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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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

The effects of long delay and transmission errors on the performance of TP-4 implementations

A set of tools that allows us to measure and examine the effects of transmission delay and errors on the performance of TP-4 implementations has been developed. The tools give insight into both the large- and small-scale behaviors of an implementation. These tools have been systematically applied to a commercial implementation of TP-4. Measurements show, among other things, that a 2-second one-way transmission delay and an effective bit-error rate of 1 error per 100,000 bits can result in a 95 percent reduction in TP-4 throughput. The detailed statistics give insight into why transmission delay and errors affect this implementations so significantly and support a number of 'lessons learned' that could be applied to TP-4 implementations that operate more robustly across networks with long transmission delays and transmission errors.

Durst, Robert C.↗
NASA NTRS2013

Modeling Weather Impact on Airport Arrival Miles-in-Trail Restrictions

When the demand for either a region of airspace or an airport approaches or exceeds the available capacity, miles-in-trail (MIT) restrictions are the most frequently issued traffic management initiatives (TMIs) that are used to mitigate these imbalances. Miles-intrail operations require aircraft in a traffic stream to meet a specific inter-aircraft separation in exchange for maintaining a safe and orderly flow within the stream. This stream of aircraft can be departing an airport, over a common fix, through a sector, on a specific route or arriving at an airport. This study begins by providing a high-level overview of the distribution and causes of arrival MIT restrictions for the top ten airports in the United States. This is followed by an in-depth analysis of the frequency, duration and cause of MIT restrictions impacting the Hartsfield-Jackson Atlanta International Airport (ATL) from 2009 through 2011. Then, machine-learning methods for predicting (1) situations in which MIT restrictions for ATL arrivals are implemented under low demand scenarios, and (2) days in which a large number of MIT restrictions are required to properly manage and control ATL arrivals are presented. More specifically, these predictions were accomplished by using an ensemble of decision trees with Bootstrap aggregation (BDT) and supervised machine learning was used to train the BDT binary classification models. The models were subsequently validated using data cross validation methods. When predicting the occurrence of arrival MIT restrictions under low demand situations, the model was able to achieve over all accuracy rates ranging from 84% to 90%, with false alarm ratios ranging from 10% to 15%. In the second set of studies designed to predict days on which a high number of MIT restrictions were required, overall accuracy rates of 80% were achieved with false alarm ratios of 20%. Overall, the predictions proposed by the model give better MIT usage information than what has been currently provided under current day operations. Traffic flow managers can use these predictions to identify potential MIT restrictions to eliminate (e.g., those occurring during low arrival demand periods), and to determine the days in which a significant number of restrictions may be required

Operation↗
NASA NTRS2017

Large-Eddy Simulation (LES) of a Compressible Mixing Layer and the Significance of Inflow Turbulence

In the context of Large Eddy Simulations (LES), the effects of inflow turbulence are investigated through the Synthetic Eddy Method (SEM). The growth rate of a turbulent compressible mixing layer corresponding to operating conditions of GeobelDutton Case 2 is investigated herein. The effects of spanwise width on the growth rate of the mixing layer is investigated such that spanwise width independence is reached. The error in neglecting inflow turbulence effects is quantified by comparing two methodologies: (1) Hybrid-RANS-LES methodology and (2) SEM-LES methodology. Best practices learned from Case 2 are developed herein and then applied to a higher convective mach number corresponding to Case 4 experiments of GeobelDutton.

les↗
NASA NTRSDate not supplied

Validation of Fitness for Duty Standards Using Pre- and Post-Flight Capsule Egress and Suited Functional Performance Tasks in Simulated Reduced Gravity (Pilot Egress Fitness)

As NASA prepares for exploration missions, it will be critical to understand and build upon known crew capabilities. Specifically, we need to know the functional capacities of crew at different stages of a mission and characterize these profiles so that the appropriate vehicle requirements and mission concepts of operations (ConOps) can be developed. One of the most complex phases of any missions is when there is a transition between gravity environments. For instance, both physiological adaptation to microgravity and subsequent re-entry into a gravity environment result in reduced functional capacity, even with rigorous adherence to inflight countermeasures. Quantification of the astronauts’ post-landing functional performance is necessary to design ConOps for exploration missions. Specifically, these two high-risk tasks may have to be performed soon after gravity transitions: •Unassisted capsule egress task after return to Earth •Planetary extravehicular activity (EVA) soon after landing on Mars or the Moon This study has been broken down into two phases. A pilot phase to assess the overall feasibility and demonstrate the capability to do these tasks shortly after landing and the full Egress Fitness study, which will be part of the CIPHER complement. This study uses a functional task approach to characterize performance of these high-risk tasks in long-duration ISS crewmembers before flight and shortly after return to Earth. Prior to any testing, each astronaut subject completes a suit fit check to ensure adequate sizing and mobility to be able to complete the EVA tasks. Pilot Egress Fitness pre-flight and post-flight testing includes an Earth based emergency egress out of a functional capsule mockup, and a short Mars gravity EVA simulation including suit donning, hatch egress, ladder descent, task board cable operations, baggage transfer over sand/rocky regolith, alignment with a rear entry port, and suit egress. Pre-flight testing can occur almost anytime pre-flight, but post-flight scheduling is much more critical with the capsule egress test occurring 1-4 hours after landing and the planetary EVA approximately 18-36 hours after landing. Data collected for both tasks includes task completion time, photo, and video. The EVA portion also includes collection of metabolic and heart rate. Pilot Egress Fitness study has completed baseline pre-flight testing on 3 astronaut subjects. Post-flight testing of the first two subjects will be completed in November 2021 and the final subject around March 2022. Results and lessons learned from this pilot study will inform the full Egress Fitness study, which will incorporate additional pre-flight sessions, longer EVA tasks, and post-flight testing on R+1, 4, and 7 to characterize the timeframe of recovery

J R Norcross↗
DOE OSTI2026

Interpretable Deep Learning for Advancing Field-Enhanced Catalysis

This DOE Early Career project developed a physics-informed, interpretable AI-and-modeling framework to understand and exploit electric-field effects in heterogeneous catalysis, with ammonia cracking and synthesis as a representative pathway. The team built and validated methods to map local electric fields on metal surfaces and nanoparticles, showing that low-coordination features (tips/edges/corners) can concentrate fields by several-fold relative to flat facets. Using DFT-generated datasets, the project created physics-guided machine learning models that rapidly predict local electric fields and field-dependent adsorption energetics with near-DFT accuracy while reducing computational cost by orders of magnitude. These predictions were integrated with microkinetic modeling to quantify how field-dipole interactions reshape reaction energetics and mechanisms, enabling large increases in predicted catalytic rates and substantial reductions in operating temperature under favorable field conditions. To accelerate discovery of earth-abundant catalysts, the project combined interpretable ML screening (with electronic-structure descriptors identified as key drivers) with a generative inverse-design workflow based on diffusion models and physics constraints. The resulting closed-loop approach, linking simulation, mechanistic modeling, and AI, provides reusable tools and datasets for designing catalysts and operating conditions in field-enhanced catalysis, with broad relevance to electrostatic catalysis, plasma catalysis, electrocatalysis, and other energy-related chemical transformations.

30 DIRECT ENERGY CONVERSION↗
NASA NTRSDate not supplied

Using Satellite Soil Moisture and Rainfall in the Landslide Hazard Assessment for Situational Awareness System

The Landslide Hazard Assessment for Situational Awareness system(LHASA)gives a global view of landslide hazard in nearly real time. Currently, it is being upgraded from version 1 to version 2, which entails improvements along several dimensions. These include the incorporation of new predictors, machine learning, and new event-based landslide inventories. As a result, LHASA version 2 substantially improves on the prior performanceand introduces a probabilistic element to the global landslide nowcast. Data from the soil moisture active-passive (SMAP) satellite has been assimilated into a globally consistent data product with a latency less than 3 days, known as SMAP Level 4. In LHASA, thesedata representthe antecedent conditions prior to landslide-triggering rainfall. In some cases, soil moisture may have accumulated over aperiod of many months. The model behind SMAP Level 4 also estimates the amount of snow on the ground, which is an important factor in some landslide events. LHASA also incorporates this information as an antecedent condition that modulates the response torainfall. Slope, lithology, and active faults were also used as predictor variables. These factors can have a strong influence on where landslides initiate.LHASA relies on precipitation estimates from the Global Precipitation Measurement mission to identify the locations where landslides are most probable. The low latency and consistent global coverage of these data make them ideal for real-time applications at continental to global scales. LHASA relies primarily on rainfall from the last 24 hours to spothazardous sites, which is rescaled by the local 99thpercentile rainfall.However, the multi-day latency of SMAP requires the use of a 2-day antecedent rainfall variable to represent the accumulation of rain between the antecedent soil moisture and current rainfall. LHASA merges these predictors with XGBoost, a commonly used machine-learning tool, relying on historical landslide inventories to develop the relationship between landslide occurrence and various risk factors. The resulting model relies heavily on current daily rainfall, but other factors also play an important role. LHASA outputsthe probability oflandslide occurrence ona grid of roughly one kilometer over all continents from 60 North to 60 South latitude. Evaluation over the period 2019-2020 showsthat LHASA version 2 doubles the accuracy of the global landslide nowcast without increasing the global false alarm rate. LHASA also identifies the areas where the human exposure to landslide hazard is most intense. Landslide hazard is divided into 4 levels: minimal, low, moderate, and high. Next, the number of persons and the length of major roads (primary and secondary roads)within each of these areas is calculated for every second-level administrative district (county). These results can be viewedthrough a web portal hosted at the Goddard Space Flight Center. In addition, users can download daily hazard and exposure data.LHASAversion 2uses machine learning and satellite data to identify areas of probable landslide hazard within hours of heavy rainfall. Itsglobal maps are significantly more accurate, and it now includes rapid estimates of exposed populations and infrastructure. In addition, a forecast mode will be implemented soon.

Thomas Stanley↗
DOE OSTI2025

Projected increases in tropical cyclone-induced U.S. electric power outage risk

Abstract While power outages caused by tropical cyclones (TCs) already pose a great threat to coastal communities, how—and why—these risks will change in a warming climate is poorly understood. To address this need, we develop a robust machine learning model to capture TC-induced power outage risk. When applied to 900 000 synthetic TCs downscaled from simulated historical and future climate conditions under a strong warming scenario, we find outage risk in the United States and Puerto Rico is expected to increase broadly by the end of the century, with some states seeing increases of 60% and higher. Further, we discover that rising rainfall rates will play an increasingly important role in TC-induced power outage risk as the climate changes, explaining more than 50% of the projected change in risk in some regions. These insights are important for guiding decision-makers in their future outage risk investment and mitigation plans.

Grid Resilience↗
DOE OSTI2021

Chapter 4: What We Can Learn from Measuring Metabolic Fluxes in Cyanobacteria

Cyanobacteria with the capability of oxygen-evolving photosynthesis play a vital role in the global carbon, oxygen, and nitrogen cycles. From a biochemical perspective, all phenotypic traits and functions of cyanobacteria are derived from the potential of their metabolism and mirrored in metabolic fluxes through an integrated metabolic network. Metabolic flux, the rate of turnover of molecules through a metabolic pathway, is therefore of great importance for an in-depth understanding of the role of cyanobacteria in the biosphere. Recent interest in cyanobacteria metabolic fluxes is also motivated by the prospect to utilize their light-driven CO2 fixation for sustainable production of valuable chemicals and biofuels. Valorization of cyanobacterial metabolism will require engineering of the native metabolic network - a challenge that can benefit from a quantitative understanding of metabolic reactions taking place intracellularly. In this chapter, we will discuss some intriguing questions relevant to metabolic fluxes in cyanobacteria: How are metabolic fluxes predicted or measured? What do we know about the fluxome inside various cyanobacteria thus far? How are they different between strains as well as in different conditions? And how can we use fluxomics information to guide metabolic engineering and synthetic biology? This chapter will highlight updated knowledge on cyanobacterial metabolism. Specifically, we will focus on providing readers a quantitative vision to understand how this photosynthetic model works.

BASIC BIOLOGICAL SCIENCES,INORGANIC, ORGANIC, PHYS↗
DOE OSTI2020

The Spatiotemporal Evolution of Granular Microslip Precursors to Laboratory Earthquakes

Laboratory earthquake experiments provide important observational constraints for our understanding of earthquake physics. Here we leverage continuous waveform data from a network of piezoceramic sensors to study the spatial and temporal evolution of microslip activity during a shear experiment with synthetic fault gouge. We combine machine learning techniques with ray theoretical seismology to detect, associate, and locate tens of thousands of microslip events within the gouge layer. Microslip activity is concentrated near the center of the system but is highly variable in space and time. While microslip activity rate increases as failure approaches, the spatiotemporal evolution can differ substantially between stick-slip cycles. These results illustrate that even within a single, well-constrained laboratory experiment, the dynamics of earthquake nucleation can be highly complex.

58 GEOSCIENCES↗
DOE OSTI2025

Dynamic in-context learning with conversational models for data extraction and materials property prediction

The advent of natural language processing and large language models (LLMs) has revolutionized the extraction of data from unstructured scholarly papers. However, ensuring data trustworthiness remains a significant challenge. In this paper, we introduce PropertyExtractor, an open-source tool that leverages advanced conversational LLMs such as Google gemini-pro and OpenAI gpt-4, blends zero-shot with few-shot in-context learning, and employs engineered prompts for the dynamic refinement of structured information hierarchies—enabling autonomous, efficient, scalable, and accurate identification, extraction, and verification of material property data. Our tests on material data demonstrate precision and recall that exceed 95% with an error rate of ∼9%, highlighting the effectiveness and versatility of the toolkit. Finally, databases for 2D material thicknesses, a critical parameter for device integration, and energy bandgap values are developed using PropertyExtractor. In particular, for the thickness database, the rapid evolution of the field has outpaced both experimental measurements and computational methods, creating a significant data gap. Our work addresses this gap and showcases the potential of PropertyExtractor as a reliable and efficient tool for the autonomous generation of various material property databases, advancing the field.

Ekuma, Chinedu E. (ORCID:0000000258527556)↗
DOE OSTI2022

Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted sum optimization problems in data processing and machine learning and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance, and identify the most effective approximation depths for quantum add and quantum multiply within the given context. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze performance trends in our results and speculate on possible future development within this computational paradigm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Addressing the Split Incentive Challenge for Enhanced Solar Adoption in Multifamily Rental Properties [Abstract]

The split incentive problem is particularly pronounced in rental markets, where landlords prioritize investments that directly increase property value or rental income. Since energy savings from solar photovoltaic (PV) systems primarily benefit tenants, landlords may perceive little return on investment unless mechanisms exist to recapture some of the financial gains. The primary objective of this project is to develop a publicly available, web-based tool to analyze the U.S. Department of Energy’s ResStock database, which models the U.S. residential building stock. The tool allows users to filter buildings by location, type, HVAC system, square footage, and other characteristics, and outputs typical electric load profiles. By leveraging location-specific electric load data, Fram Energy aims to advance business strategies that address the split incentive barrier and promote the adoption of solar PV installations in rental properties. In addition, a machine learning model will be developed to weigh the marginal contribution of building features across the dataset in predicting electricity demand, supporting guided decision making in forecasting electric load profiles. Lastly, based on each building’s location, load profile, and utility’s electricity rate, an optimized solar photovoltaic array and battery energy storage system will be sized to provide energy arbitrage opportunities.

14 SOLAR ENERGY↗
DOE OSTI2024

Depot Charging Schedule Optimization for Medium- and Heavy-Duty Battery-Electric Trucks

Charge management, which lowers charging costs for fleets and prevents straining the electrical grid, is critical to the successful deployment of medium- and heavy-duty battery-electric trucks (MHD BETs). This study introduces an energy demand and cost management framework that optimizes depot charging for MHD BETs by combining an energy consumption machine learning model and a linear program optimization model. The framework considers key factors impacting real-world MHD BET operations, including vehicle and charger configurations, duty cycles, use cases, geographic and climate conditions, operation schedules, and utilities’ time-of-use (TOU) rates and demand charges. The framework was applied to a hypothetical fleet of 100 MHD BETs in California under three different utilities for 365 days, with results compared to unmanaged charging. The optimized charging solution avoided more than 90% of on-peak charging, reduced fleet charging peak load by 64–75%, and lowered fleet energy variable costs by 54–64%. This study concluded that the proposed charge management framework significantly reduces energy costs and peak loads for MHD BET fleets while making recommendations for fleet electrification infrastructure planning and the design of utility TOU rates and demand charges.

Song, Shuhan↗
NASA NTRS2002

Advanced Metallic Thermal Protection System Development

A new Adaptable, Robust, Metallic, Operable, Reusable (ARMOR) thermal protection system (TPS) concept has been designed, analyzed, and fabricated. In addition to the inherent tailorable robustness of metallic TPS, ARMOR TPS offers improved features based on lessons learned from previous metallic TPS development efforts. A specific location on a single-stage-to-orbit reusable launch vehicle was selected to develop loads and requirements needed to design prototype ARMOR TPS panels. The design loads include ascent and entry heating rate histories, pressures, acoustics, and accelerations. Additional TPS design issues were identified and discussed. An iterative sizing procedure was used to size the ARMOR TPS panels for thermal and structural loads as part of an integrated TPS/cryogenic tank structural wall. The TPS panels were sized to maintain acceptable temperatures on the underlying structure and to operate under the design structural loading. Detailed creep analyses were also performed on critical components of the ARMOR TPS panels. A lightweight, thermally compliant TPS support system (TPSS) was designed to connect the TPS to the cryogenic tank structure. Four 18-inch-square ARMOR TPS panels were fabricated. Details of the fabrication process are presented. Details of the TPSS for connecting the ARMOR TPS panels to the externally stiffened cryogenic tank structure are also described. Test plans for the fabricated hardware are presented.

Blosser, M. L.↗
DOE OSTI2023

Battery Charge Curve Prediction via Feature Extraction and Supervised Machine Learning

Real-time onboard state monitoring and estimation of a battery over its lifetime is indispensable for the safe and durable operation of battery-powered devices. In this study, a methodology to predict the entire constant-current cycling curve with limited input information that can be collected in a short period of time is developed. A total of 10 066 charge curves of LiNiO 2 -based batteries at a constant C-rate are collected. With the combination of a feature extraction step and a multiple linear regression step, the method can accurately predict an entire battery charge curve with an error of < 2% using only 10% of the charge curve as the input information. The method is further validated across other battery chemistries (LiCoO 2 -based) using open-access datasets. The prediction error of the charge curves for the LiCoO 2 -based battery is around 2% with only 5% of the charge curve as the input information, indicating the generalization of the developed methodology for predicting battery cycling curves. The developed method paves the way for fast onboard health status monitoring and estimation for batteries during practical applications.

25 ENERGY STORAGE↗
DOE OSTI2025

A hybrid neural architecture: Online attosecond x-ray characterization

The emergence of high-repetition-rate x-ray free-electron lasers (XFELs), such as SLAC’s LCLS-II, serves as our canonical example for autonomous controls that necessitate high-throughput diagnostics paired with streaming computational pipelines capable of single-shot analysis with extremely low latency. We present the deterministic characterization with an integrated parallelizable hybrid resolver architecture, a hybrid machine learning framework designed for fast, accurate analysis of XFEL diagnostics using angular streaking-based sinogram images. This architecture integrates convolutional neural networks and bidirectional long short-term memory models to denoise input, identify x-ray sub-spike features, and extract sub-spike relative delays with sub-30 attosecond temporal resolution. Deployed on low-latency hardware, it achieves over 10 kHz throughput with 168.3 μs inference latency, indicating scalability to 14 kHz with field-programmable gate array integration. By transforming regression tasks into classification problems and leveraging optimized error encoding, we achieve high precision with low-latency performance that is critical for real-time streaming event selection and experimental control feedback signals. This represents a key development in real-time control pipelines for next-generation autonomous science, generally, and high repetition-rate x-ray experiments in particular.

Accelerator Physics (physics.acc-ph)↗
DOE OSTI2026

The Hydropower Game: An Interactive Learning Tool for the Future Hydropower Workforce

This report documents a Seedling project supported by the U.S. Department of Energy (DOE) Water Power Technologies Office (WPTO), conducted by Argonne National Laboratory (ANL) and the National Laboratory of the Rockies (NLR). The Seedling and Sapling Program provides small grants over short duration to enable early-stage research at national laboratories. This funding mechanism is intended to cultivate innovative ideas and expand research road maps in hydropower and marine energy technologies. Under this Seedling award, the project team developed an educational outreach tool, or “serious game”, built in Python and powered by the Pygame library, aimed at teaching fundamental hydropower concepts through an engaging, interactive learning experience. The game features multiple lessons covering several hydropower topics while allowing for expansion and customization in the instance of future funding availability: • Hydropower Plant Types: Players explore and compare the mechanics and applications of run-of-river, dam hydropower, and pumped-storage hydropower. • Flow Dynamics and Power Generation: Interactive tasks demonstrate how release rate and hydraulic head combine to determine power output. • Grid Operations and Load Following: Simulations illustrate how hydropower facilities respond to fluctuating electricity demand to balance the grid. • Market Integration: Levels scaffold understanding of how hydropower interfaces with the broader energy market, including operational and economic considerations. The tool was showcased at several science, technology, engineering, and mathematics (STEM) outreach events, where it was demoed to students, educators, and the general public. These events provided valuable opportunities to collect feedback on the gameplay, storyline, and educational objectives from a wide audience. The game was presented at STEMapalooza, Introduce a Girl to Engineering Day, STEMCON, and Clean Currents 2025. Insights gathered during these demonstrations informed refinements to the game’s user experience and strengthened its effectiveness as an educational tool for teaching hydropower concepts. This report outlines the game’s design philosophy, educational objectives, technical implementation, user experience insights, and potential for broader deployment within educational and workforce development contexts. It emphasizes how gamified learning can demystify complex hydropower science and inspire interest in water-power technologies. The project’s success demonstrates the value of Seedling funding in fostering creative, lowcost educational tools that support DOE’s mission to advance energy literacy and innovation. The report concludes with recommendations for expanding the tool by adding new levels, integrating assessment metrics, and exploring commercialization or deployment pathways through future Sapling funding. The official webpage of the Hydropower Game, which includes a link to the educational tool, can be accessed at www.anl.gov/hydropower/hydropower-game.

13 HYDRO ENERGY↗
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗