Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “geodesics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

G2Aero (Separable shape tensors for aerodynamic design) [SWR-22-44]

G2Aero is a flexible and practical tool for design and deformation of 2D airfoils and 3D blades using data-driven approaches. G2Aero utilizes the geometry of matrix manifolds—specifically the Grassmannian—to build a novel framework for representing physics-based separable deformations of shapes. G2Aero offers the flexibility to generate perturbations in a customizable way over any portion of the blade. The G2Aero framework utilizes data-driven methods based on a curated database of physically relevant airfoils. Specific tools include: - principal geodesic analysis over normal coordinate neighborhoods of matrix manifolds; - a variety of data-regularized deformations to nominal 2D airfoil shapes; - Riemannian interpolation connecting a sequence of airfoil cross-sections to build 3D blades from 2D data; - consistent perturbations over the span of interpolated 3D blades based on dominant modes from the data-driven analysis.

Doronina, Olga↗
DOE OSTI2026

FOILPOLARS (Grassmannian Foil Shape Sweeps for Polar Generation) [SWR-26-095]

FOILPOLARS (Grassmannian Foil Shape Sweeps for Polar Generation): Multifidelity aerodynamic polar data generation for hydrofoil/tidal-turbine airfoil sections. Foilpolars ties together three pieces: *AeroSandbox supplies the baseline airfoil coordinates (UIUC database). *G2Aero parameterizes those shapes on a Grassmannian manifold (Karcher mean + PGA basis) and samples new perturbed shapes around that basis. *XFoil (panel method) and NeuralFoil (neural-network surrogate, shipped with AeroSandbox) each solve the resulting shapes for lift, drag, moment, and pressure at the swept angles of attack, Reynolds numbers, and n_crit values. Design optimization of foil shapes in a computationally efficient way requires polars data across many candidate shapes, not just a handful of baseline foils. However, high-fidelity CFD at that scale is too costly, and naive shape perturbation strays from realistic geometries. FOILPOLARS addresses this by loading baseline airfoils (via AeroSandbox) and mapping them onto a Grassmannian manifold (via G2Aero), computing a Karcher mean and principal geodesic analysis (PGA) basis. New shapes are sampled by perturbing PGA coefficients, keeping them close to the manifold of realistic foils. Each sampled shape is evaluated across a configurable sweep of angle of attack, Reynolds number, and critical amplification factor using two solvers: XFoil (panel method) and NeuralFoil (neural-network surrogate), producing a paired dataset of lift, drag, moment, pressure, convergence, and confidence, indexed alongside each shape's PGA coefficients and shared Grassmannian basis in a single xarray dataset. From this, FOILPOLARS produces convergence summaries and comparison plots per shape, Reynolds number, and n_crit. A command-line interface exposes each pipeline stage independently, supporting data-driven design, optimization, and machine-learning workflows for foils.

Sandhu, Rimple [National Laboratory of the Rockies↗
DOE OSTI2020

Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus

For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules’ diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Twistor space origins of the Newman-Penrose map

Recently, we introduced the “Newman-Penrose map”, a novel correspondence between a certain class of solutions of Einstein’s equations and self-dual solutions of the vacuum Maxwell equations, which we showed was closely related to the classical double copy. Here, we give an alternative definition of this correspondence in terms of quantities that are defined naturally on twistor space, and a shear-free null geodesic congruence on Minkowski space whose twistorial character is articulated by the Kerr theorem. The advantage of this reformulation is that it is purely geometrical in nature, being manifestly invariant under both spacetime diffeomorphisms and projective transformations on twistor space. While the original formulation of the map may be more convenient for most explicit calculations, the twistorial formulation we present here may be of greater theoretical utility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fast Particle-Wave Interactions and Alfvén Eigenmodes in JET Tokamak Plasmas

This document serves as the closeout report of DOE Grant Award No. DE-FG02-99ER54563 with project period 1 April 2015 through 31 March 2020. The project comprised the international collaboration between MIT and EU scientists on the JET facility to improve our understanding of the physics of energetic particle-wave interactions by measuring the damping rates of stable Alfvén Eigenmodes (AEs) and unstable energetic particle driven modes. More specifically, this project involved the continued participation of MIT, the Culham Centre for Fusion Energy, the Swiss Plasma Center, and theorists from various European laboratories and from UC Irvine. Past contributions from the University of São Paulo are gratefully acknowledged. The Alfvén Eigenmode Active Diagnostic (AEAD) on JET discharges was successfully upgraded in this period and has extracted physically useful information, in primarily deuterium plasma discharges. It is expected that such experiments would be continued during the DT campaign in CY 2021 to assess the damping rates of similar modes in the presence of alpha particles, a product of fusing burning plasma. Only JET would carry out such experiments in the near term in the world. It is important to note that this collaboration was continued under DOE Grant Award No. DE-SC0014264 from 1 April 2020 through the present. In this grant period, the AEAD was upgraded with a set of individual amplifiers for each of a set of six antennas in two toroidally opposite locations. These new amplifiers allowed targeted selection of the antennas’ toroidal spectrum for AEs of interest with toroidal mode number | n | ≤ 20. The resonant detection and measurement of the damping rates of AEs was obtained from magnetic probes that could be compared with theory and simulations. This is a key topic of investigation for ITER and all other next-step fusion experiments, where such modes will interact with energetic particles produced by fusion reactions (alpha particles), Neutral Beam Injection (NBI) and Ion Cyclotron Resonance Heating (ICRH). The majority of the observations during this period were of Toroidal Alfvén Eigenmodes (TAEs) as these are most commonly observed on JET; a number of measurements were made during dedicated TAE experiments. However, a new set of lower frequency band filters were procured with the goal of studying Geodesic Acoustic Modes (GAMs), Beta (Acoustic) AEs (BAE/BAAEs), and Reverse Shear AEs (RSAEs), also predicted by theory. Commissioning and optimizations were successfully completed in this period, and the diagnostic has been in operation during the more recent JET campaigns. Initial results have been obtained in dedicated TAE experiments and successfully compared to drift-kinetic theory. A wide range of theoretical studies have been undertaken in support of the upcoming JET campaigns experiments. To supplement the ongoing use of ideal MHD codes, such as MISHKA during the studies of TAEs, gyrokinetic simulations of low frequency AEs were performed in collaboration with UC Irvine. The Gyrokinetic Toroidal Code (GTC) was used to determine the structure, frequencies and stability of AEs in JET plasmas. Thus, a solid scientific foundation has been laid for future DT campaigns in JET in the 2021 operation period when the damping rates of relevant modes in the presence of alpha particles could be assessed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

The Fermilab Holometer: A program to measure Planck scale indeterminacy

We propose an experiment at Fermilab to study a conjectured effect called "holographic noise" that may arise from new Planck scale physics: the measured positions of bodies may wander randomly from ideal geodesics of classical relativity, in measurement-dependent directions, by about a Planck length per Planck time. The experiment will search for this holographic jitter in the relation of mass-energy and space-time by looking for correlated phase noise between two neighboring 40 meter interferometers. The goal of the experiment is to provide convincing evidence for or against the hypothesis that relative transverse positions of bodies display this particular new kind of quantum noise, whose power spectrum is independent of frequency and has a spectral density determined only by the Planck time. A positive result of the experiment would be a major step forward in understanding the emergence of space time and mass-energy from a unified theory of spacetime and quantum mechanics. A negative result will impact the macroscopic interpretation of unified theories.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Higher-Order Corrections to Optimisers based on Newton's Method

The Newton, Gauss–Newton and Levenberg–Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some directions than others and the space of possible improvement in sum of squares becomes a long narrow ellipsoid in the linear model. This means that even a small amount of nonlinearity in the problem parameters can cause a proposed point far down the long axis of the ellipsoid to fall outside of the actual curved valley of improved values, even though it is quite nearby. This paper presents a differential equation that ‘follows’ these valleys, based on the technique of geodesic acceleration, which itself provides a 2 nd order improvement to the Levenberg–Marquardt iteration step. Higher derivatives of this equation are computed that allow n th order improvements to the optimisation methods to be derived. These higher-order accelerated methods up to 4 th order are tested numerically and shown to provide substantial reduction of both number of steps and computation time.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Aerodynamic Sensitivities over Separable Shape Tensors

Here, we present a comprehensive aerodynamic sensitivity analysis of airfoil parameterization informed by separable shape tensors. This parameterization approach uniquely benefits the design process by isolating various well-studied shape characteristics, such as airfoil thickness, and providing a well-regulated low-dimensional parameter domain for aerodynamic designs. Exploring the aerodynamic sensitivities of this novel parameterization can provide valuable insights for more robust designs and future manufacturing efforts. We construct a data-driven parameter space of airfoils using principal geodesic analysis of separable shape tensors informed by a curated database containing almost 20,000 suitable engineering airfoils. Analyzing the shape reconstruction error and the maximum mean discrepancy between joint distributions of aerodynamic quantities, we study the dimensionality of the learned parameter space. This simple numerical experiment demonstrates a dramatic dimension reduction that retains design effectiveness and promotes regularity of the shape representations. Finally, we generate new airfoils and use the HAM2D Reynolds-averaged Navier–Stokes solver to predict lift, drag, and moment coefficients. We compute multiple sensitivity metrics to quantify and assert the consistency of parameter influence on the aerodynamic quantities. We also explore low-dimensional polynomial ridge approximations to motivate physical intuitions and offer explanations of the approximated sensitivities.

17 WIND ENERGY↗
DOE OSTI2024

G2Aero Database of Airfoils - Curated Airfoils

This dataset contains a curated set of 19,164 airfoil shapes from various applications and the data-driven design space of separable shape tensors (PGA space), which can be used as a parameter space for machine-learning applications focused on airfoil shapes. We constructed the airfoil dataset in two main stages. First, we identified 13 baseline airfoils from the NREL 5MW and IEA 15MW reference wind turbines. We reparameterized these shapes using least-squares fits of 8-order CST parametrizations, which involve 18 coefficients. By uniformly perturbing all 18 CST coefficients by +/-20% around each baseline airfoil, we generated 1,000 unique airfoils. Each airfoil was sampled with 1,001 shape landmarks whose x-coordinates followed a cosine distribution along the chord. This process resulted in a total of 13,000 airfoil shapes, each with 1,001 landmarks. In the second phase, we gathered additional airfoils from the extensive BigFoil database, which consolidates data from sources such as the University of Illinois Urbana-Champaign (UIUC) airfoil database, the JavaFoil database, the NACA-TR-824 database, and others. We undertook a thorough pre-processing step to filter out shapes with sparse, noisy, or incomplete data. We also removed airfoils with sharp leading edge and those exceeding our threshold for trailing edge thickness. Additionally, we thinned out the collection of NACA airfoils-- parametric sweeps of NACA airfoils with increasing thickness and camber present in BigFoil database-- by selecting every fourth step in the parameter sweeps. Finally, we regularized the airfoils by reparametrizing them with an 8-order CST parametrization (with 1,001 shape landmarks with x coordinated following cosine distribution along the chord) and removing airfoils with high reconstruction errors. This data pre-processing resulted in a set of 6,164 airfoils. In total, our curated airfoil dataset comprises 19,164 airfoils, each with 1,001 landmarks, and is stored in the curated_airfoils.npz file. Using this curated airfoil dataset, we utilized the separable shape tensors framework to develop a data-driven parameterization of airfoils based on principal geodesic analysis (PGA) of separable shape tensors. This PGA space is provided in PGAspace.npz file.

airfoils↗
DOE OSTI2026

Structure–Property Relationships of Recycled Lithium-Ion Battery Cathodes: Microstructure Optimization Using Virtual Materials Testing

The increasing demand for sustainable battery technologies requires effective recycling strategies for end-of-life lithium-ion battery cathodes. In this study, virtual materials testing, a well-established framework for modeling conventionally manufactured NMC-based cathodes, is applied to partially recycled cathodes. To this end, virtual cathodes consisting of mixtures of pristine and recycled NMC particles are utilized to systematically analyze structure–property relationships depending on mixing ratios and different spatial arrangement strategies. For this purpose, a stochastic 3D model is developed that is capable of generating virtual cathodes with arbitrary volume fractions of active materials and mixing ratios of pristine and recycled NMC particles. Particularly, the stochastic 3D model can mimic the different size distributions of pristine and recycled particles that are observed in image data. Additionally, the model allows the structuring of pristine and recycled NMC either uniformly mixed or layer-wise arranged, mimicking single- and dual-layer cathodes. Subsequently, a systematic computational analysis is conducted to assess the influence of increasing active material ratios of recycled particles, ranging from 0 % to 100 %, while maintaining a constant overall active material volume fraction. The impact of particle mixing on cathode performance is evaluated by examining transport-relevant geometrical descriptors and effective properties, such as geodesic tortuosity, specific surface area, and tortuosity factor.

25 ENERGY STORAGE↗
DOE OSTI2020

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

In this work, we present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress–energy tensor is evolved in flux-conservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Furthermore, radiation four-forces are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency-dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that Method of Characteristics Moment Closure converges at least as ~N -1 , rather than the canonical Monte Carlo N -1/2 , where N is the number of samples per zone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The Multipolar Magnetic Field of the Millisecond Pulsar PSR J0030+0451

Modeling of the NICER X-ray waveform of the pulsar PSR J0030+0451, aimed at constraining the neutron star mass and radius, has inferred surface hot spots (the magnetic polar caps) that imply significantly nondipolar magnetic fields. To this end, we investigate magnetic field configurations that comprise offset dipole-plus-quadrupole components using a static vacuum field and force-free global magnetosphere models. Taking into account the compactness and observer angle values provided by Miller et al. and Riley et al., we compute geodesics from the observer plane to the polar caps to compute the resulting X-ray light curve. We explore, through Markov Chain Monte Carlo techniques, the detailed magnetic field configurations that can reproduce the observed X-ray light curve and have discovered degeneracies, i.e., diverse field configurations, which can provide sufficient descriptions of the NICER X-ray waveforms. Having obtained the force-free field structures, we then compute the corresponding synchronous γ-ray light curves following Kalapotharakos et al.; these we compare to those obtained by Fermi-LAT, to provide models consistent with both the X-ray and the γ-ray data, thereby restricting further the multipole field parameters. An essential aspect of this approach is the proper computation of the relative phase between the synchronous X- and γ-ray light curves. We conclude with a discussion of the broader implications of our study.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The Polarized Image of a Synchrotron-emitting Ring of Gas Orbiting a Black Hole

Synchrotron radiation from hot gas near a black hole results in a polarized image. The image polarization is determined by effects including the orientation of the magnetic field in the emitting region, relativistic motion of the gas, strong gravitational lensing by the black hole, and parallel transport in the curved spacetime. We explore these effects using a simple model of an axisymmetric, equatorial accretion disk around a Schwarzschild black hole. By using an approximate expression for the null geodesics derived by Beloborodov and conservation of the Walker–Penrose constant, we provide analytic estimates for the image polarization. We test this model using currently favored general relativistic magnetohydrodynamic simulations of M87*, using ring parameters given by the simulations. For a subset of these with modest Faraday effects, we show that the ring model broadly reproduces the polarimetric image morphology. Our model also predicts the polarization evolution for compact flaring regions, such as those observed from Sgr A* with GRAVITY. With suitably chosen parameters, our simple model can reproduce the EVPA pattern and relative polarized intensity in Event Horizon Telescope images of M87*. Under the physically motivated assumption that the magnetic field trails the fluid velocity, this comparison is consistent with the clockwise rotation inferred from total intensity images.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

An Extension of the Athena++ Code Framework for Radiation-magnetohydrodynamics in General Relativity Using a Finite-solid-angle Discretization

We extend the general-relativistic magnetohydrodynamics (GRMHD) capabilities of Athena++ to incorporate radiation. The intensity field in each finite-volume cell is discretized in angle, with explicit transport in both space and angle properly accounting for the effects of gravity on null geodesics, and with matter and radiation coupled in a locally implicit fashion. Here we describe the numerical procedure in detail, verifying its correctness with a suite of tests. Motivated in particular by black hole accretion in the high-accretion-rate, thin-disk regime, we demonstrate the application of the method to this problem. With excellent scaling on flagship computing clusters, the port of the algorithm to the GPU-enabled AthenaK code now allows the simulation of many previously intractable radiation-GRMHD systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

QCD–Gravity Double Copy in Regge Asymptotics: From \(2\rightarrow n\) Amplitudes to Radiation in Shockwave Collisions

This paper discusses multi-particle production in QCD and in gravity at ultrarelativistic energies, their double-copy relations, and strong parallels in emergent shockwave dynamics. Dispersive techniques are applied to derive the BFKL equation for multi-gluon production in Regge asymptotics. Identical methods apply in gravity and are captured by a gravitational Lipatov equation. The building blocks in both cases are Lipatov vertices and reggeized propagators satisfying double-copy relations; in gravity, Weinberg’s soft theorem is recovered as a limit of the Lipatov framework. BFKL evolution in QCD generates wee parton states of maximal occupancy characterized by an emergent semi-hard saturation scale. Renormalization group equations in the Color Glass Condensate (CGC) EFT describe wee parton correlations and their rapidity evolution. A shockwave picture of deeply inelastic scattering and hadron–hadron collisions follows, with multi-particle production described by Cutkosky’s rules in strong time-dependent fields. Gluon radiation in the CGC EFT has a double copy in gravitational shockwave collisions, with a similar correspondence applicable between gluon and graviton shockwave propagators. Possible extensions of this semi-classical double copy are outlined for computing multi-particle production in gravitational shockwave collisions, self-force and tidal contributions, and classical and quantum noise in the focusing of geodesics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Cosmological Consequences of Unconstrained Gravity and Electromagnetism

Motivated by the quantum description of gauge theories, we study the cosmological effects of relaxing the Hamiltonian and momentum constraints in general relativity and Gauss' law in electromagnetism. We show that the unconstrained theories have new source terms that mimic a pressureless dust and a charge density that only follows geodesics. The source terms may be the simplest explanation for dark matter and generically predict a charged component. We comment that discovery of such terms would rule out inflation and be a direct probe of the initial conditions of the universe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Mechanical coupling in the nitrogenase complex

The enzyme nitrogenase reduces dinitrogen to ammonia utilizing electrons, protons, and energy obtained from the hydrolysis of ATP. Mo-dependent nitrogenase is a symmetric dimer, with each half comprising an ATP-dependent reductase, termed the Fe Protein, and a catalytic protein, known as the MoFe protein, which hosts the electron transfer P-cluster and the active-site metal cofactor (FeMo-co). A series of synchronized events for the electron transfer have been characterized experimentally, in which electron delivery is coupled to nucleotide hydrolysis and regulated by an intricate allosteric network. We report a graph theory analysis of the mechanical coupling in the nitrogenase complex as a key step to understanding the dynamics of allosteric regulation of nitrogen reduction. This analysis shows that regions near the active sites undergo large-scale, large-amplitude correlated motions that enable communications within each half and between the two halves of the complex. Computational predictions of mechanically regions were validated against an analysis of the solution phase dynamics of the nitrogenase complex via hydrogen-deuterium exchange. These regions include the P-loops and the switch regions in the Fe proteins, the loop containing the residue β-188Ser adjacent to the P-cluster in the MoFe protein, and the residues near the protein-protein interface. In particular, it is found that: (i) within each Fe protein, the switch regions I and II are coupled to the [4Fe-4S] cluster; (ii) within each half of the complex, the switch regions I and II are coupled to the loop containing β-188Ser; (iii) between the two halves of the complex, the regions near the nucleotide binding pockets of the two Fe proteins (in particular the P-loops, located over 130 Å apart) are also mechanically coupled. Notably, we found that residues next to the P-cluster (in particular the loop containing β-188Ser) are important for communication between the two halves.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Grassmannian Shape Representations for Aerodynamic Applications: Preprint

Airfoil shape design is a classical problem in engineering, science, and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, shifting). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.

blade representation↗