereby, decreases the range of flammable strain rates. Experiments using downward facing, polymethylmethacrylate (PMMA) disks spinning in air revealed that, close to the extinction boundaries, the flat diffusion flame breaks up into rotating spiral flames (refs. 2 and 3). Remarkably, the dynamics of these spiral flame edges exhibit a number of similarities to spirals observed in biological systems, such as the electric pulses in cardiac muscles and the aggregation of slime-mold amoeba. The tail of the spiral rotates rigidly while the tip executes a compound, meandering motion sometimes observed in Belousov-Zhabotinskii reactions.

Nayagam, Vedha↗
NASA NTRSDate not supplied

Aviary: An Open-Source Multidisciplinary Design, Analysis, and Optimization Tool for Modeling Aircraft with Analytic Gradients

In recent years demands on aircraft design methods have begun to require higher degrees of coupling between disciplines and optimization in order to satisfy competing objectives involving large numbers of design parameters that define unconventional configurations. These expanding requirements have amplified a need for new and improved aircraft design, analysis, and optimization codes that are capable of performing coupled design and exploiting analytic gradients to perform gradient-based optimization where possible. To address this need, a new multidisciplinary design optimization and analysis tool called Aviary is presented. This tool, built on OpenMDAO, allows for tightly coupled, simultaneous aircraft and subsystem design using analytic gradients. Aviary includes methods from two NASA developed legacy aircraft analysis tools and provides native analytically differentiated calculations for five different disciplines (weights and sizing, aerodynamics, geometry, propulsion, and mission analysis), while also allowing external discipline analysis tools to be coupled, regardless of whether those tools can provide analytic gradients. Verification and preliminary examples and modeling efforts show Aviary’s ability to effectively model novel concepts and explore large and non-intuitive design spaces. Additionally, a multi-level user interface in Aviary creates an easy entry point for users with any level of multidisciplinary design, analysis, and optimization experience.

optimization↗
DOE OSTI2024

Cu site differentiation in tetracopper(I) sulfide clusters enables biomimetic N 2 O reduction

Copper clusters feature prominently in both metalloenzymes and synthetic nanoclusters that mediate catalytic redox transformations of gaseous small molecules. Such reactions are critical to biological energy conversion and are expected to be crucial parts of renewable energy economies. However, the precise roles of individual metal atoms within clusters are difficult to elucidate, particularly for cluster systems that are dynamic under operating conditions. Here, we present a metal site-specific analysis of synthetic Cu 4 (μ 4 -S) clusters that mimic the Cu Z active site of the nitrous oxide reductase enzyme. Leveraging the ability to obtain structural snapshots of both inactive and active forms of the synthetic model system, we analyzed both states using resonant X-ray diffraction anomalous fine structure (DAFS), a technique that enables X-ray absorption profiles of individual metal sites within a cluster to be extracted independently. Using DAFS, we found that a change in cluster geometry between the inactive and active states is correlated to Cu site differentiation that is presumably required for efficient activation of N 2 O gas. More precisely, we hypothesize that the Cu δ+ ∙∙∙Cu δ- pairs produced upon site differentiation are poised for N 2 O activation, as supported by computational modeling. These results provide an unprecedented level of detail on the roles of individual metal sites within the synthetic cluster system and how those roles interplay with cluster geometry to impact the reactivity function. We expect this fundamental knowledge to inform understanding of metal clusters in settings ranging from (bio)molecular to nanocluster to extended solid systems involved in energy conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Toward Improved Charge Separation through Conformational Control in Copper Coordination Complexes

The continued development of solar energy as a renewable resource necessitates the design and study of new approaches to sustaining photodriven charge separation (CS). To this end, we present a bioinspired approach in which triggered conformational changes are used to control electron transfer (ET) events. We report, photo-induced conformational rearrangements of a ligand are translated into changes in the coordination geometry and environment about a bound metal ion. Taking advantage of the differential coordination properties of Cu I and Cu II , these dynamics facilitate intramolecular ET from Cu I to the ligand to create a CS state. The synthesis and photophysical characterization of CuCl(dpaa R ) (dpaa = dipicolylaminoacetophenone, with R = H and OMe) is presented. These ligands incorporate a fluorophore into their framework that gives rise to a twisted intramolecular charge transfer (TICT) excited state. Excited state ligand twisting provides a tetragonal coordination geometry capable of capturing Cu II in the CS state when an internal ortho-OMe binding site is present (as in dpaaOMe). We employ NMR, IR, EPR, and optical spectroscopies, X-ray diffraction, and electrochemical methods to establish the ground state properties of the Cu I and Cu II complexes. We then investigate the photophysical dynamics of these Cu I complexes via time-resolved photoluminescence (TR-PL), and optical transient absorption (OTA) spectroscopies. We show that relative to controls lacking a TICT-active ligand, the lifetime of the CS state is enhanced ~1000-fold. Further, the presence of the ortho-OMe substituent greatly enhances the lifetime of the TICT* state and biases the coordination environment toward Cu II . The presence of Cu I decreases photoinduced degradation from 14 to <2% but does not result in significant quenching via ET. Factors affecting CS in these systems are discussed, laying the groundwork for our strategy toward solar energy conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗