Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “COORDINATE TRANSFORMATION”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

CurvilinearGrids.jl: A Julia package for curvilinear coordinate transformations

Finite-difference discretizations of partial differential equations are widespread throughout the scientific community. Oftentimes finite-differences are used to compute spatial gradients of fields on a discrete grid, which is typically a uniform or rectilinear Cartesian mesh. Arbitrary multidimensional geometry is difficult to discretize directly with finite differences, however, due to non-uniform grid spacing and non-orthogonality. Curvilinear coordinate transformations can be used as a strategy to enable arbitrary geometry. While these curvilinear transformations are straightforward, the governing PDEs require additional terms (metrics) and must adhere to strict conservation laws; these criteria complicate the application of the transformation and require careful implementation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Domain Knowledge Guided Bayesian Optimization For Autonomous Alignment Of Complex Scientific Instruments

Bayesian Optimization (BO) is a powerful tool for optimizing complex non-linear systems. However, its performance degrades in high-dimensional problems with tightly coupled parameters and highly asymmetric objective landscapes, where rewards are sparse. In such needle-in-a-haystack scenarios, even advanced methods like trust-region BO (TurBO) often lead to unsatisfactory results. We propose a domain knowledge guided Bayesian Optimization approach, which leverages physical insight to fundamentally simplify the search problem by transforming coordinates to decouple input features and align the active subspaces with the primary search axes. We demonstrate this approach's efficacy on a challenging 12-dimensional, 6-crystal Split-and-Delay optical system, where conventional approaches, including standard BO, TuRBO and multi-objective BO, consistently led to unsatisfactory results. When combined with an reverse annealing exploration strategy, this approach reliably converges to the global optimum. The coordinate transformation itself is the key to this success, significantly accelerating the search by aligning input co-ordinate axes with the problem's active subspaces. As increasingly complex scientific instruments, from large telescopes to new spectrometers at X-ray Free Electron Lasers are deployed, the demand for robust high-dimensional optimization grows. Our results demonstrate a generalizable paradigm: leveraging physical insight to transform high-dimensional, coupled optimization problems into simpler representations can enable rapid and robust automated tuning for consistent high performance while still retaining current optimization algorithms.

FOS: Computer and information sciences↗
DOE OSTI2025

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

On the Error Covariance Correction Step of an ESKF Attitude Update

The attitude states of an error-state Kalman filter (ESKF) behave differently than most other states in the system due to their multiplicative (rather than additive) nature. One way in which they differ is an error covariance correction step after an ESKF error reset, which is not required for, for example, position and velocity states. This covariance correction step is not intuitive, and it has only been recently derived for coordinate transform matrices. The author of this memo, however, found the provided derivation in [1] confusing due to a lack of clarity surrounding the invoked reference frames, and clarity is required as there are at least 4 different ways to parameterize small-angle attitude errors in an ESKF. Furthermore, while reproducing the work, the author of this memo found a more straightforward derivation that provides additional insight into the correction step. This memo offers a derivation of the attitude error covariance correction step of an ESKF, which pays specific attention to the coordinate reference frames.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Elucidating the Role of Hydrogen at c‐In 2 O 3 /a‐In 2 O 3− x Interface

Ab initio molecular dynamics simulations and hybrid functional electronic structure calculations are employed to determine the formation, the structural and electronic properties, and the dynamics of covalent (In—OH) and ionic (In—H—In) hydrogen defects at crystalline-In 2 O 3 /amorphous-In 2 O 3−x interface. This comprehensive computational study considers (i) various interstitial and substitutional hydrogen site locations within the crystalline, amorphous, and interfacial regions; (ii) several oxygen-to-hydrogen ratios; and (iii) possible defect charged states. The results reveal hydrogen's inability to fully passivate the undercoordinated under-shared in atoms in amorphous highly substoichiometric oxide, giving rise to the formation of deep electron traps even in net-charge neutral structures. These trap defects are found to be sensitive to photoexcitation, in contrast to In—OH with H's electronic states located below the valence band and to In—H—In, where H is found to maintain its charge state upon illumination. Nevertheless, H plays a critical role in photoinduced conductivity and its relaxation by promoting In—O coordination transformations at the interfacial region, including deterioration of the crystalline layer. Finally, the results help identify mobile H species and metastable H defect complexes (such as In—H—H—In, In—OH–H—In, and In—OH–O—In) that are responsible for long relaxation times of the conductivity decay.

H defects↗
DOE OSTI2025

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2026

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗
DOE OSTI2025

Single Kerr-Schild metric for Taub-NUT instanton

It is shown that a complex coordinate transformation maps the Taub-Newman-Unti-Tamburino instanton metric to a Kerr-Schild metric. This metric involves a semi-infinite line defect as the gravitational analog of the Dirac string, much like the original metric. Moreover, it facilitates three versions of classical double copy correspondence with the self-dual dyon in electromagnetism, one of which involves a nonlocal operator. The relevance to the Newman-Janis algorithm is briefly noted. Published by the American Physical Society 2025

Kim, Joon-Hwi (ORCID:000000025474123X)↗
DOE OSTI2025

Observer-Based Nonlinear Control Scheme to Reduce Oscillations and Zero Crossing in Skid-Steer Vehicles

Motion sickness is a common condition experienced by drivers of skid-steer vehicles, primarily caused by zero crossing and oscillations in undamped systems. This study proposes an observer-based nonlinear control scheme to reduce transient oscillations and zero-crossing phenomena in skid-steer vehicles, thereby potentially alleviating motion sickness. Reducing transient oscillations and zero crossing in the transient response may alleviate motion sickness. A nonlinear damping controller is designed to improve transient response by reducing oscillations and zero-crossing. To design the controller, a reduced-order kinematic model based on coordinate transformation is developed. This transformation not only converts the system modeling into a controllable form but also enhances control performance. Modeling error is addressed by considering the distance between the center of the vehicle and the sensor location. Despite these improvements, model uncertainties and external disturbances remain, which may degrade control performance. To ensure robustness and estimate such disturbances, a high-order sliding mode observer (HOSMO) is incorporated. The effectiveness of the proposed method is validated through MATLAB/Simulink and TruckMaker simulations. From the simulation results, it was shown that the proposed method reduced the mean squared error of the tracking error to within 10 % compared to the state feedback controller with the HOSMO.

Seo, Jiwon [Chung-Ang University, Seoul (Korea, Re↗
DOE OSTI2024

Multi-Factor-Coupled, Ahead-of-Time Aggregation of Power Flexibility Under Forecast Uncertainty

The increasing penetration of distributed energy resources (DERs) is significantly reshaping the role of distribution systems under active energy management. To aggregate the active-reactive power flexibility of DERs dispersed at the feeder and provide capacity support to the transmission system, it is essential to efficiently identify feasible substation power injection trajectories. This paper introduces a novel ahead-of-time flexibility characterization method to address it. First, a polyhedral non-feeder-level power flexibility region (PFR) is constructed, accounting for various time-dependent, power-coupled, and forecast error uncertainties. Then, a polyhedral feeder-level PFR is analytically derived through a coordinate transformation, which can reveal the uncertainty propagation path, i.e., how uncertainty applies to the feeder-level PFR. To facilitate the high-level application, a tractable chance-constrained Chebyshev centering optimization model is further developed to find a ball-shaped inner approximation of the feeder-level PFR. Finally, the proposed method is validated on a modified IEEE 123-bus test system. Here, both theoretical and experimental results show that, with appropriate robustness parameter settings, the proposed method can make the approximated PFR less conservative with abundant robustness against forecast error uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Earth-Centered, Earth-Fixed Inertial Navigation System & Error-State Kalman Filter Reference Manual

This is a self-contained reference document that derives the equations necessary to build a combined inertial navigation system and error-state Kalman filter. Coordinate transform, linear time invariant system, inertial sensing, and error-state Kalman filtering theory is built up from first principles. This theory is then leveraged to derive the system equations for two combined inertial navigation system and error-state Kalman filters: (1) a 15-state system modeling white-noise-integrating accelerometer and gyroscope biases, and (2) a 39-state system modeling static and first-order Gauss-Markov accelerometer and gyroscope biases, scale factor errors, and cross-axis sensitivity errors.

42 ENGINEERING↗
DOE OSTI2025

Water Mass Transformation Budgets in Finite‐Volume Generalized Vertical Coordinate Ocean Models

Water Mass Transformation (WMT) theory provides conceptual tools that in principle enable innovative analyses of numerical ocean models; in practice, however, these methods can be challenging to implement and interpret, and therefore remain under-utilized. Our aim is to demonstrate the feasibility of diagnosing all terms in the water mass budget and to exemplify their usefulness for scientific inquiry and model development by quantitatively relating water mass changes, overturning circulations, boundary fluxes, and interior mixing. We begin with a pedagogical derivation of key results of classical WMT theory. We then describe best practices for diagnosing each of the water mass budget terms from the output of Finite-Volume Generalized Vertical Coordinate (FV-GVC) ocean models, including the identification of a non-negligible remainder term as the spurious numerical mixing due to advection scheme discretization errors. We illustrate key aspects of the methodology through the analysis of a polygonal region of the Greater Baltic Sea in a regional demonstration simulation using the Modular Ocean Model v6 (MOM6). We verify the convergence of our WMT diagnostics by brute-force, comparing time-averaged (“offline”) diagnostics on various vertical grids to timestep-averaged (“online”) diagnostics on the native model grid. Finally, we briefly describe a stack of xarray-enabled Python packages for evaluating WMT budgets in FV-GVC models (culminating in the new xwmb package), which is intended to be model-agnostic and available for community use and development.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Modeling cross-beam energy transfer with sector ray tracing

Ray-based cross-beam energy transfer (CBET) models are an essential feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion implosions, but full 3D ray-based CBET calculations can have a prohibitively high computational cost. Sector ray tracing can be used to reduce the cost by orders of magnitude in cases where the coronal plasma and laser drive can be approximated as spherically symmetric. An extension of sector ray tracing (section ray tracing) can be used to relax the assumption of a spherically symmetric drive while still retaining most of the computational savings of a sector ray trace. We discuss the foundations of sector and section ray tracing and compare them to full ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Role of bath-induced many-body interactions in the dissipative phases of the Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it nonperturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant, which is applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. In conclusion, we also study the effect of on-site staggered potentials on the SSH phase diagram and discuss extensions of our method to higher dimensions.

1-dimensional systems↗
DOE OSTI2026

Legacy Devices and Interoperability: Developing a Scientific Strategy for Inclusion and Representation of Older Devices

Legacy devices across grid, transportation, and building systems present complex modernization challenges that extend far beyond simple equipment obsolescence. Pulling from presentations and break-out group discussions from this workshop on legacy devices across all three sectors, this report examines the interconnected factors driving replacement decisions, documents successful modernization initiatives from recent years, and provides strategic guidance for coordinating infrastructure transformation across these critical sectors.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

ACDC (Automated Campbell Diagram Code) [SWR-26-042]

This application provides a web-based graphical user interface to generating Campbell Diagrams and visualizing mode shapes for OpenFAST turbine models. Determining the aeroelastic stability and dynamic characteristics of wind turbines is a critical step in turbine design and analysis. Historically, extracting natural frequencies and mode shapes from OpenFAST—the industry-standard whole-turbine simulation code—has been a fragmented and tedious process. It required manual model configuration, command-line linearization execution, and complex post-processing via proprietary scripts to handle rotating-frame dynamics. To address these workflow bottlenecks, we present the Automated Campbell Diagram Code (ACDC), an open-source graphical software tool developed by the National Laboratory of the Rockies (NLR) under the DOE-funded Distributed Wind Aeroelastic Modeling (dWAM) project. ACDC streamlines the end-to-end linearization and stability analysis workflow into a single, intuitive cross-platform application. The software guides users through OpenFAST model configuration, definition of operating points, and the automated execution of steady-state trim and linearization simulations. Under the hood, ACDC automates the complex mathematical post-processing steps required for rotating systems, including Multi-Blade Coordinate (MBC) transformations, eigenanalysis, and advanced modal tracking utilizing the Modal Assurance Criterion (MAC) and spectral clustering. Finally, ACDC processes these results to automatically generate Campbell diagrams and features a robust 3D visualization engine to animate full-system mode shapes. By eliminating the reliance on external post-processing environments and manual data manipulation, ACDC significantly accelerates dynamic analysis and lowers the barrier to entry for wind energy researchers and engineers.

Summerville, Brent [National Laboratory of the Roc↗
DOE OSTI2025

Fundamental Insights into Cathode Stability: Linking Compositional Tuning and Local Coordination in Complex Metal Oxides under Aqueous Transformations

Compositional tuning of complex metal oxides in Li-ion battery materials influences their performance as well as their end-of-life behavior, in particular, the tendency to release toxic metal cations in aqueous solution. We modeled ternary variants of a parent LiCoO 2 delafossite structure by varying the metal identity and relative amounts. This yielded ten model formulations of Li(A 4/6 B 1/6 C 1/6 )O 2 , where the material is enriched with the A metal and doped with B and C, with Ni, Mn, Co, Fe, Al, V, and Ti as constituent metals. To assess their stability in aqueous conditions, metal release energetics were calculated using a combination of Density Functional Theory calculations and thermodynamics. Metal release in ternary oxides is dictated by subtle variations in the coordination environment of the leaving group. To identify governing chemical features across diverse compositions with varying local coordination environments, we leverage random forest regression and descriptor importance analysis. A key result is that metal–oxygen orbital hybridization, quantified using a projected density-of-states-derived descriptor, H d/p , provides a physically grounded measure of interaction strength that governs metal release energetics. This refined perspective goes beyond conventional oxidation state considerations and offers more robust insights for materials science. Finally, we model defect surface-bound O 2 dimer formation as a proxy for reactive oxygen species (ROS) generation. The results show that Ni-rich compositions more readily stabilize spin-polarized O 2 dimers, corroborating experimental reports of an increased ROS-driven biological response. In conclusion, our results establish a compositional and electronic basis for metal release and surface oxygen reactivity that form a rationale for complex metal oxide design principles.

36 MATERIALS SCIENCE↗