Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear equations”

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 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Core States of Neutron Stars from Anatomizing Their Scaled Structure Equations

Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass–radius sequence characterized by a maximum mass ${M}_{\mathrm{NS}}^{\max}$ at radius $R$ max . We first show analytically that the ${M}_{\mathrm{NS}}^{\max}$ and $R$ max scale linearly with two different combinations of the NS central pressure $P$ $c$ and energy density $ε$ $c$ , by dissecting perturbatively the dimensionless Tolman–Oppenheimer–Volkoff (TOV) equations governing NS internal variables. The scaling relations are then verified via 87 widely used and rather diverse phenomenological as well as 17 microscopic NS EOSs with/without considering hadron–quark phase transitions and hyperons, by solving numerically the original TOV equations. The EOS of the densest NS matter allowed before it collapses into a black hole is then obtained. Using the universal ${M}_{\mathrm{NS}}^{\max}$ and $R$ max scalings and Neutron Star Interior Composition Explorer and XMM-Newton mass–radius observational data for PSR J0740+6620, a very narrow constraining band on the NS central EOS is extracted directly from the data for the first time, without using any specific input EOS model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

N-particle irreducible actions for stochastic fluids

We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action in one-loop order and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance of n-loop correction with smaller and smaller exponential suppression.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Application of linear prolongation to coarse mesh finite difference acceleration in CASMO5

The Coarse-Mesh Finite Difference (CMFD) method has been used for over a decade to accelerate the convergence of the Method of Characteristics (MOC) solution to the two- dimensional particle transport equation in CASMO5. Numerical testing, along with widespread use in production-level calculations, have shown that the current CMFD implementation provides stability and robustness for a wide range of realistic reactor physics problems. However, the recent development of linear prolongation has attracted attention from the community as a way to further improve the performance and stability of CMFD. Two interpolation methods for linear prolongation are presented in this work and implemented into a test version of CASMO5. The performance of the proposed interpolations, referred to as the bilinear and linear directional schemes, is evaluated in terms of runtime relative to the default constant or uniform scaling update. Numerical results indicate that the use of linear prolongation can reduce the transport solver runtime on average by approximately 10% when tested with two hundred randomly selected cases. The new directional linear interpolation, combined with default constant boundary updates, is found to provide the highest reduction in runtime for the cases analyzed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Gauge invariants of linearized gravity with a general background metric

In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants per se for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. Further, if the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

New Absolute Cavity Pyrgeometer equation by application of Kirchhoff's law and adding a convection term

An equation for the Absolute Cavity Pyrgeometer (ACP) is derived from application of Kirchhoff's law and the addition of a convection term to account for the thermopile being open to the environment, unlike a domed radiometer. The equation is then used to investigate four methods to characterise key instrumental parameters using laboratory and field measurements. The first uses solar irradiance to estimate the thermopile responsivity, the second uses a minimisation method that solves for the thermopile responsivity and transmission of the cavity, and the third and fourth revisit the Reda et al. (2012) linear least squares calibration technique. Data were collected between January and November 2020, when the ACP96 and two IRIS radiometers monitoring terrestrial irradiances were available. The results indicate good agreement with IRIS irradiances using the new equation. The analysis also indicates that while the thermopile responsivity, concentrator transmission and emissivity of an ACP can be determined independently, as an open instrument, the impact of the convection term is minor in steady-state conditions but significant when the base of the instrument is being subjected to rapid artificial cooling or heating. Using laboratory characterisation of the transmission and emissivity, together with use of an estimated solar calibration of the thermopile, generated mean differences of less than 1.5 Wm -2 to the two IRIS radiometers. A minimisation method using each IRIS radiometer as the reference also provided similar results, and the derived thermopile responsivity was within 0.3 µV W -1 m 2 of the solar-calibration-derived infrared responsivity estimate of 10.5 µV W -1 m 2 estimated using a nominal solar calibration and provide irradiances within ±2 % of the terrestrial irradiance measured by the reference pyrgeometers traceable to the International System of Units (SI). The calibration method using linear least squares regression introduced by Reda et al. (2012) that relies on rapid cooling of the ACP base but utilising the new equation was found to produce consistent results but was dependent on the assumed temperature of the air above the thermopile. This study demonstrates the potential of the ACP as another independent reference radiometer for terrestrial irradiance once the magnitude of the convection coefficient and any potential variations in it have been resolved.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

JIMWLK on a quantum computer

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta 𝑗 ≤ 𝑗 max . We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with 𝑗 max for both pure and mixed Gaussian initial density matrices. For the simplest truncation, 𝑗 max =1/2, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Axion anomalies

We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral symmetry is due to the background axion field. We compute the contributions to this anomalous Ward identity due to the pseudoscalar field alone, which arise in Minkowski space, as well as the effects due to an interaction with an external gravitational field. For the case of massless fermions, these interactions induce terms in the axion effective action that can be removed by the addition of local counterterms. We demonstrate that these counterterms are generated by the transformation of the path integral measure when transforming the theory from a form where the chiral symmetry is manifest to one where the symmetry is only apparent after using the classical equations of motion. We work perturbatively in Minkowski space and include the effects of interactions with a linearized gravitational field. Using the heat kernel method, we study the transformation properties of the path integral measure, and include the effects of non-linear gravity as well as interactions with gauge fields. Finally, we verify our relation by considering derivatively coupled fermions during pseudoscalar-driven inflation and computing the divergence of the axial current in de Sitter spacetime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. In this study, test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Physics vs structure: A systematic benchmark of learning strategies for multi-zone building thermal dynamics

Recent advances in physics-informed and data-driven machine learning promise improved thermal models for advanced building control, yet there is limited quantitative evidence on when added physics structure and architectural complexity are beneficial. Here, this work presents a systematic benchmark of five representative system identification methods for modeling multi-zone building thermal dynamics: linear state-space models, multi-layer perceptrons, neural state-space models, neural ordinary differential equations, and physically-consistent neural networks. The methods are evaluated across multiple data regimes and zone coupling strategies. Using a high-fidelity multi-zone commercial building emulator, we examine short-term and long-term prediction accuracy, computational efficiency, and ease of development. Our results reveal critical trade-offs between prediction performance, model complexity, and physical consistency. We demonstrate that decoupled, nonlinear black-box models consistently outperform coupled physics-constrained architectures in both predictive accuracy and out-of-distribution robustness in majority of the test cases for the building type considered in the study. Our findings quantify the cost of complexity in building thermal modeling and provide concrete, actionable, scenario-based guidelines for selecting model classes for control-oriented applications.

Building thermal modeling↗
DOE OSTI2024

Monotonic testing of single shear-plane CLT-to-CLT joint with hardwood dowels

Reducing embodied carbon emissions in buildings and striving for carbon neutrality through sustainable design has become a primary goal in the construction industry. The industry is expanding its use of wood-engineered products, such as cross-laminated timber (CLT) to achieve those sustainability goals. Furthermore, replacing steel fasteners with lower embodied carbon alternatives is gaining increased attention in timber engineering. This paper aims to quantify the mechanical behavior of single shear-plane CLT-to-CLT joints using hardwood dowels. The study includes 154 single shear-plane experimental tests with four different CLT species, two hardwood dowel species, and two dowel diameters. Further, the test specimens were subjected to cyclic and monotonic loading until failure, and mechanical properties such as yielding and ultimate strength, serviceability and yielding stiffness, and ductility were quantified. The hardwood dowel CLT-to-CLT joints demonstrated high strength with up to 10.3 kN (2.3 kips) capacity per dowel and lateral stiffness of up to 5.2 kN/mm (30.8 k/in) per dowel. This strength and stiffness are roughly equivalent to or exceed values for mass timber wood screws, making hardwood dowels a good alternative. In addition, the observed mean ductility of joints ranged from 2.4 to 4.5. Finally, analytical equations for the joints' yielding strength, lateral serviceability stiffness, and yielding stiffness were derived with non-linear regression analysis and validated using the experimental test results.

42 ENGINEERING↗
DOE OSTI2025

Inertial collapse of a gas bubble in a shear flow near a rigid wall

Despite the extensive research on bubble collapse near rigid walls, the bubble collapse dynamics in the presence of shear flow near a rigid wall is poorly understood. We conduct direct simulations of the Navier–Stokes equations to explore the bubble dynamics and pressures during bubble collapse near a rigid, flat wall under linear shear flow conditions. We examine the dependence of the bubble collapse morphology and wall pressures on the initial bubble location and shear rate. We find that shear distorts the bubble, generating two re-entrant jets – one developing from the side opposite to the mean flow and the other from the far end toward the wall. Upon impact of the jet on the opposite side of the bubble, water-hammer shocks are produced, which propagate outward and interact with the convoluted bubble shape. The shock stretches the bubble towards the wall, resulting in a closer impact location for the jet originating from the far end compared with the case with no shear flow. The water-hammer pressure location can be approximated as the theoretical distance travelled by a particle initialised at the bubble centre with the corresponding constant shear flow velocity. The maximum wall pressures can thus be predicted by considering the distance between the far jet impingement location and the wall along the wall-normal direction. As the shear rate is increased, the maximum wall pressure increases, although only marginally. We determine the critical initial stand-off distance from the wall at which the bubble morphology is shear dominated, i.e. characterised by converging re-entrant jets.

Bhola, Sahil (ORCID:0000000236766302)↗
DOE OSTI2021

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem

The recently developed ab-initio multiple cloning (AIMC) approach based on the multicongurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to non-adiabatic dynamics with a particular strength in the proper description of decoherence effects due to branching of vibrational wavepackets at a level crossing. In this work, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-eld theory to determine the equations of motion for classical trajectories. The multi-dimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based non-adiabatic coupling approach within the AIMC method, all observable are calculated on-the-y in the non-adiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level non-adiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Statistical Study of the Nonthermal Continuum Radiation Beaming Angle Measured by the High Frequency Receiver on Van Allen Probes-A

The nonthermal continuum (NTC) radiation beaming angle is computed over the entire Van Allen Probes-A mission when the spacecraft was in the dawn sector. The conditions in the dawn sector are favorable for the wave vector to lie near/in the spacecraft's spin plane allowing a favorable estimate of the beaming angle, and the dawn sector is also advantageous in that previous studies show NTC occurrence to peak in this sector. We found that scatter plots, over the entire mission, of beaming angle versus magnetic latitude form a distinct inverted-V pattern, with the apex at/near the magnetic equator. This pattern was sharpest for frequencies ( f ) ≲ 100 kHz. Using the NTC beaming formula from the linear mode conversion theory (LMCT), we show that such an inverted-V pattern is expected due to the large variation in the plasmapause location over the entire mission. The theoretical derived pattern qualitatively reproduces the observed pattern but not quantitatively. The lack of quantitative agreement is discussed and is attributed to several factors, one factor is off-centered emissions from the radio window. The qualitative agreement strongly supports LMCT as being the dominant mechanism generating NTC for f ≲ 100 kHz. For f ≳ 100 kHz, the inverted-V pattern becomes less distinct, and strong near-equatorial beaming is observed. Finally, after considering contamination of our selections by left-handed polarized AKR, our study suggests that besides LMCT another unidentified NTC generation mechanism becomes important for f ≳ 100 kHz.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Microbially mediated mechanisms underlie soil carbon accrual by conservation agriculture under decade-long warming

Increasing soil organic carbon (SOC) in croplands by switching from conventional to conservation management may be hampered by stimulated microbial decomposition under warming. Here, we test the interactive effects of agricultural management and warming on SOC persistence and underlying microbial mechanisms in a decade-long controlled experiment on a wheat-maize cropping system. Warming increased SOC content and accelerated fungal community temporal turnover under conservation agriculture (no tillage, chopped crop residue), but not under conventional agriculture (annual tillage, crop residue removed). Microbial carbon use efficiency (CUE) and growth increased linearly over time, with stronger positive warming effects after 5 years under conservation agriculture. According to structural equation models, these increases arose from greater carbon inputs from the crops, which indirectly controlled microbial CUE via changes in fungal communities. As a result, fungal necromass increased from 28 to 53%, emerging as the strongest predictor of SOC content. Collectively, our results demonstrate how management and climatic factors can interact to alter microbial community composition, physiology and functions and, in turn, SOC formation and accrual in croplands.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

The ultrahigh pressure stability of silver: An experimental and theoretical study

We measured the atomic volume of Ag in a toroidal diamond anvil cell to a maximum pressure of 416 GPa and calculated the atomic volume and elastic constants of Ag up to 750 and 460 GPa, respectively. Our density functional theory calculations at 0 K utilize an all-electron fully relativistic method and agree well with our volume measurements, particularly at pressures above ~75 GPa. In this work, we corrected our experimental results for non-hydrostaticity using a line shift analysis, and the resulting Vinet equation of state (EOS) parameters are reported. We find that the uniaxial stress sustained by Ag increases linearly up to 4.5 GPa at a pressure of 416 GPa. Our experimental results indicate that the fcc structure of Ag remains stable to at least 416 GPa at room temperature. Our theoretical results show that C44 increases as pressure increases and reaches a maximum at ~100 GPa above which it begins to decrease, a sign that the fcc structure of Ag is becoming unstable, and at V/V 0 = 0.30, the bcc structure is lower in energy than fcc.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Testing $f(R)$ gravity with scale dependent cosmic void velocity profiles

Here, we study the impact of cosmological scale modifications to general relativity on the dynamics of halos within voids by comparing N-body simulations incorporating Hu-Sawicki f(R) gravity, with |f R0 | = 10 -6 and 10 -5 , to those of Λ CDM. By examining the radial velocity statistics within voids classified based on their size and density-profile, as “rising” (R-type) or “shell” (S-type), we find that halo motions in small R-type voids, with effective radius <15 Mpc/h, reveal distinctive differences between f(R) and Λ CDM cosmologies. To understand this observed effect, we study the linear and nonlinear fifth forces, and develop an iterative algorithm to accurately solve the nonlinear fifth force equation. We use this to characterize the Chameleon screening mechanism in voids and contrast the behavior with that observed in gravitationally collapsed objects. The force analysis underscores how smaller R-type voids exhibit the highest ratios of fifth force to Newtonian force, which source distinguishable differences in the velocity profiles and thereby provide rich environments in which to constrain gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗