Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Analytic gradients”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Onset of High-Harmonic Fast Wave Propagation in Annulus Geometry

Previous experiments on NSTX have reported high-harmonic fast wave (HHFW) power losses in the scrape-off layer (SOL), with dependencies on the wave parallel wavenumber, plasma density, and magnetic field. This study presents an analysis of HHFW propagation in the SOL plasma, focusing on parasitic coupling to the waveguide mode bounded by the steep gradient pedestal and the outer wall boundary. The analytic and finite element wave models are discussed using a 2D annulus geometry, which serves as a simplified representation of the NSTX-U plasma. The model shows that a minimum radial gap width is required to support wave propagation, analogous to the higher-order modes in coaxial geometries. The impact of several factors, including gap width, wave parallel phasing, and magnetic field strength, on parasitic wave coupling is examined, highlighting the role of the geometric dimension in relation to the wave perpendicular wavelength. The findings suggest that controlling the edge/SOL density profile (gap control) is crucial for mitigating parasitic coupling when the density in front of the antenna exceeds the density cutoff.

Baek, Seung-Gyou [Massachusetts Inst. of Technolog↗
DOE OSTI2022

Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β 2 and triaxiality γ. The deformation can be accessed in high-energy heavy ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity ε 2 and the density gradient d ⊥ in the initial state. Using an analytical estimate and a Glauber model, I show that the variances $\langleε^{2}_{2}\rangle$ or $\langle$(δd ⊥ /d ⊥ ) 2 $\rangle$ and skewnesses $\langleε^{2}_{2}δd_{⊥}/d_{⊥}\rangle$ or $\langle(δd_{⊥}/d_{⊥})^{3}\rangle$ have a simple analytical form of a'+b'β$^{2}_{2}$ and a'+[b'+c' cos(3γ)]β$^{3}_{2}$, respectively. From these, I constructed several normalized skewnesses to isolate the γ dependence from that of β 2 and show that the correlations between a normalized skewness and a variance can constrain simultaneously β 2 and γ. Assuming a linear relation with elliptic flow v 2 and mean-transverse momentum [p T ] of final-state particles, v 2 ∝ ε 2 and δ [p T ] / [p T ] ∝ δd ⊥ /d ⊥ , similar conclusions are also expected for the variances and skewnesses of v 2 and [p T ], i.e., a + bβ$^{2}_{2}$ for $\langle v^{2}_{2}\rangle$ and $\langle(δ[p_{T}] / [p_{T}])^{2}\rangle$ and a + [b + c cos (3γ)] β$^{3}_{2}$ for $\langle v^{2}_{2}δ [p_{T}] / [p_{T}]\rangle$ or $\langle(δ[p_{T}] / [p_{T}])^{3}\rangle$. My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos (3γ) ≈ 1, and near oblate nuclei, cos (3γ) ≈ –1 , with known β 2 values, followed by collisions of other species of interest with similar mass number. The (β 2 , γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. Finally, the results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2021

Gradient sensing via cell communication

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Modelling and assessing the near-wake representation and turbulence behaviour of control-oriented wake models

Due to the interaction between the wake of an upstream turbine on a downstream turbine, power losses and increased fatigue loads occur. By yawing the upstream turbine with regard to the wind direction, one can potentially reduce the power losses of the downstream turbine and reduce the fatigue loads. The evolution of the wake depends on the pressure gradient within the near-wake region and the turbulent kinetic energy and must be incorporated in existing wake steering algorithms to provide an accurate estimation of the wake flow. This paper will show a first approach to implement a near-wake model and a turbulence model in the curled wake model within the controls-oriented framework FLORIS. The near-wake model is based on an analytical expression of the velocity profile to model the pressure gradient. Furthermore, two turbulence models are incorporated within the curled wake model based on a Gaussian-distribution and a mixing length formulation. The adapted curled wake model is then assessed with the measurement data acquired in the wind tunnel at ForWind – University of Oldenburg. The evaluation of the models show good agreement for the velocity deficit and representation of the near-wake region. Furthermore, the turbulent kinetic energy behaved as expected in comparison to other work, showing a ring of high turbulent kinetic energy at non-yawed condition which is deflected to a curled shape at large yaw angles with the turbulence model based on a mixing length formulation.

FLORIS↗
DOE OSTI2021

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

Foulk III, James W.↗
DOE OSTI2020

An implicit, sharp numerical treatment of viscous terms at arbitrarily shaped liquid-gas interfaces in evaporative flows

We report a novel methodology for accurate treatment of viscous terms in evaporation problems. The proposed scheme is an extension of the sharp viscous treatment of Kang et al. (2000) [7] to 3D phase change problems. To ensure accuracy and grid converging solutions, a new implicit approach to computing viscous fluxes across the phase interfaces is proposed, which was previously unavailable in fixed grid numerical schemes. Analytical relations were derived for the jump in velocity gradients across the 2D and 3D phase interfaces, an important constituent of the proposed scheme. The relations show a non-vanishing jump in the tangential gradients across the phase interface that are associated with evaporative flux and interfacial curvature. The proposed methodology demonstrated first order accuracy in canonical test cases. It is general and applicable to arbitrarily oriented interfaces, and can be readily implemented in existing evaporation flow solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ka-band linearizer for the Ultra-Compact X-ray free-electron laser at UCLA

There is a strong demand for accelerating structures able to achieve higher gradients and more compact dimensions for the next generation of linear accelerators for research, industrial and medical applications. Notably innovative technologies will permit compact and affordable advanced accelerators as the linear collider and X-ray free-electron lasers (XFELs) with accelerating gradients over twice the value achieved with current technologies. In particular XFELs are able to produce coherent X-ray pulses with peak brightness 10 orders of magnitude greater than preceding approaches, which has revolutionized numerous research fields through imaging of the nanoscopic world at the time and length scale of atom-based systems, that is of femtosecond and Angstrom. There is a strong interest for combining these two fields, to form a proper tool with the goal of producing a very compact XFEL in order to investigate multi-disciplinary topics in chemistry, biology, materials science, medicine and physics. In the framework of the Ultra-Compact XFEL project under study at the University of California, Los Angeles, a high gradient radio-frequency accelerating structure for the longitudinal phase-space linearization with an integrated voltage of at least 15 MV working on 6th harmonic of the main Linac frequency is required. We here present the electromagnetic design of a cryogenic normal-conducting 8 cm long Ka-band standing-wave linearizer working on π mode with a target accelerating gradient beyond 100 MV/m. The studies have been performed analytically and numerically to investigate the beam dynamics and electromagnetic issues.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Unveiling the dark matter of riverine dissolved organic matter and its role in molecular chemodiversity

Chemodiversity of riverine dissolved organic matter (DOM) plays a crucial role in global elemental cycles and ecosystem function. However, DOM “dark matter”—molecules without assigned specific formulae—remain unexplored in the interpretation of chemodiversity. Here, we systematically investigated the characteristics and drivers of dark matter and its impacts on DOM chemodiversity using 551 river water and sediment samples. Compared to known matter with specific formulae, dark matter exhibited lower molecular weight and diversity, but higher compositional dissimilarity, with dissolved organic carbon (DOC) as the primary driver. Including dark matter into chemodiversity analysis changed mass, diversity, and compositional dissimilarity of DOM from –10.1 to –0.04 %, –0.7 to 4.9 %, and 0.4 to 28.8 % in waters, and from –17.5 to 5.7 %, –10.5 to 19.2 %, and –22.3 to 33.1 % in sediments, respectively. DOC mediated these ecosystem-dependent effects: lower DOC amplified the effects on chemodiversity in waters, whereas in sediments, the effects shifted from negative to positive with changing DOC. Furthermore, ignoring dark matter would overestimate the regulatory role of DOC on sediment DOM chemodiversity. In conclusion, collectively, our findings clarify the influence of dark matter on DOM chemodiversity assessments across environmental gradients, improving understanding of riverine DOM and refining its analytical framework.

Chemodiversity↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

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

Online Convex Optimization of Programmable Quantum Computers to Simulate Time-Varying Quantum Channels

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

COMPASS-FME Synoptic Site Characterization

This dataset contains soil biogeochemical and physicochemical characterization data for the COMPASS-FME synoptic sites.This dataset also contains data for the paper Patel et al. 2025 "Transition zones at the changing coastal terrestrial-aquatic interface", https://doi.org/10.1029/2025JG008978.Coastal soils are a significant but highly uncertain component of global biogeochemical cycles. These systems experience unique spatial and temporal variability in biogeochemical processes, driven by wetland-to-upland gradients and hydrological fluctuations. We studied drivers of coastal soil variability (a) at regional scales and (b) across transects from upland forest to wetland, in two contrasting regions — Lake Erie, a freshwater lacustrine system, and Chesapeake Bay, a saltwater estuarine system. Salinity-related analytes were a key driver of soil variability, not just in the saltwater system, but surprisingly, also in the freshwater system. We had hypothesized linear trends in biogeochemical parameters along the TAI – however, contrary to expectations, transition soils were not consistently intermediate between upland and wetland endmembers; the non-monotonic trends of carbon, phosphorus, iron along our transects suggest that these are key analytes to study in our regions. Rapidly changing soil factors across coastal gradients provide insights into which soil processes may act as precursors to ecosystem shifts. Our comprehensive soil characterization across the coastal transects provides essential data for mechanistic modeling of ecosystem dynamics.The data are provided as processed, csv files. Raw data and processing scripts can be accessed on GitHub (https://github.com/COMPASS-DOE/cmps-soil_characterization).A note on the nomenclature: the experimental design represents three points along the coastal gradient -- upland, transition, and wetland. "wetland" is referred to as "marsh" in the corresponding paper. The two terms can be used interchangeably for the sites in this study.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Online Distribution System State Estimation via Stochastic Gradient Algorithm

Distribution network operation is becoming more challenging because of the growing integration of intermittent and volatile distributed energy resources (DERs). This motivates the development of new distribution system state estimation (DSSE) paradigms that can operate at fast timescale based on real-time data stream of asynchronous measurements enabled by modern information and communications technology. To solve the real-time DSSE with asynchronous measurements effectively and accurately, this paper formulates a weighted least squares DSSE problem and proposes an online stochastic gradient algorithm to solve it. The performance of the proposed scheme is analytically guaranteed and is numerically corroborated with realistic data on IEEE 123-bus feeder.

distribution system state estimation↗
DOE OSTI2025

Jipole: A Differentiable ipole-based Code for Radiative Transfer in Curved Spacetimes

Recent imaging of supermassive black holes by the Event Horizon Telescope has relied on exhaustive parameter-space searches, matching observations to large, precomputed libraries of theoretical models. As observational data become increasingly precise, the limitations of this computationally expensive approach grow more acute, creating a pressing need for more efficient methods. In this work, we present Jipole, an automatically differentiable (AD), ipole-based code for radiative transfer in curved spacetimes, designed to compute image gradients with respect to underlying model parameters. These gradients quantify how parameter changes—such as the black hole’s spin or the observer’s inclination—affect the image, enabling more efficient parameter estimation and reducing the number of required images. We validate Jipole against ipole in two analytical tests and then compare pixelwise intensity derivatives from AD with those from finite-difference methods. We then demonstrate the utility of these gradients by performing parameter recovery for an analytical model in three increasingly complex cases for the injected image: ideal, blurred, and blurred with added noise. In most cases, high-accuracy fits are obtained in only a few optimization steps, failing only in cases with extremely low signal-to-noise ratios. These results highlight the potential of AD-based methods to accelerate robust, high-fidelity model-data comparisons in current and future black hole imaging efforts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Impact of molten salt inflow on the temperature distribution in thermal energy storage tanks at startup for central receiver concentrating solar power plants

Concentrating Solar Power (CSP) systems with molten salt thermal energy storage (TES) tanks are one of the most promising, renewable-based energy conversion technologies for larger-scale power generation. The TES tank is one of the most critical components in CSP plants due to its high-temperature operation (up to 565 °C), daily thermal cycling, and intermittent solar radiation conditions. The plant startup is one of the most challenging operation conditions that could lead to damaging thermal gradients due to low salt inventory levels. In this study an analytical model for the sparger ring was developed and integrated with a detailed computational fluid dynamics model of a commercial-scaled molten salt tank. The integrated model allows an accurate representation of the tank operation to evaluate the effect of molten salt inflow on the mixing process. The tank filling process during plant startup was analyzed considering sparger rings with variations in design features, including inlet orifice configurations, number of orifices, direction of the inlets, and orifice diameter. The results demonstrated that higher temperature gradients are obtained in the tank floor during the plant startup. A sparger ring configuration with a predetermined orifice inlet inclination (30°, 45° and 60°) leads to significant temperature differences in the floor, between 57 °C and 62 °C, but better homogeneity in the temperature of the salt inventory. Lower salt inflow velocities result in a more homogeneous floor temperature, with maximum temperature differences under 38 °C. The sparger ring configuration with 52 orifices of 1-in. diameter and vertical flow showed better homogeneity in the temperature differences as a function of the salt level and lower temperature gradients in the tank floor. Because large temperature gradients in the tank's floor have been identified as one of the main factors contributing to tank failures, assessing various sparger ring design features is fundamental to determining proper inflow conditions that lead to low-temperature gradients and reducing failure susceptibility.

14 SOLAR ENERGY↗
DOE OSTI2023

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work, we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the “clean and dirty” setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in the concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

97 MATHEMATICS AND COMPUTING↗