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At least 55 records · Page 3

Dynamics of Rocky Mountain Lee Waves Observed During Success

On two days during SUCCESS, the DC-8 sampled wave clouds which formed downstream of the ridges east of the Rocky Mountains. Wave morphology for both flights is deduced from temperature and 3-dimensional wind measurements from the MMS, isentrope profiles from the MTP, and linear perturbation theory. The waves observed on 960430 are smaller and found to be decaying with altitude, while the waves sampled on 960502 are vertically propagating and consist of larger, multiple wave scales. Wave orientations are consistent with the underlying topography and regions of high ice crystal concentration. Updraft velocities were estimated from the derived wave properties and are consistent with MMS vertical winds.

Dean-Day, J.↗

Use of Polarization Lidar for Investigation of Meteorological Formations

This paper presents the results of theoretical and experimental, investigations of depolarization characteristics of different meteorological formations. Experimental investigations are carried out with a monostatic lidar. The ruby laser radiation is polarized in a vertical plane. The radiation reflected is accepted by a lens system of 150 rom in diameter and a viewing angle of 12' and further it is divided by Wollaston prism into the components polarized orthogonally. In this case the principal plane of the prism is exposed parallel with the laser polarization plane. Investigations show the degree of radiation polarization, reflected from water clouds, to be changed within 1/0.7 (seldom up to 0.6) depending on their density. In most cases a signal reflected from the cloud leading edge is polarized completely. The time shift is observed between polarized and crosspolarized components of a Fignal, reflected from a cloud, depending on the density of a meteorological object. While penetrating into the cloud depth a degree of polarization decreases up to 0.8-0.7, and the character of this decrease is different for various types of clouds. For crystal clouds the shift between the components of the reflected signal is not observed and the magnitude of polarization degree amounts to 0.1/0.3 in comparison with water clouds. The polarization degree of radiation reflected by fog is not less than 0.6, and that in the rains of average intensity (about 5 mm/h) is always about 1. The authors have suggested an algorithm of numerical solution of nonstationary transfer equation in the vector form to forecast the influence of multiple scattering effects on polarization characteristics of the lidar light signal. The method of statistical simulation (Monte-Carlo technique) forms the basis of the algorithm. Numerical estimates obtained for a model of stratocumulus at lambda = 0.6943 microns under boundary conditions close to the conditions of natural experiment being discussed proved to be in a good agreement with the results of observation. Specifically, Fig. 1 shows the profiles of polarization (p) versus depth (L) of the following drop formations: fog (curve 1) with horizontal meteorological visibility of 4 km two stratocumulus at a height of 1100 m with the attenuation factors delta = 0.01m(exp -1) (curve 2) and delta = 0.05m(exp -1) (curve 3). Curve 3 shows the results of numerical estimates and the value of their statistical error.

Balin, Yu. S.↗

Multiple scattering lidar returns from stratus clouds

Multiple scattering lidar returns from stratus clouds were measured using a multi-field-of-view (MFOV) lidar operating at 1.054 microns. The detector consists of four concentric silicon photodiodes which define half-angle fields of view (FOV) of 3.8, 12.5, 25 and 38.5 mrad. The central FOV receives the conventional lidar signal, while the outer FOV's receive only multiply scattered contributions. The ratios of the signals in the outer FOV's to the signal in the central FOV is an indication of the lateral spreading of the scattered component of the laser pulse as it propagates through the cloud. MFOV lidar returns from stratus clouds measured between October 1991 and March 1992 can be divided into two distinct types, those with large multiple scattering ratios and those with small ratios. An example of each type of return is shown. Both measurements were made at an elevation angle of 45 degrees. Clouds with small multiple scattering signals probably have a high concentration of much larger particles on the order of hundreds of micrometers in size. This is a typical size range for suspended ice crystals or precipitations. Stratus clouds often have a high concentration of ice crystals even when there is no precipitation. Large ice crystals would give smaller signals in the outer FOV's because much of the scattered intensity is contained in a narrow diffraction peak with an angular width on the order of milliradians. The result is that for a given extinction, many more orders of scattering are required for the laser pulse to spread out. So far we have not been able to do simulations of MFOV lidar returns from ice crystal clouds because of uncertainties about the phase function of the crystals, particularly the magnitude of the backscatter peak at 180 degrees. On two occasions, MFOV lidar returns measured just prior to snowfall, showed a striking vertical profile. An example is shown. From 900 to 1300m, the multiply scattered signals are negligible compared to the return in the central FOV. Abruptly, at 1300m strong signals begin in the outer FOVs. These results could be explained by the presence of a cloud layer composed of water droplets at a range of 1300m (or 900m above ground) with snow precipitations forming at the bottom of the cloud. By measuring the polarization ratio of lidar signals, Pal and Carswell have observed snow precipitating from a cloud layer composed of water droplets. Based on these results, we believe that analysis of multiple scattering lidar returns can yield important information on the phase of cloud particles.

Hutt, D. L.↗

An Analysis of Depolarization Streaks for Anticipating Lightning in Thundersnow

Infrequent lightning events, particularly in stratiform precipitation, present a unique decision-support challenge to National Weather Service (NWS) forecasters and core partners. Anticipating thundersnow events, which are rare compared to warm season lightning, are especially difficult to anticipate due to slanted updrafts within the comma-head region of a mid-latitude cyclone. Researchers and operational forecasters have observed depolarization streaks in differential reflectivity (ZDR) as a result of ice crystal layers prior to thundersnow initiation. These depolarization streaks form as a result of ice crystals aligning themselves with enhancements in the electric field in stratiform precipitation and are associated with ZDR values near zero. During the 7 March 2018 winter storm, a teacher in New Jersey was struck by lightning while dismissing students and depolarization streaks were observed in weather radar observations. Therefore, it is advantageous to examine depolarization streaks in ZDR to determine whether it can be used to anticipate lightning potential in winter-time events. Multiple events will be analyzed using the National Lightning Detection Network (NLDN) and the Geostationary Lightning Mapper (GLM) to determine if thundersnow flashes coincide with ZDR depolarization streaks in weather radars. This study also expands on collaboration between the NWS Huntsville Forecast Office and NASA Short-term Prediction Research and Transition (SPoRT) program to determine how depolarization streaks can be used operationally to anticipate lightning within stratiform regions. Preliminary work has indicated noticeable potential in correlating depolarization streak as a precursor to thundersnow flashes in a variety of geographical regions.

Autumn Millard↗

The magma ocean concept and lunar evolution

The model of lunar evolution in which the anorthositic plagioclase-rich oldest crust of the moon is formed over a period of 300 Myr or less by crystallization as it floats on a global ocean of magma tens or hundreds of km thick is examined in a review of petrological and theoretical studies. Consideration is given to the classification of lunar rocks, the evidence for primordial deep global differentiation, constraints on the depth of the molten zone, the effects of pressure on mineral stability relationships, mainly-liquid vs mainly-magmifer ocean models, and the evidence for multiple ancient differentiation episodes. A synthesis of the model of primordial differentiation and its aftereffects is presented, and the generalization of the model to the earth and to Mars, Mercury, Venus, and the asteroids is discussed.

Warren, P. H.↗

Multiple Igneous Bodies for Nakhlites and Chassignites as Inferred from Olivine Cooling Rates using Calcium Zoning

Nakhlites and chassignites are ultramafic cumulate rocks of clinopyroxene and olivine, respec-tively, considered to have been formed in a thick lava flow or shallow intrusion near the Martian surface [e.g., 1,2]. Although more than 100 Martian meteorites have been found so far, most of them are shergottites and only nine nakhlites and three chassignites are known (considering paired samples) [3]. In contrast to shergottites which show large variations in both mineralogy and ages, nakhlites and chassignites are suggested to have been petrogenetically related, crystallized at about the same time and been ejected by the same impact event because of their identical crystallization (approximately 1.3 Ga) and cosmic-ray exposure (10-11 My) ages [e.g., 1]. In this study we discuss the possibility of a common igneous body for all samples belonging to these two groups as suggested by previous studies [e.g., 4]. To do this we estimated cooling rates of olivine using Ca zoning profiles, especially by paying attention to the newest samples of each group (NWA 10720 nakhlite and NWA 8694 chassignite).

Mikouchi, T.↗

Interfacial and Hydrodynamic Behavior of Thin Spherical Bubbles of Smectic Liquid Crystal in Microgravity

The Observation and Analysis of Smectic Islands in Space (OASIS) project comprises a series of experiments that probe the interfacial and hydrodynamic behavior of thin spherical bubbles of smectic liquid crystal in microgravity. Smectic films are the thinnest known structures formed of condensed phases, making them ideal for studies of two-dimensional (2D) coarsening dynamics and thermocapillary phenomena. The OASIS flight hardware was launched on SpaceX-6 in April 2015 and experiments were carried out on the International Space Station using four different smectic A and C liquid crystal materials in separate sample chambers. We will describe the behavior of collective island dynamics on the bubbles, including temperature-gradient-induced thermomigration, 2D Rayleigh-Plateau Instability, Oswald ripening dynamics, the single and multiple island diffusion on the curved surface and coalescence-driven coarsening dynamics of island emulsions in microgravity. On Earth, such island emulsions would rapidly sediment to the bottom of the bubble and coalesce, but in microgravity, coarsening of the emulsion can be observed free of gravitational effects.

liquid crystal↗

The Oxidation State of Sulfur in Martian Apatite- Implications for Redox of Surficial Processes

Meteorites from Mars record fO2 values of ∆IW = -1 to +6.5 [1, 2]. This relatively large range in fO2 has been attributed to igneous processes like differentiation and assimilation, or sometimes to alteration [2, 3], modifying the range inherited from the Martian mantle, which is thought to be closer to the values recorded by lunar basalts (~∆IW -1 [e.g., 1]). Trace element compositions reveal that those Martian meteorites that are light Rare Earth Elements (LREE) enriched record higher fO2 values than those that are LREE-depleted [2]. Sulfur (S) has been used to track redox and alteration processes on Mars because it can be present in multiple redox states varying from S2- in magmatic sulfides to S6+ in sedimentary sulfate deposits and alteration products like jarosite [4, 5]. Apatite (Ca5(PO4)3(F,Cl,OH)) is found in many of the Martian meteorites as a late stage crystallizing mineral. It can incorporate both S^(2-) [6] or S^(6+) [7] or mixtures of both [7, 8] in its crystal structure, and it has been hypothesized that the relative proportions of S^(2-) and S^(6+) in apatite will depend on the prevailing fO2 in which it formed (along with P, T, and major element composition). Note: Extended abstract on document.

P. Chowdhury↗

Compact programmable photonic variable delay devices

Optical variable delay devices for providing variable true time delay to multiple optical beams simultaneously. A ladder-structured variable delay device comprises multiple basic building blocks stacked on top of each other resembling a ladder. Each basic building block has two polarization beamsplitters and a polarization rotator array arranged to form a trihedron; Controlling an array element of the polarization rotator array causes a beam passing through the array element either going up to a basic building block above it or reflect back towards a block below it. The beams going higher on the ladder experience longer optical path delay. An index-switched optical variable delay device comprises of many birefringent crystal segments connected with one another, with a polarization rotator array sandwiched between any two adjacent crystal segments. An array element in the polarization rotator array controls the polarization state of a beam passing through the element, causing the beam experience different refractive indices or path delays in the following crystal segment. By independently control each element in each polarization rotator array, variable optical path delays of each beam can be achieved. Finally, an index-switched variable delay device and a ladder-structured variable device are cascaded to form a new device which combines the advantages of the two individual devices. This programmable optic device has the properties of high packing density, low loss, easy fabrication, and virtually infinite bandwidth. The device is inherently two dimensional and has a packing density exceeding 25 lines/cm.sup.2. The delay resolution of the device is on the order of a femtosecond (one micron in space) and the total delay exceeds 10 nanosecond. In addition, the delay is reversible so that the same delay device can be used for both antenna transmitting and receiving.

Yao, X. Steve↗

Photonic variable delay devices based on optical birefringence

Optical variable delay devices for providing variable true time delay to multiple optical beams simultaneously. A ladder-structured variable delay device comprises multiple basic building blocks stacked on top of each other resembling a ladder. Each basic building block has two polarization beamsplitters and a polarization rotator array arranged to form a trihedron; Controlling an array element of the polarization rotator array causes a beam passing through the array element either going up to a basic building block above it or reflect back towards a block below it. The beams going higher on the ladder experience longer optical path delay. An index-switched optical variable delay device comprises of many birefringent crystal segments connected with one another, with a polarization rotator array sandwiched between any two adjacent crystal segments. An array element in the polarization rotator array controls the polarization state of a beam passing through the element, causing the beam experience different refractive indices or path delays in the following crystal segment. By independently control each element in each polarization rotator array, variable optical path delays of each beam can be achieved. Finally, an index-switched variable delay device and a ladder-structured variable device are cascaded to form a new device which combines the advantages of the two individual devices. This programmable optic device has the properties of high packing density, low loss, easy fabrication, and virtually infinite bandwidth. The device is inherently two dimensional and has a packing density exceeding 25 lines/cm2. The delay resolution of the device is on the order of a femtosecond (one micron in space) and the total delay exceeds 10 nanosecond. In addition, the delay is reversible so that the same delay device can be used for both antenna transmitting and receiving.

Yao, X. Steve↗

FIB-TEM Investigations of Fe-NI-Sulfides in the CI Chondrites Alais and Orgueil

The CI chondrites are primitive meteorites with bulk compositions matching the solar photosphere for all but the lightest elements. They have been extensively aqueously altered, and are composed primarily of fine-grained phyllosilicate matrix material which is host to carbonates, sulfates, sulfides, and minor amounts of olivine and pyroxene. The alteration, while extensive, is heterogeneous. For example, CI-chondrite cubanite and carbonate grains differ on mm to sub-mm scales, demonstrating multiple aqueous episodes. CI-chondrite variability is also evidenced by degree of brecciation, abundance and size of coarse-grained phyllosilicates, olivine and pyroxene abundance, as well as Ni-content and size of sulfide grains. Our previous work revealed Orgueil sulfide grains with variable Ni-contents, metal:S ratios, crystal structures and textures. We continue to explore the variability of CI-chondrite pyrrhotite (Po, (FeNi)1-xS) and pentlandite (Pn, (Fe,Ni)9S8) grains. We investigate the microstructure of sulfides within and among CI-chondrite meteorites in order to place constraints on the conditions under which they formed.

Berger, Eve L.↗

Constraints on Mechanisms of Chondrule Formation from Chondrule Precursors and Chronology of Transient Heating Events in the Protoplanetary Disk

The mineralogy, petrography, and oxygen-isotope compositions of porphyritic chondrules—dominant chondrule type in most chondrite groups—suggest formation by incomplete melting of isotopically diverse precursors during localized transient heating events in dust-rich regions of the protoplanetary disk characterized by 16O-poor compositions (D17Odust+gas~ –7‰ to +4‰) relative to the inferred Sun’s value (D17O ~ –28 ± 2‰). The chondrule precursors included Ca,Al-rich inclusions (CAIs), amoeboid olivine aggregates (AOAs), chondrules of earlier generations, fine-grained matrix-like material, and possibly fragments of pre-existing planetesimals. Like porphyritic chondrules, igneous CAIs formed by melting of isotopically diverse precursors during transient heating events, but in an isotopically distinct, solar-like reservoir of the protoplanetary disk (D17O dust + gas ~ –24‰), probably near the proto Sun. Based on a narrow range of the initial 26Al/27Alratios inferred from the internal Al-Mg isochrons in igneous CAIs, their melting started at the very beginning of Solar System formation (t0), defined by the CV CAIs with U-corrected Pb-Pb age of 4567.3 ± 0.16 Ma and the canonical 26Al/27Al ratio of (5.25 ± 0.02) ¥ 10–5, and lasted at least 0.3 Ma. The U-corrected Pb-Pb absolute and 26Al-26Mg relative ages of porphyritic chondrules from type 3 ordinary, CO, CV, and CR carbonaceous chondrites (assuming uniform distribution of 26Al in the disk at the canonical level) suggest chondrule formation started at t0 and lasted for about 4 Ma. These observations may preclude formation of the majority of porphyritic chondrules by splashing of differentiated planetesimals and by collisions between planetesimals; instead, they are consistent with melting of dust balls by bow shocks or magnetized turbulence in the disk. Some porphyritic chondrules in equilibrated (petrologic type 4–6) ordinary chondrites contain relict fragments of coarse-grained chromite, ilmenite, phosphates, and albitic plagioclase. The similar mineral assemblage is commonly observed in type 4–6 ordinary chondrites, but is absent in type 3 chondrites, suggesting these chondrules formed by incomplete melting of thermally metamorphosed ordinary chondrite material, possibly by impacts. The CB metal-rich carbonaceous chondrites contain exclusively magnesian non-porphyritic chondrules crystallized from complete melts. These chondrules formed in a gas-melt plume generated by a hypervelocity (≥20 km/s) collision between planetesimals ~4.8 Ma after t0 in a transition or a debris disk. One of the colliding bodies was probably differentiated. The CH metal-rich carbonaceous chondrites contain chondrules formed by different mechanisms. The magnesian non-porphyritic chondrules formed in the CB impact plume ~4.8 Ma after t0. The chemically diverse (magnesian, ferroan, and Al-rich) porphyritic chondrules formed by incomplete melting of isotopically diverse precursors in the protoplanetary disk, most likely prior the CB impact plume event. We conclude that there are multiple mechanisms of chondrule formation that operated over the entire life-time of the disk.

Chondrules↗

A petrologic and ion microprobe study of a Vigarano Type B refractory inclusion - Evolution by multiple stages of alteration and melting

A Type B Ca-, Al-rich 6-m-diam inclusion (CAI) found in the Vigarano C3V chondrite was inspected using optical and scanning electron microscopies and ion microprobe analyses. It was found that the primary constituents of the CAI inclusion are (in percent), melilite (52), fassaite, (20), anorthite (18), spinel (10), and trace Fe-Ni metal. It is noted that, while many of the properties of the inclusion indicate solidification from a melt droplet, the Al-26/Mg-26 isotopic systematics and some textural relationships are incompatible with single-stage closed system crystallization of a homogeneous molten droplet, indicating that the history of this inclusion must have been more complex than melt solidification alone. Moreover, there was unusually high content of Na in melilite, suggesting that the droplet did not form by melting of pristine high-temperature nebular condensates.

Macpherson, Glenn J.↗

Improved Crystal Quality By Detached Solidification in Microgravity

Many microgravity directional solidification experiments yielded ingots with portions that grew without contacting the ampoule wall, leading to greatly improved crystallographic perfection. Our long term goals have been: (1) To develop a complete understanding of all of the phenomena of detached solidification.; (2) To make it possible to achieve detached solidification reproducibly; (3) To increase crystallographic perfection through detached solidification. We have three major achievements to report here: (1) We obtained a new material balance solution for the Moving Meniscus Model of detached solidification. This solution greatly clarifies the physics as well as the roles of the parameters in the system; (2) We achieved detached solidification of InSb growing on earth in BN-coated ampoules; (3) We performed an extensive series of experiments on freezing water that showed how to form multiple gas bubbles or tubes on the ampoule wall. However, these did not propagate around the wall and lead to fully detached solidification unless the ampoule wall was extremely rough and non-wetted.

Regel, Liya L.↗

Oxide Scales Formed on NiTi and NiPtTi Shape Memory Alloys

Ni-49Ti and Ni-30Pt-50Ti (at.%) shape memory alloys were oxidized isothermally in air over the temperature range of 500 to 900 C. The microstructure, composition, and phase content of the scales were studied by SEM, EDS, XRD, and metallography. Extensive plan view SEM/EDS identified various features of intact or spalled scale surfaces. The outer surface of the scale was a relatively pure TiO2 rutile structure, typified by a distinct highly striated and faceted crystal morphology. Crystal size increased significantly with temperature. Spalled regions exhibited some porosity and less distinct features. More detailed information was obtained by correlation of SEM/EDS studies of 700 C/100 hr cross-sections with XRD analyses of serial or taper-polishing of plan surfaces. Overall, multiple layers exhibited graded mixtures of NiO, TiO2, NiTiO3, Ni(Ti) or Pt(Ni,Ti) metal dispersoids, Ni3Ti or Pt3Ti depletion zones, and substrate, in that order. The NiTi alloy contained a 3 at.% Fe impurity that appeared in embedded localized Fe-Ti-rich oxides, while the NiPtTi alloy contained a 2 v/o dispersion of TiC that appeared in lower layers. The oxidation kinetics of both alloys (in a previous report) indicated parabolic growth and an activation energy (250 kJ/mole) near those reported in other Ti and NiTi studies. This is generally consistent with TiO2 existing as the primary scale constituent, as described here.

Smialek, James L.↗

Characterization of erosion of metallic materials under cavitation attack in a mineral oil

Cavitation erosion and erosion rates of eight metallic materials representing three crystal structures were studied using a 20-kHz ultrasonic magnetostrictive oscillator in viscous mineral oil. The erosion rates of the metals with an fcc matrix were 10 to 100 times higher than that of an hcp-matrix titanium alloy. The erosion rates of iron and molybdenum, with bcc matrices, were higher than that of the titanium alloy but lower than those of the fcc metals. Scanning electron microscopy indicates that the cavitation pits are initially formed at the grain boundaries and precipitates and that the pits that formed at the triple points grew faster than the others. Transcrystalline craters formed by cavitation attack over the surface of grains and roughened the surfaces by multiple slip and twinning. Surface roughness measurements show that the pits that formed over the grain boundaries deepended faster than other pits. Computer analysis revealed that a geometric expression describes the nondimensional erosion curves during the time period 0.5 t(0) t 2.5 t(0), where t(0) is the incubation period. The fcc metals had very short incubation periods; the titanium alloy had the longest incubation period.

Rao, B. C. S.↗

NASA Tech Briefs, February 2004

Topics include: Simulation Testing of Embedded Flight Software; Improved Indentation Test for Measuring Nonlinear Elasticity; Ultraviolet-Absorption Spectroscopic Biofilm Monitor; Electronic Tongue for Quantitation of Contaminants in Water; Radar for Measuring Soil Moisture Under Vegetation; Modular Wireless Data-Acquisition and Control System; Microwave System for Detecting Ice on Aircraft; Routing Algorithm Exploits Spatial Relations; Two-Finger EKG Method of Detecting Evasive Responses; Updated System-Availability and Resource-Allocation Program; Routines for Computing Pressure Drops in Venturis; Software for Fault-Tolerant Matrix Multiplication; Reproducible Growth of High-Quality Cubic-SiC Layers; Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites; Liquid-Crystal Thermosets, a New Generation of High-Performance Liquid-Crystal Polymers; Formulations for Stronger Solid Oxide Fuel-Cell Electrolytes; Simulation of Hazards and Poses for a Rocker-Bogie Rover; Autonomous Formation Flight; Expandable Purge Chambers Would Protect Cryogenic Fittings; Wavy-Planform Helicopter Blades Make Less Noise; Miniature Robotic Spacecraft for Inspecting Other Spacecraft; Miniature Ring-Shaped Peristaltic Pump; Compact Plasma Accelerator; Improved Electrohydraulic Linear Actuators; A Software Architecture for Semiautonomous Robot Control; Fabrication of Channels for Nanobiotechnological Devices; Improved Thin, Flexible Heat Pipes; Miniature Radioisotope Thermoelectric Power Cubes; Permanent Sequestration of Emitted Gases in the Form of Clathrate Hydrates; Electrochemical, H2O2-Boosted Catalytic Oxidation System; Electrokinetic In Situ Treatment of Metal-Contaminated Soil; Pumping Liquid Oxygen by Use of Pulsed Magnetic Fields; Magnetocaloric Pumping of Liquid Oxygen; Tailoring Ion-Thruster Grid Apertures for Greater Efficiency; and Lidar for Guidance of a Spacecraft or Exploratory Robot.

Source record↗

Characterization of erosion of metallic materials under cavitation attack in a mineral oil

Cavitation erosion and erosion rates of eight metallic materials representing three crystal structures were studied. The erosion experiments were conducted with a 20-kHz ultrasonic magnetostrictive oscillator in a viscous mineral oil. The erosion rates of the metals with an fcc matrix were 10 to 100 times higher than that of an hop-matrix titanium alloy. The erosion rates of iron and molybdenum, with bcc matrices, were higher than that of the titanium alloy but lower than those of those of the fcc materials. Studies with scanning electron microscopy indicated that the cavitation pits were initially formed at the grain boundaries and precipitates and that the pits formed at the junction of grain boundaries grew faster than the others. Transcrystalline craters formed by cavitation attack over the surface of grains and roughened the surfaces by multiple slip and twinning. Surface roughness measurements showed that the pits that formed over the grain boundaries deepened faster than pits. Computer analysis revealed that a geometric expression describes the nondimensional erosion curves during the time period 0.5 t (sub 0) t 2.5 t (sub 0), where t (sub 0) is the incubation period. The fcc metals had very short incubation periods; the titanium alloy had the longest incubation period.

Rao, B. C. S.↗