SEARCH · Engineering Papers

Results for “exponential growth”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS2005

Developing a Framework for Effective Network Capacity Planning

As Internet traffic continues to grow exponentially, developing a clearer understanding of, and appropriately measuring, network's performance is becoming ever more critical. An important challenge faced by the Information Resources Directorate (IRD) at the Johnson Space Center in this context remains not only monitoring and maintaining a secure network, but also better understanding the capacity and future growth potential boundaries of its network. This requires capacity planning which involves modeling and simulating different network alternatives, and incorporating changes in design as technologies, components, configurations, and applications change, to determine optimal solutions in light of IRD's goals, objectives and strategies. My primary task this summer was to address this need. I evaluated network-modeling tools from OPNET Technologies Inc. and Compuware Corporation. I generated a baseline model for Building 45 using both tools by importing "real" topology/traffic information using IRD's various network management tools. I compared each tool against the other in terms of the advantages and disadvantages of both tools to accomplish IRD's goals. I also prepared step-by-step "how to design a baseline model" tutorial for both OPNET and Compuware products.

Yaprak, Ece↗

NASA NTRS1992

All-YBa2Cu3O(7-x) edge-geometry weak links

High quality YBa2Cu3O(7-x)/normal-metal/YBa2Cu3O(7-x) edge-geometry weak links are fabricated using nonsuperconducting Y-Ba-Cu-O barrier layers deposited by laser ablation at reduced growth temperatures. Devices incorporating 25-100-A-thick barrier layers exhibit current-voltage characteristics consistent with the resistively-shunted-junction model, as well as ac Josephson steps. Magnetic field modulation of the critical currents shows Fraunhofer-like behavior with a periodicity which scales with device area. The critical currents vary exponentially with barrier thickness indicating an effective normal metal coherence length of 20 A. The average resistances scale linearly with Y-Ba-Cu-O interlayer thickness and device area. The scaling behavior of the device parameters combined with the well-behaved magnetic field modulation of the critical currents demonstrates good barrier-layer uniformity with low pinhole densities. Near the transition temperature, the critical currents exhibit a temperature dependence proportional to (1 - T/Tc) squared.

Hunt, B. D.↗

NASA NTRS1987

Development of confidence limits by pivotal functions for estimating software reliability

The utility of pivotal functions is established for assessing software reliability. Based on the Moranda geometric de-eutrophication model of reliability growth, confidence limits for attained reliability and prediction limits for the time to the next failure are derived using a pivotal function approach. Asymptotic approximations to the confidence and prediction limits are considered and are shown to be inadequate in cases where only a few bugs are found in the software. Departures from the assumed exponentially distributed interfailure times in the model are also investigated. The effect of these departures is discussed relative to restricting the use of the Moranda model.

Dotson, Kelly J.↗

NASA NTRS2000

Magnetic Field Suppression of Flow in Semiconductor Melt

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

Fedoseyev, A. I.↗

NASA NTRS1988

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

The development of Tollmien-Schlichting waves (TSWs) and Taylor-Goertler vortices (TGVs) in fully developed viscous curved-channel flows is investigated analytically, with a focus on their nonlinear interactions. Two types of interactions are identified, depending on the amplitude of the initial disturbances. In the low-amplitude type, two TSWs and one TGV interact, and the scaled amplitudes go to infinity on a finite time scale; in the higher-amplitude type, which can also occur in a straight channel, the same singularity occurs if the angle between the TSW wavefront and the TGV is greater than 41.6 deg, but the breakdown is exponential and takes an infinite time if the angle is smaller. The implications of these findings for external flow problems such as the design of laminar-flow wings are indicated. It is concluded that longitudinal vortices like those observed in the initial stages of the transition to turbulence can be produced unless the present interaction mechanism is destroyed by boundary-layer growth.

Hall, P.↗

NASA NTRS2010

Root Zone Respiration on Hydroponically Grown Wheat Plant Systems

Root respiration is a biological phenomenon that controls plant growth and physiological development during a plant's lifespan. This process is dependent on the availability of oxygen in the system where the plant is located. In hydroponic systems, where plants are submerged in a solution containing vital nutrients but no type of soil, the availability of oxygen arises from the dissolved oxygen concentration in the solution. This oxygen concentration is dependent on the , gas-liquid interface formed on the upper surface of the liquid, as given by Henry's Law, depending on pressure and temperature conditions. Respiration rates of the plants rise as biomass and root zone increase with age. The respiration rate of Apogee wheat plants (Triticum aestivum) was measured as a function of light intensity (catalytic for photosynthesis) and CO2 concentration to determine their effect on respiration rates. To determine their effects on respiration rate and plant growth microbial communities were introduced into the system, by Innoculum. Surfactants were introduced, simulating gray-water usage in space, as another factor to determine their effect on chemical oxygen demand of microbials and on respiration rates of the plants. It is expected to see small effects from changes in CO2 concentration or light levels, and to see root respiration decrease in an exponential manner with plant age and microbial activity.

Soler-Crespo, R. A.↗

NASA NTRS2023

Virus Infection of Phytoplankton Increases Average Molar Mass and Reduces Hygroscopicity of Aerosolized Organic Matter

Viral infection of phytoplankton is a pervasive mechanism of cell death and bloom termination, which leads to the production of dissolved and colloidal organic matter that can be aerosolized into the atmosphere. Earth-observing satellites can track the growth and death of phytoplankton blooms on weekly time scales but the impact of viral infection on the cloud forming potential of associated aerosols is largely unknown. Here, we determine the influence of viral-derived organic matter, purified viruses, and marine hydrogels on the cloud condensation nuclei activity of their aerosolized solutions, compared to organic exudates from healthy phytoplankton. Dissolved organic material derived from exponentially growing and infected cells of well-characterized eukaryotic phytoplankton host-virus systems, including viruses from diatoms, coccolithophores and chlorophytes, was concentrated, desalted, and nebulized to form aerosol particles composed of primarily of organic matter. Aerosols from infected phytoplankton cultures resulted in an increase in critical activation diameter and average molar mass in three out of five combinations evaluated, along with a decrease in organic kappa (hygroscopicity) compared to healthy cultures and seawater controls. The infected samples also displayed evidence of increased surface tension depression at realistic cloud water vapor supersaturations. Amending the samples with xanthan gum to simulate marine hydrogels increased variability in organic kappa and surface tension in aerosols with high organic to salt ratios. Our findings suggest that the pulses of increased dissolved organic matter associated with viral infection in surface waters may increase the molar mass of dissolved organic compounds relative to surface waters occupied by healthy phytoplankton or low phytoplankton biomass.

Atmospheric science↗

NASA NTRS2002

An Irreversible Constitutive Law for Modeling the Delamination Process Using Interface Elements

An irreversible constitutive law is postulated for the formulation of interface elements to predict initiation and progression of delamination in composite structures. An exponential function is used for the constitutive law such that it satisfies a multi-axial stress criterion for the onset of delamination, and satisfies a mixed mode fracture criterion for the progression of delamination. A damage parameter is included to prevent the restoration of the previous cohesive state between the interfacial surfaces. To demonstrate the irreversibility capability of the constitutive law, steady-state crack growth is simulated for quasi-static loading-unloading cycle of various fracture test specimens.

Goyal, Vinay K.↗

NASA NTRS2002

An Irreversible Constitutive Law for Modeling the Delamination Process using Interface Elements

Goyal, Vinay K.↗

NASA NTRS2006

The Need for High Spatial Resolution Multispectral Thermal Remote Sensing Data In Urban Heat Island Research

Although the study of the Urban Heat Island (UHI) effect dates back to the early 1800's when Luke Howard discovered London s heat island, it has only been with the advent of thermal remote sensing systems that the extent, characteristics, and impacts of the UHI have become to be understood. Analysis of the UHI effect is important because above all, this phenomenon can directly influence the health and welfare of urban residents. For example, in 1995, over 700 people died in Chicago due to heat-related causes. UHI s are characterized by increased temperature in comparison to rural areas and mortality rates during a heat wave increase exponentially with the maximum temperature, an effect that is exacerbated by the UHI. Aside from the direct impacts of the UHI on temperature, UHI s can produce secondary effects on local meteorology, including altering local wind patterns, increased development of clouds and fog, and increasing rates of precipitation either over, or downwind, of cities. Because of the extreme heterogeneity of the urban surface, in combination with the sprawl associated with urban growth, thermal infrared (TIR) remote sensing data have become of significant importance in understanding how land cover and land use characteristics affect the development and intensification of the UHI. TIR satellite data have been used extensively to analyze the surface temperature regimes of cities to help observe and measure the impacts of surface temperatures across the urban landscape. However, the spatial scales at which satellite TIR data are collected are for the most part, coarse, with the finest readily available TIR data collected by the Landsat ETM+ sensor at 60m spatial resolution. For many years, we have collected high spatial resolution (10m) data using an airborne multispectral TIR sensor over a number of cities across the United States. These high resolution data have been used to develop an understanding of how discrete surfaces across the urban environment (e.g., rooftops, pavements) interact from a surface-lower atmosphere energy flux perspective, to force the development of the UHI. Moreover, the airborne TIR sensor we used in our UHI studies was a multispectral sensor that had six channels in the 8-12pm range. The advantages of collecting multispectral TIR data became readily evident as a valuable tool for better calculation of unique surface thermal energy responses for urban materials over the 8-12 micrometer region, and also for getting a better handle on surface emissivity characteristics for these discrete surfaces. In this presentation, we will provide evidence on the virtues of how high spatial resolution multispectral TIR data can provide for better analysis of the UHI that cannot now be attained via TIR data obtained from satellites. Furthermore, we wish to provide compelling evidence on why future TIR satellite sensors should collect data at fine spatial resolutions (e.g. less than or equal to 30m) to better allow for measurement of surface thermal energy fluxes from discrete urban surfaces, and to better understand how surface fluxes from different urban materials in cities around the world in different climatic regimes, affect development of the UHI characteristics.

Quattrochi, Dale A.↗

NASA NTRSDate not supplied

Run Time Improvement Efforts for the Roman Space Telescope Thermal Analysis

"Observatory thermal models for large, complex missions, such as the Wide Field InfraRed Survey Telescope (WFIRST) mission, produce an immense amount of data to be processed. Configuration management of the model throughout the project life cycle has mainly focused on which versions of the subsystem models form the current observatory level configuration. However, the results produced by the model are not nearly as well The Roman Space Telescope (RST), formerly known as the Wide Field InfraRed Survey Telescope, is the next great astrophysics observatory mission to follow the James Webb Space Telescope with a planned launch in 2026. As a large scale, flagship mission for NASA with challenging wave front error stability requirements, a single model approach for both thermal discipline analysis and thermo-optical distortion analysis has been used since the early days of the project. In alleviating the need to maintain two separate models for different analysis types, it imposes run time penalties on the thermal analysis with a large model with significant radiation heat exchange. Throughout the lifecycle of the project, the component models have steadily grown in size, resulting in a continuous growth of the overall observatory model with each update and consequently a considerable increase in the model run time. While ongoing efforts to reduce run time are continuously investigated, previous efforts had primarily focused on timestep size and total simulation time to reach quasi-equilibrium. More recently, studies were performed on the total number of radiation couplings (radks) included in the model, which has a nearly linear impact on run time, but increases exponentially with node count. As standard practice for spacecraft analysis, small radks were excluded from the temperature solution based on the assumption that their interchange/view factors have a negligible impact on heat flow. Four approaches were investigated to reduce the model run time while minimizing the impact on accuracy: (1) the Equivalent Radiation Network node, (2) Progressive Radk Inclusion as solution proceeds, (3) Targeted Radk Filtering for critical/non critical areas, and lastly (4) Representation of culled radks with Backloads. Furthermore, the investigation of model run time also revealed that cold cases took noticeably longer to run than hot cases; the root computational inefficiencies were explored along with the computation penalty of linearization of the external radks and recalculation of temperature dependent linear couplings at each timestep. This paper outlines the details of each of the above approaches and their impact on run time and model accuracy.

Thermal Analysis↗

NASA NTRSDate not supplied

Run Time Improvement Efforts for the Roman Space Telescope Thermal Analysis

Observatory thermal models for large, complex missions, such as the Wide Field InfraRed Survey Telescope (WFIRST) mission, produce an immense amount of data to be processed. Configuration management of the model throughout the project life cycle has mainly focused on which versions of the subsystem models form the current observatory level configuration. However, the results produced by the model are not nearly as well The Roman Space Telescope (RST), formerly known as the Wide Field InfraRed Survey Telescope, is the next great astrophysics observatory mission to follow the James Webb Space Telescope with a planned launch in 2026. As a large scale, flagship mission for NASA with challenging wave front error stability requirements, a single model approach for both thermal discipline analysis and thermo-optical distortion analysis has been used since the early days of the project. In alleviating the need to maintain two separate models for different analysis types, it imposes run time penalties on the thermal analysis with a large model with significant radiation heat exchange. Throughout the lifecycle of the project, the component models have steadily grown in size, resulting in a continuous growth of the overall observatory model with each update and consequently a considerable increase in the model run time. While ongoing efforts to reduce run time are continuously investigated, previous efforts had primarily focused on timestep size and total simulation time to reach quasi-equilibrium. More recently, studies were performed on the total number of radiation couplings (radks) included in the model, which has a nearly linear impact on run time, but increases exponentially with node count. As standard practice for spacecraft analysis, small radks were excluded from the temperature solution based on the assumption that their interchange/view factors have a negligible impact on heat flow. Four approaches were investigated to reduce the model run time while minimizing the impact on accuracy: (1) the Equivalent Radiation Network node, (2) Progressive Radk Inclusion as solution proceeds, (3) Targeted Radk Filtering for critical/non critical areas, and lastly (4) Representation of culled radks with Backloads. Furthermore, the investigation of model run time also revealed that cold cases took noticeably longer to run than hot cases; the root computational inefficiencies were explored along with the computation penalty of linearization of the external radks and recalculation of temperature dependent linear couplings at each timestep. This paper outlines the details of each of the above approaches and their impact on run time and model accuracy.

Thermal Analysis↗

NASA NTRSDate not supplied

Bioreactor Development for CO2-Based In Situ Resource Utilization Manufacturing

Sustainable long-duration manned missions on both the Moon and Mars will require in situ resource utilization (ISRU). Carbon dioxide (CO2) has great potential as a harvestable resource, making up 95% of the atmosphere on Mars and being produced as respiratory waste in spacecraft and future planetary habitats. Through ISRU, biomanufacturing has the capability to produce a near limitless array of products from local space resources. Here, a CO2-based ISRU recombinant protein producing bioreactor and associated biomanufacturing organisms were designed to produce a highly stable carbonic anhydrase (CA). Candidate organisms were selected by growth characterization on acetate and formic acid, carbon substrates that are synthesized via electrochemical conversion of CO2. To improve growth on the CO2 producing substrate formic acid and for direct integration of ISRU CO2, a synthetic Calvin-Benson-Bassam cycle was designed for use in Escherichia coli. Multiplex genetic modification in E. coli was facilitated by a tailored CRISPR/Cas9 and λ red recombineering two-vector system. For expression of CA, a blue light regulated T7 promoter was employed for dynamic and small molecule free induction. Efficient bioproduction through a fed-batch exponential feeding strategy was determined via mass balance analysis from ISRU substrates to biomass and CA yield. Flux balance analysis was used to model ISRU substrate metabolism and metabolic pathway engineering in candidate organisms under cultivation strategy conditions for both metabolism reconstruction and pathway design optimization. Finally, a small-scale, disposable bag bioreactor for use in the NASA Bioculture System infrastructure was designed to enable CO2-based CA biomanufacturing in reduced-gravity environments.

biomanufacturing↗

NASA NTRS1994

Particle-in-cell simulations of the critical ionization velocity effect in finite size clouds

The critical ionization velocity (CIV) mechanism in a finite size cloud is studied with a series of electrostatic particle-in-cell simulations. It is observed that an initial seed ionization, produced by non-CIV mechanisms, generates a cross-field ion beam which excites a modified beam-plasma instability (MBPI) with frequency in the range of the lower hybrid frequency. The excited waves accelerate electrons along the magnetic field up to the ion drift energy that exceeds the ionization energy of the neutral atoms. The heated electrons in turn enhance the ion beam by electron-neutral impact ionization, which establishes a positive feedback loop in maintaining the CIV process. It is also found that the efficiency of the CIV mechanism depends on the finite size of the gas cloud in the following ways: (1) Along the ambient magnetic field the finite size of the cloud, L (sub parallel), restricts the growth of the fastest growing mode, with a wavelength lambda (sub m parallel), of the MBPI. The parallel electron heating at wave saturation scales approximately as (L (sub parallel)/lambda (sub m parallel)) (exp 1/2); (2) Momentum coupling between the cloud and the ambient plasma via the Alfven waves occurs as a result of the finite size of the cloud in the direction perpendicular to both the ambient magnetic field and the neutral drift. This reduces exponentially with time the relative drift between the ambient plasma and the neutrals. The timescale is inversely proportional to the Alfven velocity. (3) The transvers e charge separation field across the cloud was found to result in the modulation of the beam velocity which reduces the parallel heating of electrons and increases the transverse acceleration of electrons. (4) Some energetic electrons are lost from the cloud along the magnetic field at a rate characterized by the acoustic velocity, instead of the electron thermal velocity. The loss of energetic electrons from the cloud seems to be larger in the direction of plasma drift relative to the neutrals, where the loss rate is characterized by the neutral drift velocity. It is also shown that a factor of 4 increase in the ambient plasma density, increases the CIV ionization yield by almost 2 orders of magnitude at the end of a typical run. It is concluded that a larger ambient plasma density can result in a larger CIV yield because of (1) larger seed ion production by non-CIV mechanisms, (2) smaller Alfven velocity and hence weak momentum coupling, and (3) smaller ratio of the ion beam density to the ambient ion density, and therefore a weaker modulation of the beam velocity. The simulation results are used to interpret various chemical release experiments in space.

Moghaddam-Taaheri, E.↗

NASA NTRSDate not supplied

Bioreactor Development for CO2-Based In Situ Resource Utilization Manufacturing

Sustainable long-duration manned missions on both the Moon and Mars will require in situ resource utilization (ISRU). Carbon dioxide (CO2) has great potential as a harvestable resource, making up 95% of the atmosphere on Mars and being produced as respiratory waste in spacecraft and future planetary habitats. Through ISRU, biomanufacturing has the capability to produce a near limitless array of products from local space resources, which include pharmaceuticals, bioplastics, chemical feedstocks, and industrial enzymes. Here, a CO2-based ISRU recombinant protein bioreactor and associated biomanufacturing organisms were designed to produce a highly stable carbonic anhydrase (CA). Initial work characterized candidate organisms for growth on acetate and formic acid, carbon substrates that can be synthesized via electrochemical conversion of CO2. To improve growth on the CO2 producing substrate formic acid and for direct integration of ISRU CO2, a synthetic Calvin-Benson-Bassam cycle was designed for use in Cyberlindnera jadinii and Escherichia coli. Genetic modifications in E. coli will be facilitated by a tailored CRISPR/Cas9 and λ red recombineering two-vector system. For expression of CA, a blue light regulated T7 promoter was employed for dynamic and small molecule free induction. Efficient bioproduction through a fed-batch exponential feeding strategy was determined via mass balance calculations from ISRU substrates to biomass and CA yield. Flux balance analysis was used to model ISRU substrate metabolism and metabolic pathway engineering in candidate organisms under cultivation strategy conditions for both metabolism reconstruction and pathway design optimization. Finally, a small-scale, disposable bag bioreactor concept for use in the NASA Bioculture System infrastructure was designed to enable CO2-based CA production in reduced-gravity environments.

Biomanufacturing, Pathway Engineering, Flux Balanc↗

NASA NTRS1992

Physical vapor transport of mercurous chloride under a nonlinear thermal profile

Our study investigates numerically the flow field characteristics during the growth of mercurous chloride (Hg2Cl2) crystals in a rectangular ampoule under terrestrial and microgravity conditions for a nonlinear thermal gradient. With a residual gas lighter than the nutrient, the solutal Grashof number is dominant. We observe that in tilted configurations, when solutal convection is dominant, the maximum transport rate occurs at approximately 40 percent. For the vertical configurations, we were able to obtain solutions only for the cases either below the critical Rayleigh numbers or the stabilized configurations. The total mass flux decreases exponentially with an increase of pressure of residual gas, but it increases following a power law with the temperature difference driving the transport. The nonlinear thermal gradient appears to destabilize the flow field when thermal convection is dominant for both vertical top-heated and bottom-heated configurations. However, when the solutal Grashof number is dominant, the density gradient resulting from the solutal gradient appears to stabilize the flow for the bottom-heated configuration. The flow field for the top-heated configuration is destabilized for high Grashof numbers. The microgravity environment provides a means for lowering convection. For gravity levels of 10(exp -3) g(0) or less, the Stefan wind drives the flow, and no recirculating cell is predicted.

Mennetrier, Christophe↗

NASA NTRS2000

Ontogeny of vestibular compound action potentials in the domestic chicken

Compound action potentials of the vestibular nerve were measured from the surface of the scalp in 148 chickens (Gallus domesticus). Ages ranged from incubation day 18 (E18) to 22 days posthatch (P22). Responses were elicited using linear acceleration cranial pulses. Response thresholds decreased at an average rate of -0.45 dB/day. The decrease was best fit by an exponential model with half-maturity time constant of 5.1 days and asymptote of approximately -25.9 dB re:1.0 g/ms. Mean threshold approached within 3 dB of the asymptote by ages P6-P9. Similarly, response latencies decreased exponentially to within 3% of mature values at ages beyond P9. The half-maturity time constant for peripheral response peak latencies P1, N1, and P2 was comparable to thresholds and ranged from approximately 4.6 to 6.2 days, whereas central peaks (N2, P3, and N3) ranged from 2.9 to 3.4 days. Latency-intensity slopes for P1, N1, and P2 tended to decrease with age, reaching mature values within approximately 100 hours of hatching. Amplitudes increased as a function of age with average growth rates for response peaks ranging from 0.04 to 0.09 microV/day. There was no obvious asymptote to the growth of amplitudes over the ages studied. Amplitude-intensity slopes also increased modestly with age. The results show that gravity receptors are responsive to transient cranial stimuli as early as E19 in the chicken embryo. The functional response of gravity receptors continues to develop for many days after all major morphological structures are in place. Distinct maturational processes can be identified in central and peripheral neural relays. Functional improvements during maturation may result from refinements in the receptor epithelia, improvements in central and peripheral synaptic transmission, increased neural myelination, as well as changes in the mechanical coupling between the cranium and receptor organ.

NASA Discipline Developmental Biology↗

NASA NTRS1985

Spectral estimation of green leaf area index of oats

Green leaf area index (LAI) is a measure of vegetative growth and development and is frequently used as an input parameter in yield estimation and evapotranspiration models. Extensive destructive sampling is usually required to achieve accurate estimates of green LAI in natural situations. In this investigation, a statistical modeling approach was used to predict the green LAI of oats from bidirectional reflectance data collected with multiband radiometers. Stepwise multiple regression models based on two sets of spectral reflectance factors accounted for 73 percent and 65 percent of the variance in green LAI of oats. Exponential models of spectral data transformations of greenness, normalized difference, and near-infrared/red ratio accounted for more of the variance in green LAI than the multiple regression models.

Best, R. G.↗