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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

A Comparative Study of Probability Collectives Based Multi-agent Systems and Genetic Algorithms

We compare Genetic Algorithms (GA's) with Probability Collectives (PC), a new framework for distributed optimization and control. In contrast to GA's, PC-based methods do not update populations of solutions. Instead they update an explicitly parameterized probability distribution p over the space of solutions. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. The PC approach works in both continuous and discrete problems. It does not suffer from the resolution limitation of the finite bit length encoding of parameters into GA alleles. It also has deep connections with both game theory and statistical physics. We review the PC approach using its motivation as the information theoretic formulation of bounded rationality for multi-agent systems. It is then compared with GA's on a diverse set of problems. To handle high dimensional surfaces, in the PC method investigated here p is restricted to a product distribution. Each distribution in that product is controlled by a separate agent. The test functions were selected for their difficulty using either traditional gradient descent or genetic algorithms. On those functions the PC-based approach significantly outperforms traditional GA's in both rate of descent, trapping in false minima, and long term optimization.

Huang, Chien-Feng↗
NASA NTRS2020

Toward Transition Modeling in a Hypersonic Boundary Layer at Flight Conditions

An accurate physics-based transition prediction method integrated with computational fluid dynamics (CFD) solvers is pursued for hypersonic boundary layer flows over slender hypersonic vehicles at flight conditions. The geometry and flow conditions are selected to match relevant trajectory locations from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7-degree half-angle cone with 2.5 mm nose radius, freestream Mach numbers in the range of 3.8 – 5.5 and freestream unit Reynolds numbers in the range of 3.3 × 10(exp 6) – 21.4 × 10(exp 6) m(exp -1). Earlier research had shown that the onset of transition during the HIFiRE-1 flight experiment correlated with an amplification factor of N ≈ 13.5 for the planar Mack modes. However, to incorporate the N-factor correlations into a CFD code, we investigate surrogate models for disturbance amplification that avoid the direct computation of stability characteristics. A commonly used approach for low-speed flows is based on an a priori database of stability characteristics for locally similar profiles. However, the results presented in this paper demonstrate that the application of this approach to hypersonic boundary layers over blunt spherical nose-tip cones leads to large, unacceptable errors in the predictions of amplification factors, mainly due to its failure in accounting for the effects of the entropy layer on the boundary-layer profiles along the length of the model. We propose and demonstrate an alternate approach that employs the stability computations for a canonical set of blunt cone configurations to train a physics-informed convolutional neural network model that is shown to provide substantially improved transition predictions for hypersonic flow configurations with entropy-layer effects. Furthermore, the excellent performance of the neural network model is also confirmed for cone configurations with nose radius and half-angle values that do not correspond to those used to build the database. Finally, the convolutional neural network model is shown to outperform the linear stability calculations for underresolved basic states.

Pedro Paredes↗
NASA NTRS2022

Technology Maturation for Cloud Ice Radiometers

Global measurements of ice in clouds, both the amount and particle size distribution, are critically needed to reduce uncertainties in global climate models. The retrieval of this information is best achieved with a range of receiver channels across the submillimeter wave range. Advancement of low noise Indium Phosphide (InP) MMIC amplifier technology to 25-nm gate length enabled us to develop miniature submillimeter-wave receivers for a CubeSat scale instrument that achieves 6 km spatial resolution. We developed the 25-nm InP MMICs and radiometer receivers for 240, 310, 380, 670 GHz. The 25-nm InP MMIC technology was thermal vacuum tested to reduce risk for future space mission.

Duffy, Maxwell↗
NASA NTRS2022

TechEdSat-13: The First Flight of a Neuromorphic Processor

Neuromorphic processors, inspired by the wiring of the brain, permit certain classes of Artificial Intelligence/Machine Learning (AI/ML) algorithms to run far more efficiently. Ultimately, such systems will make the small- and nano-satellite platforms even more useful in terms of greatly improved power, communication and internal data management. In addition, on-board processing of images and data will help to not only rapidly interpret the information, but also reduce the amount of data that needs to be transmitted to ground stations. This initial flight experiment uses the Intel/Loihi processor combined with a custom interface board and three communication channels to run the AI/ML scripts. These will vary with increasing length and complexity during the course of the mission. The algorithms will use the (at first) limited sensor data to ‘learn’ - with comparisons to similar architecture in comparable ground experiments. Some of the applications for successor flights in the TES-n flight series include Cognitive Communications, whereby the overall communication system is optimized per overflight – by optimizing timing and data transmission functions. Lastly, the performance of the Loihi 14nm process technology will be monitored for performance in the LEO radiation environment, thus looking for induced hardware and software errors. This information will help guide future radiation protection techniques to extend the lifetime and overall utility. The TES-13 is a 3U nanosat successfully launched by the Virgin Orbit Launcher-1 on January 13, 2022, and will presage more flights and AI/ML applications to come.

TechEdSat↗
NASA NTRS1993

The rheology and composition of cryovolcanic flows on icy satellites

The rheologic properties of terrestrial lavas have been related to morphologic features of their flows, such as levees, banked surfaces, multilobate structures, and compressible folds. These features also have been used to determine rheologies and constrain the compositions of extraterrestrial flows. However, with rare exceptions, such features are not resolvable in Voyager images of the satellites of outer planets. Often only flow length and edge thickness of cryovolcanic flows can be measured reasonably accurately from Voyager images. The semiempirical lava-flow model presented here is a renewed effort to extract useful information from such measurements.

Kargel, Jeffrey S.↗
NASA NTRS1993

Inversion of gravity and bathymetry in oceanic regions for long-wavelength variations in upper mantle temperature and composition

Long-wavelength variations in geoid height, bathymetry, and SS-S travel times are all relatable to lateral variations in the characteristic temperature and bulk composition of the upper mantle. The temperature and composition are in turn relatable to mantle convection and the degree of melt extraction from the upper mantle residuum. Thus the combined inversion of the geoid or gravity field, residual bathymetry, and seismic velocity information offers the promise of resolving fundamental aspects of the pattern of mantle dynamics. The use of differential body wave travel times as a measure of seismic velocity information, in particular, permits resolution of lateral variations at scales not resolvable by conventional global or regional-scale seismic tomography with long-period surface waves. These intermediate scale lengths, well resolved in global gravity field models, are crucial for understanding the details of any chemical or physical layering in the mantle and of the characteristics of so-called 'small-scale' convection beneath oceanic lithosphere. In 1991 a three-year project to the NASA Geophysics Program was proposed to carry out a systematic inversion of long-wavelength geoid anomalies, residual bathymetric anomalies, and differential SS-S travel time delays for the lateral variation in characteristic temperature and bulk composition of the oceanic upper mantle. The project was funded as a three-year award, beginning on 1 Jan. 1992.

Solomon, Sean C.↗
NASA NTRS1995

Laser diagnostics for microgravity droplet studies

An instrument has been designed, built, and tested for performing laser diagnostic measurements of droplet combustion in low-gravity-flight aircraft. Nonintrusive measurements are of particular importance for droplet combustion (the simplest example of non-premixed combustion) and transport in microgravity environments, where physical contact would introduce an unacceptable level of perturbations. The resolution of these diagnostics can also isolate transport to length scales much smaller than the droplet diameter. These techniques can be configured to instantaneously map an entire flow field in two and three dimensions, providing either qualitative or quantitative information on the distribution of a desired scalar or vector quantity. Detailing the gas-phase flow field and position of the flame front can be achieved using planar laser-induced fluorescence (PLIF) of OH or another flame front marker. An alternative approach is to obtain LIF from a diagnostic seed included in the liquid phase fuel; it would be consumed at the flame front. The main advantage to this approach is that it is easier to choose the wavelength of the molecular absorption which coincides with convenient laser wavelengths rather than finding lasers which can be configured to access OH. Our present method uses a nitrogen-pumped dye laser tuned to a sodium absorption and addition of small concentrations of NaCl to the fuel. Particle image velocimetry (PIV) is a laser-based technique which has recently had its practicality greatly enhanced by the development of high-resolution CCD cameras and the increase in speed and capacity of computer systems. With this technique, a seeded flow is illuminated with a double-pulsed laser sheet to generate a double exposure image on a film or CCD camera. Computer analysis of the image is used to determine the particle velocity vectors and, thus, the gas velocity within the plane of the laser sheet. Our current experiment uses PIV for measuring relative droplet gas-phase velocities in a parabolic flight environment. The results show successful application of PLIF relative to luminosity and radical emission near 308 nm. PIV results are less successful due to gas thermal expansion deflecting the seed particles away from the measurement volume. PIV is applicable for measurements in the absence of combustion.

Winter, Michael↗
NASA NTRS2000

Vertical Roughness of the Polar Regions of Mars from Mars Orbiter Laser Altimeter Pulse-Width Measurements

The sub-kilometer scale vertical roughness of the martian surface in the polar regions can be investigated using calibrated, optical pulse width data provided by the Mars Orbiter Laser Altimeter (MOLA). Garvin and others have previously discussed initial observations of what we have called "total vertical roughness" or TVR, as derived from MOLA optical pulse width observations acquired during the pre-mapping phases of the Mars Global Surveyor (MGS) mission. Here we present the first assessment of the Mars polar region properties of the TVR parameter from more than nine months of continuous mapping by MOLA as part of the MGS mapping mission. Other than meter-scale surface properties directly inferred from Mars Orbiter Camera (MOC) images, MOLA measurements of footprint-scale TVR represent the only direct measurements of the local vertical structure of the martian surface at approx. 150 m length scales. These types of data have previously been shown to correlate with geologic process histories for terrestrial desert surfaces on the basis of Shuttle Laser Altimeter (SLA) observations. Additional information is obtained in the original extended abstract.

Garvin, J. B.↗
NASA NTRS2006

Improving the Near-Earth Micrometeoroid and Orbital Debris Environment Definition with LADC

The Large Area Debris Collector (LADC) is a 10 m(sup 2) aerogel and acoustic sensor system designed to characterize and collect submillimeter micrometeoroids and orbital debris on the International Space Station (ISS). The project is led by the U.S. Naval Research Laboratory (NRL) with major collaboration by the NASA Orbital Debris Program Office at Johnson Space Center. The U.S. Department of Defense Space Test Program (STP) is responsible for the integration, deployment, and retrieval of the system. The deployment is scheduled for August 2007 with an orbital collection period of one to two years. The combined area time product of LADC will provide a much needed orbital debris population update in the size regime that is important to the safety community - 100 mm and larger. Another key element for LADC is the source identification of the collected samples. Impact features such as track length and track volume can be used to estimate the impact speed and direction of any selected residual embedded in aerogel. Acoustic sensors can provide impact timing and impact location information. The combined dynamical signatures make it possible to reconstruct the orbits of some of the collected samples and lead to their source identification. Compositional analysis on the residuals can also separate debris from meteoroids and provide additional population breakdown for orbital debris (e.g., Al, paint, steel, Al2O3). To maximize the science return and minimize potential contamination from other ISS modules, a careful selection of the location and orientation of LADC on the ISS is needed. Key issues and engineering constraints encountered during mission preparation, and the expected science return based on the mission configuration, are summarized in this paper.

Liou, J.-C.↗
NASA NTRSDate not supplied

Comparison of Orion Flywheel to Commercially Available Flywheel Device

INTRODUCTION: The chosen exercise device for the Orion Multi-purpose Crew Vehicle (MPCV) for Artemis missions is the Orion Flywheel (OFW), which was selected in 2017 from a pool of exercise devices. The Orion Flywheel is to be installed in the MPCV for its first use during the Artemis II mission and will be utilized for subsequent Artemis missions. The OFW provides the capability to perform both resistive and aerobic exercises while taking up a small volume and not requiring power. Aerobic exercise consists of rowing while resistive exercise includes the deadlift, harness squat, and deadlift high pull among others. The efficacy of the OFW as an exercise countermeasure to spaceflight deconditioning has not yet been fully evaluated. A future HRP-funded study using head-down tilt bed rest is planned to evaluate the efficacy of the OFW to mitigate aerobic and muscular deconditioning. The OFW, made by KBR, is a specialized device that poses high costs for purchase and maintenance. The aim of the study is to determine if a commercially available alternative could be used as a backup for the OFW during the bed rest study or as an alternative in other studies. This study seeks to compare the loading profile and mechanics of a commercial flywheel device (kBox Pro) with the three resistance settings of the OFW using a controlled, instrumented setup to validate its acceptability as a backup. METHODS: An experimental setup was designed to simulate human use of the OFW. Flywheel devices can have varied actuated inertial mass and strap length. The inertial mass refers to the flywheel itself or the object that spins as the result of the movement of the strap. The OFW has three gears actuated with a lever, with the low gear used for aerobic rowing and the medium and high gears used for resistance exercises. These gears correspond to increasing flywheel inertia, which corresponds to a certain number and sizes of inertial plates on a commercial flywheel. The kBox Pro has varied sizes of inertial discs that are installed to the external shaft of the device and can be configured to roughly match the inertia seen in the OFW per gear setting. The strap length can be adjusted to allow for different ranges of motion. The experimental setup allows for the simulation of rowing, harness squats, and deadlift high pulls with corresponding exercise strap lengths. All three OFW gears are to be tested, as well as multiple combinations of kBox discs. The setup was created using a system of pulleys and cables to minimize friction loss. The system is actuated through the dropping of a connected mass which, through the pulley system, pulls the strap of the exercise device upwards as if a human was exercising. A string potentiometer and tensile force transducer are used to measure strap displacement and strap force, respectively. The masses dropped are exercise chains that simulate the decrease in force observed throughout a typical exercise. As the chains are lowered to the ground, they begin to spool and therefore are no longer subjecting the exercise device’s strap to their load. This setup was designed to provide realistic loads and protect the OFW from damage, an important precaution because it’s the only available unit for research and ground operations. Data is to be collected across simulated exercises and with different strap lengths, with the same conditions collected on both the OFW and the kBox Pro. RESULTS: Data collection is ongoing for the kBox and the Orion Flywheel. CONCLUSIONS: Study results will inform if the OFW and a kBox Pro device can be deemed mechanically similar. Depending on the results, additional data collection may be required to assess the user experience between the devices. A key result of this study is a mechanical characterization of the OFW device, demonstrating the load and force profile using a repeatable test method. This data will guide next steps on potential kBox Pro modifications needed to produce a comparable exercise experience to the OFW.

Exercise↗
NASA NTRSDate not supplied

TechEdSat-13: The First Flight of an AI/ML Neuromorphic Processor

Neuromorphic processors, inspired by the wiring of the brain, permit certain classes of Artificial Intelligence/Machine Learning (AI/ML) algorithms to run far more efficiently. Ultimately, such systems will make the small- and nano-satellite platforms even more useful in terms of greatly improved power, communication and internal data management. In addition, on-board processing of images and data will help to not only rapidly interpret the information, but also reduce the amount of data that needs to be transmitted to ground stations. This initial flight experiment uses the Intel/ Loihi processor combined with a custom interface board and three communication channels to run the AI/ML scripts. These will vary with increasing length and complexity during the course of the mission. The algorithms will use the (at first) limited sensor data to ‘learn’ - with comparisons to similar architecture in comparable ground experiments. Some of the applications for successor flights in the TES-n flight series include Cognitive Communications, whereby the overall communication system is optimized per overflight – by optimizing timing and data transmission functions. Lastly, the performance of the Loihi 14nm process technology will be monitored for performance in the LEO radiation environment, thus looking for induced hardware and software errors. This information will help guide future radiation protection techniques to extend the lifetime and overall utility. The TES-13 is a 3U nanosat successfully launched by the Virgin Orbit Launcher-1 on January 13, 2022, and will presage more flights and AI/ML applications to come.

TechEdSat↗
NASA NTRS1979

Shoreline as a controlling factor in commercial shrimp production

The author has identified the following significant results. An ecological model was developed that relates marsh detritus export and shrimp production. It was based on the hypothesis that the shoreline is a controlling factor in the production of shrimp through regulation of detritus export from the marsh. LANDSAT data were used to develop measurement of shoreline length and areas of marsh having more than 5.0 kilometers of shoreline per square kilometer of area for the Louisiana coast, demonstrating the capability of remote sensing to provide important geographic information. These factors were combined with published tidal ranges and salinities to develop a mathematical model that predicted shrimp production for nine geographic units of the Louisiana coast, as indicated by the long term average commercial shrimp yield.

Faller, K. H.↗
NASA NTRS1986

Development of a takeoff performance monitoring system

The development and testing of a real-time takeoff performance monitoring system is discussed. The algorithm is madeup of two segments: a pretakeoff segment and a real-time segment. One-time inputs of ambient conditions and airplane configuration information are used in the pretakeoff segment to generate schedule performance data for that takeoff. The real-time segment uses the scheduled performance data generated in the pretakeoff segment, runway length data, and measured parameters to monitor the performance of the airplane throughout the takeoff roll. Airplane and engine performance deficiencies are detected and annunciated. An important feature of this algorithm is the one-time estimation of the runway rolling friction coefficient. The algorithm was tested using a six degree of freedom airplane model in a computer simulation. Results from a series of sensitivity analysis are also included.

Srivatsan, R.↗
NASA NTRS1987

Development of a takeoff performance monitoring system

Discussed are the development and testing of a real-time takeoff performance monitoring algorithm. The algorithm is made up of two segments: a pretakeoff segment and a real-time segment. One-time imputs of ambient conditions and airplane configuration information are used in the pretakeoff segment to generate scheduled performance data for that takeoff. The real-time segment uses the scheduled performance data generated in the pretakeoff segment, runway length data, and measured parameters to monitor the performance of the airplane throughout the takeoff roll. Airplane and engine performance deficiencies are detected and annunciated. An important feature of this algorithm is the one-time estimation of the runway rolling friction coefficient. The algorithm was tested using a six-degree-of-freedom airplane model in a computer simulation. Results from a series of sensitivity analyses are also included.

Srivatsan, Raghavachari↗
NASA NTRS1987

Development of a takeoff performance monitoring system

The development and testing of a real-time takeoff performance monitoring system is discussed. The algorithm is made up of two segments: a pretakeoff segment and a real-time segment. One-time inputs of ambient conditions and airplane configuration information are used in the pretakeoff segment to generate schedule performance data for that takeoff. The real-time segment uses the scheduled performance data generated in the pretakeoff segment, runway length data, and measured parameters to monitor the performance of the airplane throughout the takeoff roll. Airplane and engine performance deficiencies are detected and annunciated. An important feature of this algorithm is the one-time estimation of the runway rolling friction coefficient. The algorithm was tested using a six degree of freedom airplane model in a computer simulation. Results from a series of sensitivity analysis are also included.

Srivatsan, R.↗
NASA NTRS1989

Considerations for a design and operations knowledge support system for Space Station Freedom

Engineering and operations of modern engineered systems depend critically upon detailed design and operations knowledge that is accurate and authoritative. A design and operations knowledge support system (DOKSS) is a modern computer-based information system providing knowledge about the creation, evolution, and growth of an engineered system. The purpose of a DOKSS is to provide convenient and effective access to this multifaceted information. The complexity of Space Station Freedom's (SSF's) systems, elements, interfaces, and organizations makes convenient access to design knowledge especially important, when compared to simpler systems. The life cycle length, being 30 or more years, adds a new dimension to space operations, maintenance, and evolution. Provided here is a review and discussion of design knowledge support systems to be delivered and operated as a critical part of the engineered system. A concept of a DOKSS for Space Station Freedom (SSF) is presented. This is followed by a detailed discussion of a DOKSS for the Lyndon B. Johnson Space Center and Work Package-2 portions of SSF.

Erickson, Jon D.↗
NASA NTRS1992

On the typography of flight-deck documentation

Many types of paper documentation are employed on the flight-deck. They range from a simple checklist card to a bulky Aircraft Flight Manual (AFM). Some of these documentations have typographical and graphical deficiencies; yet, many cockpit tasks such as conducting checklists, way-point entry, limitations and performance calculations, and many more, require the use of these documents. Moreover, during emergency and abnormal situations, the flight crews' effectiveness in combating the situation is highly dependent on such documentation; accessing and reading procedures has a significant impact on flight safety. Although flight-deck documentation are an important (and sometimes critical) form of display in the modern cockpit, there is a dearth of information on how to effectively design these displays. The object of this report is to provide a summary of the available literature regarding the design and typographical aspects of printed matter. The report attempts 'to bridge' the gap between basic research about typography, and the kind of information needed by designers of flight-deck documentation. The report focuses on typographical factors such as type-faces, character height, use of lower- and upper-case characters, line length, and spacing. Some graphical aspects such as layout, color coding, fonts, and character contrast are also discussed. In addition, several aspects of cockpit reading conditions such as glare, angular alignment, and paper quality are addressed. Finally, a list of recommendations for the graphical design of flight-deck documentation is provided.

Degani, Asaf↗
NASA NTRS2013

Advanced Exploration Systems (AES) Logistics Reduction and Repurposing Project: Advanced Clothing Ground Study Final Report

All human space missions require significant logistical mass and volume that will become an excessive burden for long duration missions beyond low Earth orbit. The goal of the Advanced Exploration Systems (AES) Logistics Reduction & Repurposing (LRR) project is to bring new ideas and technologies that will enable human presence in farther regions of space. The LRR project has five tasks: 1) Advanced Clothing System (ACS) to reduce clothing mass and volume, 2) Logistics to Living (L2L) to repurpose existing cargo, 3) Heat Melt Compactor (HMC) to reprocess materials in space, 4) Trash to Gas (TTG) to extract useful gases from trash, and 5) Systems Engineering and Integration (SE&I) to integrate these logistical components. The current International Space Station (ISS) crew wardrobe has already evolved not only to reduce some of the logistical burden but also to address crew preference. The ACS task is to find ways to further reduce this logistical burden while examining human response to different types of clothes. The ACS task has been broken into a series of studies on length of wear of various garments: 1) three small studies conducted through other NASA projects (MMSEV, DSH, HI-SEAS) focusing on length of wear of garments treated with an antimicrobial finish; 2) a ground study, which is the subject of this report, addressing both length of wear and subject perception of various types of garments worn during aerobic exercise; and 3) an ISS study replicating the ground study, and including every day clothing to collect information on perception in reduced gravity in which humans experience physiological changes. The goal of the ground study is first to measure how long people can wear the same exercise garment, depending on the type of fabric and the presence of antimicrobial treatment, and second to learn why. Human factors considerations included in the study consist of the Institutional Review Board approval, test protocol and participants' training, and a web-based data collection questionnaire. Cardiovascular exercise was chosen as the activity in this experiment for its profuse sweating effect and because it is considered a more severe treatment applied to the clothes than every-day usage. Study garments were exercise T-shirts and shorts purchased from various vendors. Fabric construction, fabric composition, and finishing treatment were defined as the key variables. The study was divided into three balanced experiments: a cotton-polyester-wool (CPW) T-shirts study with 61 participants, a polyester-modacrylic-polyester/cocona (PMC) T-shirts study with 40 participants, and a shorts study with 70 participants. In the CPW study, the T-shirts were made of 100% cotton, or of 100% polyester or of 100% wool, and categorized into open and tight knit constructions. In the PMC study, the T-shirts were made of 100% polyester, or of 82% modacrylic, or of 95% polyester with 5% cocona fiber, without construction distinction. The shorts were made either of 100% cotton or of 100% polyester, and were knitted or woven. Some garments were treated with Bio-Protect 500 antimicrobial finish according to the experimental design. The data collected from the questionnaire included garment identification, level of exertion, duration of exercise session, number of exercise sessions, an ordinal preference scale for nine sensory elements, and reason for retiring a used garment. From the analysis of the combined CPW and PMC shirt studies, there are statistically significant differences among the mean lifetimes of various types of shirts. The exercise shirts with the longest mean lifetimes are untreated wool (600 minutes), treated cotton (526 minutes), and untreated modacrylic (515 minutes). From the combined CPW and PMC shirt studies, the most preferred material was untreated open-knit wool, which is one of the two materials that jointly were worn the longest, untreated wool, both open-knit and tight-knit. For the CP shorts study, there were no statistically significant differences in mean lifetimes of the exercise shorts at the 5% significance level due to the treatment combinations. There was therefore no justification to examine differences among levels of main effects or interactions. The preference for shorts was in this order: untreated woven polyester, untreated knitted polyester, untreated woven cotton, and treated knitted cotton. The nine preference scales were tabulated to determine the preference responses at the end of those exercise periods which were prior to the period when a garment was retired and a new garment was started. The assumption is that an unfavorable assessment of a garment leads to its retirement. The scent scale response was predominantly unfavorable at the end of the exercise period immediately prior to the exercise period when a new garment was started.

Byrne, Vicky↗