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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.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

Abstract An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H 4 , H 2 O, and BeH 2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum Hamiltonian algorithms for maximum independent sets

ABSTRACT We compare two quantum Hamiltonian algorithms that address the maximum independent set problem: one based on the emergent non-Abelian gauge matrix in adiabatic evolution of an energetically isolated manifold of states; the other based on designed application of single-qubit operations. We demonstrate that they are mathematically equivalent in the sense that one is the other’s interaction picture. Despite their mathematical equivalence, our numerical simulations show significant differences between them in performance, which is explained analytically. Intriguingly, this equivalence unveils that the PXP model, recently prominent in quantum dynamics research, can be viewed as quantum diffusion over the median graph of all independent sets governed by the non-Abelian gauge matrix.

Science & Technology - Other Topics↗
DOE OSTI2025

Weakly supervised anomaly detection with event-level variables

We introduce a new topology for weakly supervised anomaly detection searches, diobject plus X. In this topology, one looks for a resonance decaying to two standard model particles produced in association with other anomalous event activity (X). This additional activity is used for classification. We demonstrate how anomaly detection techniques which have been developed for dijet searches focusing on jet substructure anomalies can be applied to event-level anomaly detection in this topology. To robustly capture event-level features of multiparticle kinematics, we employ new physically motivated variables derived from the geometric structure of a collision’s phase space manifold. As a proof of concept, we explore the application of this approach to several benchmark signals in the di-𝜏 and di-𝜇 plus X final states. We demonstrate that our anomaly detection approach can reach discovery-level significances for signals that would be missed in a conventional bump-hunt approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Neutralizing topological obstructions to bubbles of nothing

Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g 2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry

Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

PSF–NET: A Nonparametric Point-spread Function Model for Ground-based Optical Telescopes

Ground-based optical telescopes are seriously affected by atmospheric turbulence induced aberrations. Understanding properties of these aberrations is important both for instrument design and image restoration method development. Because the point-spread function can reflect performance of the whole optic system, it is appropriate to use the point-spread function to describe atmospheric turbulence induced aberrations. Assuming point-spread functions induced by the atmospheric turbulence with the same profile belong to the same manifold space, we propose a nonparametric point-spread function—PSF–NET. The PSF–NET has a cycle convolutional neural network structure and is a statistical representation of the manifold space of PSFs induced by the atmospheric turbulence with the same profile. Testing the PSF–NET with simulated and real observation data, we find that a well trained PSF–NET can restore any short exposure images blurred by atmospheric turbulence with the same profile. Besides, we further use the impulse response of the PSF–NET, which can be viewed as the statistical mean PSF, to analyze interpretation properties of the PSF–NET. We find that variations of statistical mean PSFs are caused by variations of the atmospheric turbulence profile: as the difference of the atmospheric turbulence profile increases, the difference between statistical mean PSFs also increases. The PSF–NET proposed in this paper provides a new way to analyze atmospheric turbulence induced aberrations, which would benefit the development of new observation methods for ground-based optical telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Analysis of internal flows relative to the space shuttle main engine

Cooperative efforts between the Lockheed-Huntsville Computational Mechanics Group and the NASA-MSFC Computational Fluid Dynamics staff has resulted in improved capabilities for numerically simulating incompressible flows generic to the Space Shuttle Main Engine (SSME). A well established and documented CFD code was obtained, modified, and applied to laminar and turbulent flows of the type occurring in the SSME Hot Gas Manifold. The INS3D code was installed on the NASA-MSFC CRAY-XMP computer system and is currently being used by NASA engineers. Studies to perform a transient analysis of the FPB were conducted. The COBRA/TRAC code is recommended for simulating the transient flow of oxygen into the LOX manifold. Property data for modifying the code to represent LOX/GOX flow was collected. The ALFA code was developed and recommended for representing the transient combustion in the preburner. These two codes will couple through the transient boundary conditions to simulate the startup and/or shutdown of the fuel preburner. A study, NAS8-37461, is currently being conducted to implement this modeling effort.

Source record↗
NASA NTRS1996

O2 A Band Studies for Cloud Detection and Algorithm Improvement

Detection of cloud parameters from space-based spectrometers can employ the vibrational bands of O2 in the (sup b1)Sigma(sub +)(sub g) yields X(sub 3) Sigma(sup -)(sub g) spin-forbidden electronic transition manifold, particularly the Delta nu = 0 A band. The GOME instrument uses the A band in the Initial Cloud Fitting Algorithm (ICFA). The work reported here consists of making substantial improvements in the line-by-line spectral database for the A band, testing whether an additional correction to the line shape function is necessary in order to correctly model the atmospheric transmission in this band, and calculating prototype cloud and ground template spectra for comparison with satellite measurements.

Chance, K. V.↗
DOE OSTI2022

Derivative-free optimization of a rapid-cycling synchrotron

Here, we develop and solve a constrained optimization model to identify an integrable optics rapid-cycling synchrotron lattice design that performs well in several capacities. Our model encodes the design criteria into 78 linear and nonlinear constraints, as well as a single nonsmooth objective, where the objective and some constraints are defined from the output of Synergia, an accelerator simulator. We detail the difficulties of the 23-dimensional simulation-constrained decision space and establish that the space is nonempty. We use a derivative-free manifold sampling algorithm to account for structured nondifferentiability in the objective function. Our numerical results quantify the dependence of solutions on constraint parameters and the effect of the form of objective function.

43 PARTICLE ACCELERATORS↗
NASA NTRS1971

Acoustic testing of a 1.5 pressure ratio low tip speed fan with casing tip bleed (QEP Fan B scale model)

A scale model of the bypass flow region of a 1.5 pressure ratio, single stage, low tip speed fan was tested with a rotor tip casing bleed slot to determine its effects on noise generation. The bleed slot was located 1/2 inch (1.3 cm) upstream of the rotor leading edge and was configured to be a continuous opening around the circumference. The bleed manifold system was operated over a range of bleed rates corresponding to as much as 6% of the fan flow at approach thrust and 4.25% of the fan flow at takeoff thrust. Acoustic results indicate that a bleed rate of 4% of the fan flow reduces the fan maximum approach 200 foot (61.0 m) sideline PNL 0.5 PNdB and the corresponding takeoff thrust noise 1.1 PNdB below the level with zero bleed. However, comparison of the standard casing (no bleed slot) and the slotted bleed casing with zero bleed shows that the bleed slot itself caused a noise increase.

Kazin, S. B.↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Cislunar Trajectory Design and Maneuver Autonomy for NASA's Moon to Mars Architecture

NASA’s Moon to Mars architecture is an ambitious roadmap of manned cislunar and deep space exploration. The extensive amount of orbital assets required will place a significant burden on ground-based resources, such as communication networks and operations facilities. Spacecraft autonomy is essential for maintaining a vast number of complex missions beyond Earth orbit. To achieve full autonomy, spacecraft must be able to employ methods of robust maneuver design without an explicit dependence on commands sent from the ground. This level of autonomy is needed not only for stationkeeping, but also for outbound transfers. To address the need of spacecraft maneuver design autonomy, this work investigates the use of neural networks (NNs) in a supervised learning environment. A supervised learning approach for NNs allows for a curated training data set, consisting exclusively of perturbations applied to a desired mission concept of operations (ConOps). The proposed approach allows humans on the ground to design a specific mission ConOps before flight, then employ NNs to fly the mission robustly and autonomously. This investigation numerically tests maneuver autonomy in four highly sensitive regions of flight: orbit raising, translunar injection burns, powered lunar flybys, and invariant manifold insertion burns. These straining cases are contextualized by testing them in a demonstration mission, targeting an Earth-Moon L3 orbit. The study first establishes feasibility by automating impulsive burn maneuvers. However, some guidance algorithms will need more intensive commands, such as inertial pointing and angular rates. To validate this method, NN maneuver autonomy is applied to a finite burn model of the demonstration mission. The use of sequential, mission specific maneuvers provide an appropriate testbed to demonstrate the robustness of a NN trained on feasible perturbed states. Moreover, these scenarios provide preliminary proof-of-concept for fully autonomous missions that execute maneuvers without dependence upon explicit command uplinks. As a result, the technological advancement proposed in this work may significantly ease the strain on ground-based mission operations. This would enable complex and autonomous mission execution in cislunar and deep space regimes, filling a technology gap required to support future manned missions.

NASA↗
NASA NTRS2017

Pressure-Fed LOX/LCH4 Reaction Control System for Spacecraft: Transient Modeling and Thermal Vacuum Hotfire Test Results

An integrated cryogenic liquid oxygen, liquid methane (LOX/LCH4) reaction control system (RCS) was tested at NASA Glenn Research Center's Plum Brook Station in the Spacecraft Propulsion Research Facility (B-2) under vacuum and thermal vacuum conditions. The RCS is a subsystem of the Integrated Cryogenic Propulsion Test Article (ICPTA), a pressure-fed LOX/LCH4 propulsion system composed of a single 2,800 lbf main engine, two 28 lbf RCS engines, and two 7 lbf RCS engines. Propellants are stored in four 48 inch diameter 5083 aluminum tanks that feed both the main engine and RCS engines in parallel. Helium stored cryogenically in a composite overwrapped pressure vessel (COPV) flows through a heat exchanger on the main engine before being used to pressurize the propellant tanks to a design operating pressure of 325 psi. The ICPTA is capable of simultaneous main engine and RCS operation. The RCS engines utilize a coil-on-plug (COP) ignition system designed for operation in a vacuum environment, eliminating corona discharge issues associated with a high voltage lead. There are two RCS pods on the ICPTA, with two engines on each pod. One of these two engines is a heritage flight engine from Project Morpheus. Its sea level nozzle was removed and replaced by an 85:1 nozzle machined using Inconel 718, resulting in a maximum thrust of 28 lbf under altitude conditions. The other engine is a scaled down version of the 28 lbf engine, designed to match the core and overall mixture ratios as well as other injector characteristics. This engine can produce a maximum thrust of 7 lbf with an 85:1 nozzle that was additively manufactured using Inconel 718. Both engines are film-cooled and capable of limited duration gas-gas and gas-liquid operation, as well as steady-state liquid-liquid operation. Each pod contains one of each version, such that two engines of the same thrust level can be fired as a couple on opposite pods. The RCS feed system is composed of symmetrical 3/8 inch lines that tap off of the main propellant manifold to send LOX and LCH4 outboard to the RCS pods. A Thermodynamic Vent System (TVS) is used to condition propellants at each pod by venting through an orifice and then routing the cold expansion products back through tubing that is welded along a large portion of the main RCS feed lines. Prior to final installation on the ICPTA, the RCS engines were tested in a small vacuum chamber at the Johnson Space Center (JSC) Energy Systems Test Area (ESTA) to verify functionality of the new COP ignition system and check out operation of the vacuum nozzles. After engine-level testing, the RCS engines were installed on the vehicle and a series of integrated hot-fire tests were performed at JSC consisting of various pulsing and steady-state firings as well as integrated main engine/RCS operation. The ICPTA was then integrated into the Plum Brook B-2 facility for vacuum and thermal/vacuum testing. Testing in the B-2 facility was composed of multiple thermal and pressure environments. The first set of tests were performed under ambient temperature and altitude pressure conditions. These tests consisted of a range of minimum impulse bit (MIB) pulsing sequences with low duty cycle, analogous to a coast phase in which the RCS is primarily used for station keeping. The primary goal of this sequence is to understand how propellant conditions were effected without an active TVS. In this scenario, consistent gas-gas operation is desirable since it results in a smaller MIB and more efficient propellant consumption. Multiple skin thermocouples are mounted on the feedlines, in addition to a submerged thermocouple on each commodity, in order to gather thermal data on the system. Higher duty cycle pulsing tests were then performed, analogous to an ascent or landing mission phase. The primary goal of this sequence was to examine how well the engines self-conditioned without active TVS when starting from a quiescent state. The TVS was then activated during some tests to demonstrate the capability to quickly condition the engines for higher pulsing demand scenarios. A thermocouple at the TVS outlet allows for the calculation of energy absorbed by the vented propellant. Lastly, tests with longer pulses and multiple engines firing either in sequence or simultaneously were run in order to gather transient system response data on waterhammer. Six total high-speed pressure transducers are installed on the RCS system, one sensor at the end of each propellant manifold line on the pods, and one at the tap-off location for each commodity. This will allow for the accurate characterization of waterhammer in the system under various propellant conditions and firing sequences. Other instrumentation for this test series includes nozzle throat thermocouples, chamber pressure measurement, heat soakback measurement, and tank wall plume impingement temperature measurement. The next set of tests were performed to demonstrate simultaneous main engine and RCS operation. Data from this test will be used to examine if there is any change to nominal operation of the RCS as a result of feed system interaction or other phenomenon. Some of these tests began under high vacuum conditions (target ambient pressure less than 1x10(exp -3) torr) and others began at altitude conditions. The last set of tests were performed with the B-2 cold wall active. Under these tests, many of the same low duty cycle MIB tests were repeated in order to characterize how propellant conditions changed with the lower heat leak. In this scenario the RCS manifold experiences much less heat leak, resulting in a change to how well the engines self-condition. As a result, an increase in maximum waterhammer pressures and a change in natural frequency of the system was expected due to higher density propellants. The lower heat leak should also result in a change to the MIB pulse profile, and data will be examined to understand how MIB repeatability is affected in the different operating environments. Parallel to the test efforts, a set of transient model development efforts were made to predict RCS performance. The primary effort was aimed at producing a SINDA/FLUINT model to predict propellant conditioning up to the engine inlet as a function of different environmental and operating parameters, with the goal of predicting chamber pressure, TVS performance, and propellant consumption over time. Preliminary results for this effort will be presented in comparison with test data. Additional modeling efforts were made using SINDA/FLUINT to predict waterhammer in the system since the software is capable of handling multiphase transient fluid dynamics. These results will be compared with the high-speed pressure transducer test data for validation purposes.

Atwell, Matthew J.↗
DOE OSTI2023

Vibronic Relaxation Pathways in Molecular Spin Qubit Na 9 [Ho(W 5 O 18 ) 2 ]·35H 2 O under Pressure

In order to explore how spectral sparsity and vibronic decoherence pathways can be controlled in a model qubit system with atomic clock transitions, we combined diamond anvil cell techniques with synchrotron-based far infrared spectroscopy and first-principles calculations to reveal the vibrational response of Na 9 [Ho(W 5 O 18 ) 2 ]·35H 2 O under compression. Because the hole in the phonon density of states acts to reduce the overlap between the phonons and f manifold excitations in this system, we postulated that pressure might move the HoO 4 rocking, bending, and asymmetric stretching modes that couple with the M J = ±5, ±2, and ±7 levels out of resonance, reducing their interactions and minimizing decoherence processes, while a potentially beneficial strategy for some molecular qubits, pressure slightly hardens the phonons in Na 9 [Ho(W 5 O 18 ) 2 ]·35H 2 O and systematically fills in the transparency window in the phonon response. The net result is that the vibrational spectrum becomes less sparse and the overlap with the various M J levels of the Ho 3+ ion actually increases. These findings suggest that negative pressure, achieved using chemical means or elongational strain, could further open the transparency window in this rare earth-containing spin qubit system, thus paving the way for the use of device surfaces and interface elongational/compressive strains to better manage decoherence pathways.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Learning effective SDEs from Brownian dynamic simulations of colloidal particles

We construct a reduced, data-driven, parameter dependent effective stochastic differential equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian dynamics simulations. We use diffusion maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers–Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian dynamic simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Further, our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.

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

Spin-orbital correlations from complex orbital order in MgV 2⁢ O 4

MgV 2 ⁢O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 ⁢O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹⁡𝑑⁢$\overline{3}$⁢𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ ⁢60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ ⁢40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2⁢ O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2⁢ O 4 displays a high-temperature orbital memory of the low-temperature spin order.

Frustrated magnetism↗
NASA NTRS2016

Estimating Flow-Through Balance Momentum Tares with CFD

This paper describes the process used for estimating flow-through balance momentum tares. The interaction of jet engine exhausts on the BOEINGERA Hybrid Wing Body (HWB) was simulated in the NFAC 40x80 wind tunnel at NASA Ames using a pair of turbine powered simulators (TPS). High-pressure air was passed through a flow-through balance and manifold before being delivered to the TPS units. The force and moment tares that result from the internal shear and pressure distribution were estimated using CFD. Validation of the CFD simulations for these complex internal flows is a challenge, given limited experimental data due to the complications of the internal geometry. Two CFD validation efforts are documented, and comparisons with experimental data from the final model installation are provided.

Balance Momentum Tare↗
DOE OSTI2025

The Viskores User's Guide, Release 1.1

High-performance computing relies on ever finer threading. Advances in processor technology include ever greater numbers of cores, hyperthreading, accelerators with integrated blocks of cores, and special vectorized instructions, all of which require more software parallelism to achieve peak performance. Traditional visualization solutions cannot support this extreme level of concurrency. Extreme scale systems require a new programming model and a fundamental change in how we design algorithms. To address these issues we created Viskores: the visualization toolkit for multi/many-core architectures. Viskores supports a number of algorithms and the ability to design further algorithms through a top-down design with an emphasis on extreme parallelism. Viskores also provides support for finding and building links across topologies, making it possible to perform operations that determine manifold surfaces, interpolate generated values, and find adjacencies. Although Viskores provides a simplified high-level interface for programming, its template-based code removes the overhead of abstraction.

97 MATHEMATICS AND COMPUTING↗