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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Study on Intelligent Compaction-Equipment Logistics Scheduling and Propagation Characteristics of Vibration Wave in Nonlinear Systems with Multistability Based on Field Test

The equipment scheduling and propagation characteristics of vibration wave from vibratory roller ⟶ filling material nonlinear systems with multistability are the core problems of subgrade intelligent construction technology, and the logistics scheduling of the equipment is directly related to the construction efficiency. Aiming at the shortages, one typical subgrade located at the Gu’an station of Beijing-Xiong’an city railway is selected to research and finish the field tests; some findings are shown as follows: first, some valuable suggestions about the logistics scheduling of intelligent equipment are proposed, which can break the barriers between the organizations and improve construction efficiency; second, when the vibration wave propagates from the vibratory roller ⟶ surface of filling material ⟶ different buried depths of filling material, the peak acceleration of vibration wave gradually decreases and is hyperbolic distribution approximately. At the same time, the sensitive of attenuation is shown as follows: Z R 2 >0.9), and the concrete functional relationship among different amplitudes of harmonics can be summarized as y = Ae −BX ; fourth, the vibration energy is mainly concentrated near 10–30 Hz in the vibratory roller, but when the vibration wave propagates from vibratory roller⟶filling material, the vibration energy gradually decreases with the increase in depth, and the marginal spectrum gradually changes from one peak to two peaks, that is, 30–50 Hz and 50–100 Hz; fifth, the vibration energy in the vibrational wheel is distributed averagely in the compaction process, and the effective compaction time is two seconds, which will be helpful for revealing the propagation characteristics of vibration wave, optimizing the compaction quality control models and providing some support for the development of intelligent compaction theory of railway subgrade.

Han, Yixuan↗
DOE OSTI2022

Crystallography of hyperbolic lattices

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. Here we show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians.

2-dimensional systems↗
DOE OSTI2016

Modification and validation of an analytical source model for external beam radiotherapy Monte Carlo dose calculations

Purpose: A dose calculation tool, which combines the accuracy of the dose planning method (DPM) Monte Carlo code and the versatility of a practical analytical multisource model, which was previously reported has been improved and validated for the Varian 6 and 10 MV linear accelerators (linacs). The calculation tool can be used to calculate doses in advanced clinical application studies. One shortcoming of current clinical trials that report dose from patient plans is the lack of a standardized dose calculation methodology. Because commercial treatment planning systems (TPSs) have their own dose calculation algorithms and the clinical trial participant who uses these systems is responsible for commissioning the beam model, variation exists in the reported calculated dose distributions. Today’s modern linac is manufactured to tight specifications so that variability within a linac model is quite low. The expectation is that a single dose calculation tool for a specific linac model can be used to accurately recalculate dose from patient plans that have been submitted to the clinical trial community from any institution. The calculation tool would provide for a more meaningful outcome analysis. Methods: The analytical source model was described by a primary point source, a secondary extra-focal source, and a contaminant electron source. Off-axis energy softening and fluence effects were also included. The additions of hyperbolic functions have been incorporated into the model to correct for the changes in output and in electron contamination with field size. A multileaf collimator (MLC) model is included to facilitate phantom and patient dose calculations. An offset to the MLC leaf positions was used to correct for the rudimentary assumed primary point source. Results: Dose calculations of the depth dose and profiles for field sizes 4 × 4 to 40 × 40 cm agree with measurement within 2% of the maximum dose or 2 mm distance to agreement (DTA) for 95% of the data points tested. The model was capable of predicting the depth of the maximum dose within 1 mm. Anthropomorphic phantom benchmark testing of modulated and patterned MLCs treatment plans showed agreement to measurement within 3% in target regions using thermoluminescent dosimeters (TLD). Using radiochromic film normalized to TLD, a gamma criteria of 3% of maximum dose and 2 mm DTA was applied with a pass rate of least 85% in the high dose, high gradient, and low dose regions. Finally, recalculations of patient plans using DPM showed good agreement relative to a commercial TPS when comparing dose volume histograms and 2D dose distributions. Conclusions: A unique analytical source model coupled to the dose planning method Monte Carlo dose calculation code has been modified and validated using basic beam data and anthropomorphic phantom measurement. While this tool can be applied in general use for a particular linac model, specifically it was developed to provide a singular methodology to independently assess treatment plan dose distributions from those clinical institutions participating in National Cancer Institute trials.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1973

The starting transient of solid propellant rocket motors with high internal gas velocities

A comprehensive analytical model which considers time and space development of the flow field in solid propellant rocket motors with high volumetric loading density is described. The gas dynamics in the motor chamber is governed by a set of hyperbolic partial differential equations, that are coupled with the ignition and flame spreading events, and with the axial variation of mass addition. The flame spreading rate is calculated by successive heating-to-ignition along the propellant surface. Experimental diagnostic studies have been performed with a rectangular window motor (50 cm grain length, 5 cm burning perimeter and 1 cm hydraulic port diameter), using a controllable head-end gaseous igniter. Tests were conducted with AP composite propellant at port-to-throat area ratios of 2.0, 1.5, 1.2, and 1.06, and head-end pressures from 35 to 70 atm. Calculated pressure transients and flame spreading rates are in very good agreement with those measured in the experimental system.

Peretz, A.↗
DOE OSTI2014

Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium of an internal ring current system

Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium are studied analytically and numerically, where the plasma is confined by only poloidal magnetic field generated by an internal ring current. The plasma current due to finite pressure can be divided into two components; one remains at isotropic pressure and the other arises from pressure anisotropy. When p{sub ⊥}, the pressure perpendicular to the magnetic field, is larger than p{sub ∥}, the pressure parallel to the magnetic field, those two components of plasma current tend to cancel each other to reduce the total amount of plasma current. Equilibrium beta limit is also examined, where the beta is a ratio of the plasma pressure to the magnetic pressure. The equilibrium beta limit decreases as the pressure anisotropy becomes strong. The beta value is strictly limited by ellipticity of the equilibrium equation when p{sub ∥}>p{sub ⊥}. On the other hand, when p{sub ⊥}>p{sub ∥}, although the tendency of the beta limit agrees with the ellipticity condition of the equilibrium equation, equilibria with a hyperbolic region can be obtained by iterative procedure with practically reasonable convergence criteria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. Here, these bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Production terms in relativistic extended thermodynamics of gas with internal structure via a new BGK model

The goal of this paper is to obtain a precise expression for the production tensor in a dissipative hyperbolic relativistic theory of gas with internal structure. For this aim, we use a variant of relativistic BGK model for the Boltzmann–Chernikov kinetic equation. Moreover, we deduce some inequalities for the coefficients requiring the entropy principle and the convexity of entropy density. As a limiting case, the expression of the production tensor in the case of monatomic gas is also evaluated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Tuning Anisotropic Optical Properties of Inorganic and Hybrid Organic–Inorganic MXenes via Topochemical Surface Modification

Surface groups are central to the properties of MXenes, yet their role in optical anisotropy remains largely unexplored. Here, we use a topochemical route to synthesize single crystals of stacked Ti 3 C 2 Cl 2 and hybrid organic–inorganic MXenes (h-MXenes) with lateral sizes of 38–75 μm, rotational registry, and tunable interlayer spacing. Solid-state NMR spectroscopy shows that topochemical substitution generates mixed amido, imido, and hydride surface motifs, which modify the electronic structure of the Ti 3 C 2 inorganic core. Imaging spectroscopic ellipsometry with micron-scale spatial resolution enables reconstruction of the complex dielectric tensor of individual multilayer crystals. Ti 3 C 2 Cl 2 exhibits a type-II hyperbolicity above 930 nm, whereas h-MXenes do not display hyperbolicity within the measured 300–1700 nm window, instead showing reduced in-plane conductivity, suppressed out-of-plane light absorption, and a chain-length-dependent blue shift of a near-infrared absorption feature. These results demonstrate topochemical surface modification as a direct handle for engineering MXenes as surface-programmable optical media.

Hybrid materials↗
DOE OSTI2021

Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. Furthermore, the new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Review on the growth, properties and applications of self-assembled oxide–metal vertically aligned nanocomposite thin films—current and future perspectives

Self-assembled oxide–metal nanocomposite thin films have aroused great research interest owing to their wide range of functionalities, including metamaterials with plasmonic and hyperbolic optical properties, and ferromagnetic, ferroelectric and multiferroic behaviors. Oxide–metal nanocomposites typically self-assemble as metal particles in an oxide matrix or as a vertically aligned nanocomposite (VAN) with metal nanopillars embedded in an oxide matrix. Among them, the VAN architecture is particularly interesting due to the vertical strain control and highly anisotropic structure, enabling the epitaxial growth of materials with large lattice mismatch. In this review, the driving forces behind the formation of self-assembled oxide–metal VAN structures are discussed. Specifically, an updated in-plane strain compensation model based on the areal strain compensation concept has been proposed in this review, inspired by the prior linear strain compensation model. It provides a guideline for material selection for designing VAN systems, especially those involving complex orientation matching relationships. Based on the model, several case studies are discussed, comparing the microstructure and morphology of different oxide–metal nanocomposites by varying the oxide phase. Specific examples highlighting the coupling between the electrical, magnetic and optical properties are also discussed in the context of oxide–metal nanocomposites. Finally, future research directions and needs are also discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Computational Response Theory for Dynamics

Quantifying the sensitivity - how a quantity of interest (QoI) varies with respect to a parameter – and response – the representation of a QoI as a function of a parameter - of a computer model of a parametric dynamical system is an important and challenging problem. Traditional methods fail in this context since sensitive dependence on initial conditions implies that the sensitivity and response of a QoI may be ill-conditioned or not well-defined. If a chaotic model has an ergodic attractor, then ergodic averages of QoIs are well-defined quantities and their sensitivity can be used to characterize model sensitivity. The response theorem gives sufficient conditions such that the local forward sensitivity – the derivative with respect to a given parameter - of an ergodic average of a QoI is well-defined. We describe a method based on ergodic and response theory for computing the sensitivity and response of a given QoI with respect to a given parameter in a chaotic model with an ergodic and hyperbolic attractor. This method does not require computation of ensembles of the model with perturbed parameter values. The method is demonstrated and some of the computations are validated on the Lorenz 63 and Lorenz 96 models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Yee, H. C.↗
NASA NTRS1983

Aerocapture and aeroassisted orbital transfer - A high performance leverage space technology

Single pass aerocapture and aeroassisted orbital transfer designs are discussed for modifying spacecraft orbits using planetary atmospheres. Aerodynamic drag can be used to shift a hyperbolic flyby trajectory to a planetary orbit by having the spacecraft altering its in-plane L/D ratio to maintain constant drag until the desired velocity is attained. The spacecraft would then move out of the atmosphere, sometimes with a small propulsive assist. Sample missions to Uranus, Jupiter, and Titan are mentioned, with mission scenarios commencing with a Shuttle launch. Biconic-shaped spacecraft are cited as having the best L/D for insertion accuracy, a low hypersonic ballistic coefficient, and volumeric efficiency. Aeroassisted orbital transfer involves atmospheric braking in order to shed velocity on a return trip from higher orbits. No decision has yet been made as to the spacecraft shape, but calculations indicate that aeroassist braking before return to LEO for rendezvous with the Shuttle has the potential for the lowest cost/mass to GEO of any delivery system currently under consideration.

Cruz, M. I.↗
NASA NTRS2003

Flow Field Measurement of Mixing Driven by Buoyancy

Mixing driven by buoyancy-induced flows inside a cavity consists of stretching and folding of an interface. Measurement of the flow field using particle imaging velocimetry shows that during stretching the flow field has a single elliptic point, thus dominated by a single vortex. However, global bifurcation that results in folding introduces a hyperbolic point whereby the flow field degenerates to multiple vortex interactions. The short-lived coherent structure observed during mixing which results in the Rayleigh- Taylor morphology is attributed to vortex interactions. The mixing characteristics of non-homogeneous fluids driven by buoyancy are important towards understanding transport phenomenon in a microgravity environment. Mixing consists of stretching and folding of an interface due to a flow field whose intensity depends on the body force. For miscible liquids, the characteristic of the flow field determines whether mass transport is governed by diffusion or bulk stirring which induces mixing. For technologically important processes, transport of mass is governed by the coupling of the body force to scalar gradients such as concentration and or temperature' 2 3 . In order to lend insight into these classes of problems we consider a model experimental system to study mixing driven by buoyancy-induced flows. The characteristics of mixing is addressed from detail measurements of the flow field using particle imaging velocimetry (PIV), and its corresponding interface dynamics using image processing techniques.

Batur, C.↗
NASA NTRSDate not supplied

Rocket Lab Venus - Enabling Low-Cost Interplanetary Missions

Rocket Lab’s mission to Venus [1], launching in January 2025, aims to demonstrate that small launch vehicles, such as Electron, and high-energy small spacecraft, such as Photon, can enable a new paradigm of regular, low-cost interplanetary missions. The Electron launch vehicle will deliver the Photon spacecraft carrying the entry probe into low earth orbit, at which point Photon will take over and put both itself and the attached probe on an Earth-Venus transfer trajectory, with assistance from a Lunar flyby. The primary science objective of the mission is to sample the Venusian cloud layers between atitudes of 45 and 60 km above the surface with an autofluorescing nephelometer. The ~1kg scientific instrument will be carried by a small ~17 kg direct entry probe which will separate from the Photon spacecraft approximately 30 minutes prior to atmospheric entry. The probe outer mould line is a scaled down version of the Deep Space 2 probes [2]. NASA’s newly developed 3D Woven Carbon Phenolic, a derivative of the Heatshield for Extreme Entry Environment Technology (HEEET) material [3], is an enabling technology for this mission, and it will comprise the probe forebody heat shield.The probe will communicate directly back to the Earth during its descent via a small on-board radio frequency (RF) antenna. The hyperbolic Venus encounter will see the probe enter the Venusia atmosphere at approximately 11 km/s with an entry flight path angle (EFPA) of about 10°. This relatively low entry angle was selected to increase the duration of the descent phase, reduce the peak deceleration, and reduce the sensitivity of the nominal entry environments to navigational errors. For reference, the Pioneer Venus probes entered at EFPAs varying from about 25° to 70°, resulting in peak decelerations between around 220 and 450 g’s and peak stagnation point heat fluxes ranging from about 40 to 75 MW/m2 [4]. In comparison, the Rocket Lab Venus probe will experience a lower preak deceleration of around 60 g’s and a lower peak stagnation point heat flux of about 15 MW/m2, at the cost of a greater total heat load and correspondingly higher thermal protection system (TPS) mass fraction. This paper recounts the development history of the TPS for the Rocket Lab Venus probe, with a focus on the unique requirements of the mission. In particular, the effect on the TPS design of the mission’s tight budget, short development timeline, slim mass and RF link margins, and mild but long duration entry heating. Rocket Lab’s initial investigations into a ‘hybrid’ TPS [5] based on a scaled version of the Pioneer Venus full-density carbon phenolic forebody shield, and the abandonment of this approach in favour of NASA’s 3D Woven Carbon Phenolic is presented. Additionally, the leveraging of previous testing under the HEEET project at higher conditions and the associated TPS margining strategy that was adopted to avoid the need for extensive mission-specific arc jet testing is discussed. Finally, this paper concludes with a brief consideration of the feasibility of a future low-cost aerocapture technology demonstrator mission based on the 2025 Rocket Lab Venus mission and entry probe.

Lyle Campbell↗
DOE OSTI2015

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

User's manual for the HYPGEN hyperbolic grid generator and the HGUI graphical user interface

The HYPGEN program is used to generate a 3-D volume grid over a user-supplied single-block surface grid. This is accomplished by solving the 3-D hyperbolic grid generation equations consisting of two orthogonality relations and one cell volume constraint. In this user manual, the required input files and parameters and output files are described. Guidelines on how to select the input parameters are given. Illustrated examples are provided showing a variety of topologies and geometries that can be treated. HYPGEN can be used in stand-alone mode as a batch program or it can be called from within a graphical user interface HGUI that runs on Silicon Graphics workstations. This user manual provides a description of the menus, buttons, sliders, and typein fields in HGUI for users to enter the parameters needed to run HYPGEN. Instructions are given on how to configure the interface to allow HYPGEN to run either locally or on a faster remote machine through the use of shell scripts on UNIX operating systems. The volume grid generated is copied back to the local machine for visualization using a built-in hook to PLOT3D.

Chan, William M.↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗