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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

The feasibility study and evaluation of applying expert system techniques to the mission operations for the AXAF-I spacecraft

Advanced X-ray Astrophysics Facility - Imaging (AXAF-I) is a spacecraft for X-ray emitting sources observation and has been tentatively scheduled for a space shuttle launch in late 1998 at the Kennedy Space Center. Its main objectives are 'to determine the nature of astronomical objects ranging from normal stars to quasars, to understand the nature of the physical processes which take place in and between astronomical objects, and to add to our understanding of the history and evolution of the universe.' The AXAF-I will have an expected five year life time for the science mission phase. During the science mission phase, the monitoring and management operation of the flight and ground systems is personnel intensive, requiring system experts on duty around the clock. The purpose of the expert system presented in this report is intended to reduce the level of expertise, training, and personnel requirement for the mission operation. The telemetry data from the spacecraft can be divided into two categories: the science observation data and the engineering status data. The science data contains the outputs from the X-ray sensing devices and will be forwarded to the AXAF-I Science Center for interpretation; while the engineering status data will be monitored by the Operation Control Center (OCC) for the operation diagnosis of the spacecraft. The expert system is designed to assist the operation controllers at the OCC to perform the daily mission operations. Since there are hundreds of engineering telemetry data points and the interpretation of the telemetry depends on many factors, e.g., sun or eclipse, the monitoring of the AXAF-I is not a trivial task. In this phase of expert system development, the focus has been limited to the engineering data interpretation, i.e., warnings will be provided to the operation controllers to signal any anomaly. The system is hosted in a Silicon Graphics Indigo-2 workstation running the IRIX operating system. The expert system tool used is the G2 system from Gensym (Gensy).

Chang, Kai H.↗
DOE OSTI2026

Impacts of A‐Site Composition on the Cation Dissolution‐Mediated Surface Restructuring of Layered Nickelate Oxide Electrocatalysts During Alkaline Oxygen Evolution Reaction

The oxygen evolution reaction (OER) is a key anodic counter‐reaction for electrochemical production of fuels and chemicals. It is hindered by sluggish four‐electron transfer kinetics requiring highly oxidative operating potentials to achieve commercially relevant rates. NiFeO x H y electrocatalysts are among the most promising for OER in alkaline electrolytes. The Ni(OH) 2 /NiOOH redox couple has been reported as the active phase in Ni‐based electrocatalysts; however, its activity is often hindered by deactivation arising from the formation of OER‐inactive insulating species. Limited strategies exist for mitigating this deactivation. This study aims to address this by interrogating the evolution of OER active sites as a function of precatalyst composition and structural properties using a series of layered, crystalline Ni‐based Ruddlesden–Popper (RP) oxides (A 2 NiO 4+δ ). In situ evolution of the active NiO x H y surface is probed through Ni‐site OER turnover frequency analysis, and electrochemical impedance spectroscopy coupled with scanning transmission electron microscopy. We show that the stability of layered nickelate oxide electrocatalysts is governed by the dynamic competition between cation dissolution and Ni‐site reversibility, which can be tuned through the A‐site composition of RP oxides. These findings yield insights toward engineering OER oxide precatalysts that optimize the stability of in situ‐generated OER active phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2006

From Prime to Extended Mission: Evolution of the MER Tactical Uplink Process

To support a 90-day surface mission for two robotic rovers, the Mars Exploration Rover mission designed and implemented an intensive tactical operations process, enabling daily commanding of each rover. Using a combination of new processes, custom software tools, a Mars-time staffing schedule, and seven-day-a-week operations, the MER team was able to compress the traditional weeks-long command-turnaround for a deep space robotic mission to about 18 hours. However, the pace of this process was never intended to be continued indefinitely. Even before the end of the three-month prime mission, MER operations began evolving towards greater sustainability. A combination of continued software tool development, increasing team experience, and availability of reusable sequences first reduced the mean process duration to approximately 11 hours. The number of workshifts required to perform the process dropped, and the team returned to a modified 'Earth-time' schedule. Additional process and tool adaptation eventually provided the option of planning multiple Martian days of activity within a single workshift, making 5-day-a-week operations possible. The vast majority of the science team returned to their home institutions, continuing to participate fully in the tactical operations process remotely. MER has continued to operate for over two Earth-years as many of its key personnel have moved on to other projects, the operations team and budget have shrunk, and the rovers have begun to exhibit symptoms of aging.

mission operations↗
NASA NTRS2006

From Prime to Extended Mission: Evolution of the MER Tactical Uplink Process

To support a 90-day surface mission for two robotic rovers, the Mars Exploration Rover mission designed and implemented an intensive tactical operations process, enabling daily commanding of each rover. Using a combination of new processes, custom software tools, a Mars-time staffing schedule, and seven-day-a-week operations, the MER team was able to compress the traditional weeks-long command-turnaround for a deep space robotic mission to about 18 hours. However, there was never an intention of maintaining the pace of this process indefinitely. Even before the end of the three-month prime mission, MER operations began evolving towards greater sustainability. A combination of continued software tool development, increasing team experience, and availability of reusable sequences first reduced the mean process duration to approximately 11 hours. The number of workshifts required to perform the process dropped, and the team returned to a modified 'Earth-time' schedule. Additional process and tool adaptation eventually provided the option of planning multiple Martian days of activity within a single workshift, making 5- day-a-week operations possible. The vast majority of the science team returned to their home institutions, continuing to participate fully in the tactical operations process remotely. MER has continued to operate for over two Earth-years as many of its key personnel have moved on to other projects, the operations team and budget have shrunk, and the rovers have begun to exhibit symptoms of aging.

Mars exploration↗
NASA NTRS2018

CubeX: A Compact X-Ray Telescope Enables Both X-Ray Fluorescence Imaging Spectroscopy and Pulsar Timing Based Navigation

This paper describes the benefits of a miniaturized X-ray telescope payload in the context of a lunar mission. The first part describes the payload in detail, the second part summarizes a small satellite mission concept that utilizes its compact form factor and performance. The CubeX instrument can be used for both X-ray fluorescence (XRF) imaging spectroscopy and X-ray pulsar timing based navigation (XNAV). Using our recent technological advances in X-ray optics and sensors, CubeX combines high angular resolution (<1 arcminutes) Miniature Wolter-I X-ray optics (MiXO) with a common focal plane consisting of high spectral resolution (<150 eV at 1 keV) CMOS X-ray sensors and a high timing resolution (< 1 usec) SDD X-ray sensor. This novel combination of the instruments enables both XRF measurements and XNAV operations without moving parts. The high angular resolution of the MiXO opens a wide range of orbital configurations for observation. Given that performance, the instrument has unprecedented small volume (~1×1×6U), mass (<6 kg), and power (<9W) requirements and opens a wide range of applications for a variety of targets and missions including NEOs and Martian moons. In this paper we illustrate one potential application for a lunar mission concept: The elemental composition of the Moon holds keys to understanding the origin and evolution of both the Moon and the Earth. X-ray fluorescence (XRF), induced either by solar X-ray flux or energetic ions, carries decisive signatures of surface elemental composition. X-ray observations, therefore, give a unique, powerful diagnostic tool for remotely determining elemental abundances including major rock forming elements such as Mg, Al, Na, Si, Fe, and Ca. Through high-resolution XRF imaging spectroscopy, CubeX searches for small patches of elusive lower crust and mantle material excavated within and around impact craters. CubeX identifies regional compositional variations and allows straightforward comparison of elemental distributions with the surface topography from LRO and the gravity data from GRAIL. The elemental compositions of the lower crust and the mantle are sensitive to the conditions of the giant impact which led to the Moon's formation and the subsequent lunar magma ocean (LMO), and thus they are key missing pieces in understanding the formation and early evolution of the Moon. In between XRF observations, CubeX also leverages the technology of high resolution X-ray imaging and time series measurements to conduct XNAV operations and evaluate their performance. Deep space navigation is a critical issue for small planetary missions. XNAV can enable low-cost autonomous deep-space navigation, and has the potential to greatly assist, or even outperform, NASA's Deep Space Network (DSN) or ESA's European Space Tracking (ESTRACK). CubeX is designed to perform sequential observations of 3-4 millisecond pulsars (MSPs) to solve the spacecraft trajectory for absolute navigation, and explore the remote sensing capability of XNAV. In the presented mission concept, the Moon's relative proximity enables a straightforward evaluation of the XNAV performance through DSN.

x-ray spectroscopy↗
DOE OSTI2026

Science Uses Deployment Operations-Advanced Wireless: Exploring Open Radio Access Network Technologies for Energy Science

Open Radio Access Network is emerging as a solution to the increasing demand for more flexible, cost-effective, and advanced mobile network infrastructures. This evolution is driven by advancements in wireless technologies and the growing complexity of deploying and managing these networks. O-RAN represents a significant shift in wireless technology, building upon the 3rd Generation Partnership Project framework to foster openness, flexibility, and interoperability. By decoupling hardware and software components, Open Radio Access Network enables a multi-vendor ecosystem that encourages innovation and diverse solutions. Open Radio Access Network's potential extends beyond traditional wireless applications, with growing interest in its role in advancing energy systems, particularly in the context of smart grids, microgrids, and the integration of renewable energy sources. While the role of open-wireless technologies in driving energy transformation is increasingly recognized, further exploration is needed. Vendors and utilities are investigating how Open Radio Access Network technologies can optimize energy use cases and improve the performance of 5G and beyond applications. This report outlines efforts under the Science Uses Deployment Operations Advance Wireless project, a collaboration between the National Laboratory of the Rockies' Cybersecurity Research Center, Argonne National Laboratory, Lawrence Berkeley National Laboratory, and the Department of Energy's Energy Science Network research and operations staff. The focus of this project is on due diligence, through testing and evaluation, preparing for the deployment of advanced wireless infrastructure for scientific use cases, with an emphasis on Open Radio Access Network technology, its components, integrations, and its ability to support vertical stack application across the energy sector. Additionally, the report highlights the value cases for utilities, underscoring how adopting open wireless standards can accelerate the evolution of energy systems, foster innovation, and improve the integration of critical energy technologies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2019

Effectiveness of Redundant Communications Systems in Maintaining Operational Control of Small Unmanned Aircraft

NASA has been researching prototype technologies for an Unmanned Aircraft System (UAS) Traffic Management (UTM) system to facilitate enabling of safe and efficient civilian low-altitude airspace and UAS operations, in a series of Technical Capability Levels (TCL) activities that are increasingly complex. In TCL1, completed in 2015, visual line-of-sight operations such as agriculture, firefighting and infrastructure monitoring were addressed with a focus on geofencing and operations scheduling. Technologies and requirements needed for beyond visual line-of-sight (BVLOS) operations in sparsely populated areas were examined in TCL2 in 2016, and those for operations over moderately populated areas in TCL3 in 2017 and 2018. TCL4 will build on the earlier TCLs and focus on technologies and requirements for operations in higher-density urban areas for tasks such as news gathering, package delivery and for managing large-scale contingencies. This paper describes a communications test conducted in TCL3 and discusses insights gained from the test. In the test, operators were directed to equip UAS with redundant Command and Control (C2) communications systems, send a maneuver command to Unmanned Aircraft (UA) via the primary system, then verify execution of the sent command. This exercise was repeated with each redundant system. The test was designed to assess effectiveness of redundant C2 systems in maintaining operational control of UA. Several UAS were configured with varying arrangements to achieve redundancy, including two identical radio modems using the same frequency band, WiFi and Long-Term Evolution (LTE) cellular modems, etc. From the test, digital data such as time maneuver command sent, time maneuver verified, etc., were collected. Descriptions of methods to detect loss of C2 communications and contingency steps for such event were collected and assessed. The final paper will include a detailed analysis of the collected data leading to the following insights. First, effectiveness of redundant C2 systems depends on several factors, such as operational environment and communications service availability. For example, use of two identical point-to-point radio to connect operator and UA on the same frequency band can be effective in mitigating radio malfunction when operating in an environment where possibility of Radio Frequency (RF) interference is low, such as over open plains. However, the same arrangement may not be effective where high level of RF transmissions in broad spectrum ranges can be expected, such as over or near urban areas. For redundant systems that consist of external communications services, such as cellular and satellite communications network, redundancy is maintained only in the areas where more than one services are available. Therefore, UAS operators should have the means to plan for and monitor the performance of external communications services they are relying on to control UA. Second, communications performance needs, such as the minimum data transfer rate and the maximum tolerable latency, should be assessed to reflect the potential hazard that can come from loss of UA control. For example, UA operations over desolate area pose less hazard to people than operations over densely populated area and performance need for the former would be less than the latter.

Jung, Jaewoo↗
NASA NTRS2017

Transforming Satellite Data into Weather Forecasts

A NASA project spans the gap between research and operations, introducing new composites of satellite imagery to weather forecasters to prepare for the next generation of satellites. Satellite imagery has been an immense benefit to weather forecasters. With it, they can assess aviation hazards such as low clouds, monitor thunderstorms, and track the evolution of dust plumes. Satellite sensors are continually evolving to provide ever greater imaging capabilities, and researchers continue to develop advanced techniques to identify hazards in satellite imagery. However, barriers can prevent experimental products from reaching forecasters in the operational environment. A NASA project has developed an interactive process whereby weather forecasters learn to interpret the latest satellite imagery and apply it to their operations. Forecasters then provide feedback to the researchers who are developing algorithms and products to further improve future products. This effort has taken on greater importance with the anticipated launch of a new series of satellites that will provide substantially greater amounts of data than are currently available.

Emily Berndt↗
DOE OSTI2019

Capacitance-Based Dimensional Change Sensors for In-Pile Materials Measurements

Advanced fuel compositions, such as accident tolerate fuels (ATF), are an active area of developing in the nuclear power industry. The long-term performance of these newly developed fuels is estimated through physics-based simulation models of irradiation-, temperature-, pressure-, etc.-induced material degradation. As these fuels are deployed in test reactors, measurement and characterization of the fuel pin evolution is used to validate prediction models. In-pile material evolution parameters, such as fuel rod pressurization, fuel stack and cladding elongation, and cladding diameter, are commonly measured using a linear voltage differential transformer (LVDT). However, LVDTs are bulky and limited to lower (350-500C) temperature operation. The high power density and small size of most experimental positions in high performance research reactors used for accelerated materials irradiation studies generally precludes the use of LVDTs in these reactors. There is a critical need for sensors that provide real-time data regarding material evolution under highly accelerated irradiation. These sensors would ideally have a small profile and the ability to withstand irradiation at extremely high dose rates and temperatures for extended periods of time. A capacitance-based sensor is currently under development at the University of Tennessee to provide a direct measurement of in-pile dimensional change during irradiation. Sensor response was simulated using AutoCAD Electromagnetic field simulator (EMS) for a variety of sensor materials and configurations and fuel pin swelling conditions. Initial results of these simulations are summarized and areas of ongoing research and development are discussed.

Naughton, Tyler↗
NASA NTRS2005

Increasing the Automation and Autonomy for Spacecraft Operations with Criteria Action Table

The Criteria Action Table (CAT) is an automation tool developed for monitoring real time system messages for specific events and processes in order to take user defined actions based on a set of user-defined rules. CAT was developed by Lockheed Martin Space Operations as a part of a larger NASA effort at the Goddard Space Flight Center (GSFC) to create a component-based, middleware-based, and standard-based general purpose ground system architecture referred as GMSEC - the GSFC Mission Services Evolution Center. CAT has been integrated into the upgraded ground systems for Tropical Rainfall Measuring Mission (TRMM) and Small Explorer (SMEX) satellites and it plays the central role in their automation effort to reduce the cost and increase the reliability for spacecraft operations. The GMSEC architecture provides a standard communication interface and protocol for components to publish/describe messages to an information bus. It also provides a standard message definition so components can send and receive messages to the bus interface rather than each other, thus reducing the component-to-component coupling, interface, protocols, and link (socket) management. With the GMSEC architecture, components can publish standard event messages to the bus for all nominal, significant, and surprising events in regard to satellite, celestial, ground system, or any other activity. In addition to sending standard event messages, each GMSEC compliant component is required to accept and process GMSEC directive request messages.

Li, Zhen-Ping↗
DOE OSTI2023

Wind Turbine Generator Reliability Analysis to Reduce Operations and Maintenance (O&M) Costs

Wind turbine major systems (blades, pitch, main bearing, gearbox, and generator) are integrated into a composite system. Specifications for these systems and components are developed to achieve symmetry of operation, avoiding negative interaction. For instance, the main bearing, gearbox, and generator (drivetrain) components are interdependent, functioning in unison for efficient energy production. Hence, wind resource and grid interactions affecting the drivetrain impact the performance and reliability of the turbine generator. This paper discusses generator reliability covering the technology evolution over the last 20 years. EPRI's Wind Network for Enhanced Reliability (WinNER) web-based tool and Shermco Industries databases are presented, and conclusions are drawn regarding failures specific to generator design, manufacturing, and operating conditions. Additionally, this paper compares the life expectancy of stator-fed configurations and doubly fed generator systems.

17 WIND ENERGY↗
NASA NTRS2018

Marrying Social Media Approaches and Space Flight Control: Eight Years at SpaceOps

Three previous SpaceOps papers [1-3] - published in 2010, 2012 (honored by the Conference as a "Best Paper"), and 2014 - have discussed paths to using social media concepts and techniques to enhance space flight controller effectiveness by a) reducing clutter of nonverbal communications (e.g., visual flow with minimal headers and shared content instead of multiple copies), b) moving some voice communication to non-verbal transmission (virtually eliminating "say again" requests because non-verbal comm can be re-read), thus making remaining voice comm easier to focus on, and c) reducing short-term and long-term flight stress on flight control personnel. This paper shows how Marshall Space Flight Center's (MSFC) ISS Payload Operations Integration Center (POIC) is realizing the above goals via the Communications Dashboard (CommDash) software suite deployed in 2017 (including enhancements to the Console Log Tool (CoLT) discussed in earlier papers). Two larger-scope benefits spawned by CommDash evolution are also chronicled: a) emergence of an Agile Software Development (ASD) process adapted to the not-always-nimble environment of government projects, and b) the sprouting of a Human Factors Engineering (HF or HFE) community of practice within MSFC's Payload and Mission Operations Division (PMOD).

Scott, David W.↗
NASA NTRS1993

Satellite observations of a polar low over the Norwegian Sea by Special Sensor Microwave Imager, Geosat, and TIROS-N Operational Vertical Sounder

Many polar lows are generated at the boundary between sea ice and the ocean, in regions of large temperature gradients, where in situ observations are rare or nonexistent. Since satellite observations are frequent in high-latitude regions, they can be used to detect polar lows and track their propagation and evolution. The Special Sensor Microwave/Imager (SSM/I) providing estimates of surface wind speed, integrated cloud liquid water content, water vapor content, and precipitation size ice-scattering signal over the ocean; the Geosat radar altimeter measuring surface wind speed and significant wave height; and the TIROS-N Operational Vertical Sounder (TOVS) allowing the determination of temperature and humidity profiles in the atmosphere have been used in synergy for a specific case which occurred in the Norwegian Sea on January, 23-24 1988. All three instruments show sharp atmospheric gradients associated with the propagation of this low across the ocean, which permit the detection of the polar low at a very early stage and tracking it during its development, propagation, and decay. The wind speed gradients are measured with good qualitative agreement between the altimeter and SSM/I. TOVS retrieved fields prior to the formation of the low confirm the presence of an upper level trough, while during the mature phase baroclinicity can be observed in the 1000-500 hPa geopotential thicknesses.

Claud, Chantal↗
DOE OSTI2023

Pathways Toward Efficient and Durable Anion Exchange Membrane Water Electrolyzers Enabled By Electro‐Active Porous Transport Layers

Abstract Green hydrogen, produced via water electrolysis using renewable electricity, will play a crucial role in decarbonizing industrial and heavy‐duty transportation sectors. Anion exchange membrane water electrolyzers (AEMWEs) can overcome many of the performance and cost limitations of incumbent technologies, however, still suffer from durability challenges due to oxidative instability of anion‐exchange ionomers. Herein, the use of an electro‐active porous transport layer as anode (PTL‐electrode) is demonstrated to enable efficient and durable AEMWEs. The stainless‐steel PTL‐electrodes are shown to have superior performance and durability compared to traditional catalyst layers containing ionomer and nanoparticle catalysts. An AEMWE cell operating at 2 A cm −2 for over 600 h exhibited a degradation rate of just 5 µV h −1 . During operation, the surface composition of the stainless steel transforms into a mixture of iron and nickel oxyhydroxides, contributing to enhanced oxygen‐evolution reaction activity. The combination of experimental work and modeling elucidates how the bulk structure of the PTL‐electrode offers an additional design dimension to further improve electrolyzer performance. Lastly, a surface modification strategy is applied to a PTL‐electrode to achieve an even higher performing AEMWE (2.3 vs 2.0 A cm −2 at 1.8 V). Overall, this work lays out pathways toward more efficient, durable, and affordable AEMWEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Cosmological moduli and non-perturbative production of axions

Cosmological moduli generically come to dominate the energy density of the early universe, and thereby trigger an early matter dominated era. Such non-standard cosmological histories are expected to have profound effects on the evolution and production of axion cold dark matter and dark radiation, as well as their prospects for detection. We consider moduli-axion couplings and investigate the early history of the coupled system, considering closely the evolution of the homogeneous modulus field, the back-reaction from the axion, and the energy densities of the two fields. A particular point of interest is the enhancement of axion production from modulus decay, due to tachyonic and parametric resonant instabilities, and the implications of such production on the cosmological moduli problem, axion dark radiation, and the available parameter space for axion dark matter. Using an effective field theory approach, WKB-based semi-analytical analysis, and detailed numerical estimates of the co-evolution of the system, we evaluate the expected decay efficiency of the modulus to axions. The effects of higher-order operators are studied and implications for UV-complete frameworks such as the Large Volume Scenarios in Type IIB string theory are considered in detail.

Axions and ALPs↗
DOE OSTI2022

Effect of fuel composition and EGR on spark-ignited engine combustion with LPG fueling: Experimental and numerical investigation

This paper presents an experimental and numerical investigation of a spark-ignited (SI) cooperative fuel research (CFR) engine fueled with different liquefied petroleum gas (LPG) fuels and exhaust gas recirculation (EGR). Here, the effects of LPG fuel composition on engine combustion characteristics are initially evaluated at two different compression ratios (CR). Results show normal combustion at CR 7 and heavy knocking combustion at CR 10 for all the tested fuels, with a more substantial impact for the LPG fuel with high proportions of n-butane species. The Livengood-Wu (LW) integral method is then used to analyze the knock occurrence risk of individual fuel based on the reactivity of the tested fuels. The introduction of EGR then demonstrates the potential of knock intensity reduction below the borderline knock limit. A zonal-based kinetic interactions study is also performed to understand the knock mitigation effectiveness of EGR over the pressure–temperature domain relevant to SI engine operation. Finally, a multidimensional, computational fluid dynamics (CFD) simulation model is shown to predict the LPG combustion characteristics and presents the evolution of in-cylinder temperature and chemical species to demonstrate the development of end-gas autoignition events without and with EGR.

02 PETROLEUM↗
DOE OSTI2025

X-ray Micro-Computed Tomography for Structural Analysis of All-Solid-State Battery at Pouch Cell Level

Characterizing the microstructure of all-solid-state batteries (ASSBs) during fabrication and operation is vital for their advancement, particularly as scaling to pouch cell levels introduces challenges in probing large-scale microstructural evolution. This work highlights the potential of synchrotron X-ray micro-computed tomography (sXCT) as a nondestructive, rapid (<30 min), and high-resolution technique for visualizing and quantifying key microstructural features, including overhang, porosity, contact loss, active surface area, and tortuosity, in all-solid-state pouch cells. The large field of view (up to millimeters) of sXCT enables detailed analysis at an industry-relevant scale, bridging the gap between laboratory research and commercial applications. Furthermore, integrating realistic sXCT-derived 3D models into multiphysics simulations could provide insights into chemo-mechanical degradation, particularly at the edges of the pouch cells, offering a pathway for designing robust, high-performance ASSBs. This perspective establishes sXCT as an indispensable tool for advancing both the understanding and the engineering of next-generation energy storage systems.

25 ENERGY STORAGE↗
DOE OSTI2021

Nonuniqueness of generalized quantum master equations for a single observable

When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does not always need to be achieved through projections-one can also use conservation laws for this purpose. Such an operation should be considered as distinct from any kind of projection; that is, projection onto a single observable yields a different form of master equation compared to that resulting from a projection followed by the application of a constraint. Here, we give a simple example to show this point and give relationships that the different memory kernels must satisfy to yield the same dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗