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NASA NTRS2003

Magmatic Processes That Produced Lunar Fire Fountains

Reanalysis of the Apollo 15 A, B, and C green glass beads from slide 15426,72, led to the discovery of patchy, highly vesicular glass rims adhering to beads. These rims are high in S and Ni and low in MgO, but otherwise compositionally similar to the green glasses. We find that these rims represent a unique melt composition that places constraints on lunar magmatic processes. Combining the compositional data for the vesicular glass rims with new minor element data for the green glass beads leads us to hypothesize that the vesicular rim fluid originated near the green glass source, at about 2.2 GPa. These findings support the theory of a heterogeneous lunar mantle, and suggest that sulfur did not drive the eruption from depth, but that degassing volatiles into the vacuum did drive the final fire fountain eruption.

Elkins-Tanton, Linda T.↗
NASA NTRS2008

Foam Spray Cooling Heat Transfer Performance Study

Previous studies have shown that spray cooling heat flux enhancement may be attained using enhanced surfaces. However, most enhanced surface spray cooling studies have been limited to extended and/or embedded surface structures. This study investigates the effect of foam on spray cooling heat flux. The foam used was graphite Poco Foam. The foam piece was attached to a copper block with a cross-sectional area of 2.0 cm(sup 2) using high thermal conductivity epoxy as the thermal interface material (TIM). Measurements were also obtained on a heater block with a flat surface for purposes of baseline comparison. A 2x2 nozzle array was used with PF-5060 as the working fluid. Thermal performance data was obtained under nominally degassed conditions (chamber pressure of 41.4 kPa). Results show that the highest heat flux (CHF) attained was 113 W/cm(sup 2) using the graphite Poco Foam.

Silk, E. A.↗
NASA NTRS2007

Hardware Outgassing Certification

This viewgraph presentation reviews the outgassing of hardware to be used in space environments, to reduce the contamination levels such that the effects of the remaining contaminants are acceptable. The process of degassing materials that are to be used for constructing space hardware is detailed, and the data collection and analysis process is also detailed.

Hughes, David↗
NASA NTRS2009

Solubility of Sulfur in Shergottitic Silicate Melts Up to 0.8 GPA: Implications for S Contents of Shergottites

Shergottites have high S contents (1300 to 4600 ppm; [1]), but it is unclear if they are sulfide saturated or under-saturated. This issue has fundamental implications for determining the long term S budget of the martian surface and atmosphere (from mantle degassing), as well as evolution of the highly siderophile elements (HSE) Au, Pd, Pt, Re, Rh, Ru, Ir, and Os, since concentrations of the latter are controlled by sulfide stability. Resolution of sulfide saturation depends upon temperature, pressure, oxygen fugacity (and FeO), and magma composition [2]. Expressions derived from experimental studies allow prediction of S contents, though so far they are not calibrated for shergottitic liquids [3-5]. We have carried out new experiments designed to test current S saturation models, and then show that existing calibrations are not suitable for high FeO and low Al2O3 compositions characteristic of shergottitic liquids. The new results show that existing models underpredict S contents of sulfide saturated shergottitic liquids by a factor of 2.

Righter, K.↗
NASA NTRS2009

Relative Shock Effects in Mixed Powders of Calcite, Gypsum, and Quartz: A Calibration Scheme from Shock Experiments

The shock behavior of calcite and gypsum is important in understanding the Cretaceous/Tertiary event and other terrestrial impacts that contain evaporite sediments in their targets. Most interest focuses on issues of devolatilization to quantify the production of CO2 or SO2 to better understand their role in generating a temporary atmosphere and its effects on climate and biota [e.g., papers in 1,2,3,4]. Devolatilization of carbonate is also important because the dispersion and fragmentation of ejecta is strongly controlled by the expansion of large volumes of gas during the impact process as well [5,6]. Shock recovery experiments for calcite yield seemingly conflicting results: early experimental devolatilization studies [7,8,9] suggested that calcite was substantially outgassed at 30 GPa (> 50%). However, the recent petrographic work of [10,11,12] presented evidence that essentially intact calcite is recovered from 60 GPa experiments. [13] reported results of shock experiments on anhydrite, gypsum, and mixtures of those phases with silica. Their observations indicate little or no devolatilization of anhydrite shocked to 42 GPa and that the fraction of sulfur, by mass, that degassed is approx.10(exp -2) of theoretical prediction. In another (preliminary) report of shock experiments on calcite, anhydrite, and gypsum, [14] observe calcite recrystallization when shock loaded at 61 GPa, only intensive plastic deformation in anhydrite shock loaded at 63 GPa, and gypsum converted to anhydrite when shock loaded at 56 GPa. [15] shock loaded anhydrite and quartz to a peak pressure of 60 GPa. All of the quartz grains were trans-formed to glass and the platy anhydrite grains were completely pseudomorphed by small crystallized anhydrite grains. However, no evidence of interaction between the two phases could be observed and they suggest that recrystallization of anhydrite grains is the result of a solid state transformation. [16] reanalyzed the calcite and anhydrite shock wave experiments of [17] using improved equations of state of porous materials and vaporized products. They determined the pressures for incipient and complete vaporization to be 32.5 and 122 GPa for anhydrite and 17.8 and 54.1 GPa for calcite, respectively, a factor of 2 to 3 lower than reported earlier by [17].

Bell, Mary S.↗
NASA NTRS2009

Liquid Water on Enceladus from Observations of Ammonia and Ar-40 in the Plume

Jets of water ice from surface fractures near the south pole of Saturn's icy moon Enceladus produce a plume of gas and particles. The source of the jets may be a liquid water region under the ice shell-as suggested most recently by the discovery of salts in E-ring particles derived from the plume-or warm ice that is heated, causing dissociation of clathrate hydrates. Here we report that ammonia is present in the plume, along with various organic compounds, deuterium and, very probably, Ar-40. The presence of ammonia provides strong evidence for the existence of at least some liquid water, given that temperatures in excess of 180 K have been measured near the fractures from which the jets emanate. We conclude, from the overall composition of the material, that the plume derives from both a liquid reservoir (or from ice that in recent geological time has been in contact with such a reservoir) as well as from degassing, volatile-charged ice. As part of a general comprehensive review of the midsize saturnian satellites at the conclusion of the prime Cassini mission, PI McKinnon and co-I Barr contributed to three review chapters.

Waite, J. H., Jr.↗
NASA NTRS2011

Sm-Nd Isotopic Studies of Ureilite Novo Urei

Ureilites are ultramafic (harzburgitic) achondrites composed predominantly of olivine and pyroxenes, abundant carbon (graphites and shock-produced diamonds), some metal and sulfides. These rocks probably represent ultramafic mantles of differentiated parent asteroidal bodies. Age determinations of these rocks by Rb-Sr and Sm-Nd methods have been difficult because of their extremely low abundances of these parent-daughter elements. Nevertheless, Sm-Nd isochron ages were reported for Kenna, Goalpara, MET 78008 and PCA 82506 yielding ages of 3.74+/-0.02 Ga, approx.3.7 Ga, 4.09+/-0.08 Ga, 4.23+/-0.06 Ga, respectively [1-4]. These "young" Sm-Nd ages may represent secondary metasomatism events [1] related to impacts [5], as indicated by the similarly young Ar-39-Ar-40 degassing ages of 3.3-4.1 Ga for ureilites Kenna, Novo Urei and Havero [6]. Alternatively, it has been suggested that these rocks may have been contaminated with terrestrial crustal materials and the isochrons do not have any age significance [2,7]. Indications of old approx.4.56 Ga ages for ureilites were reported from the U-Pb and Sm-Nd model ages for MET 78008 [8]. More reliable evidences for old formation ages of ureilites were reported recently using the short-lived chronometers Hf-182-W-182, Al-26-Mg-26 and Mn-53-Cr-53. The deficits of 182W in ureilites suggest the metal-silicate segregation occurred very early, approx.1-2 Ma after CAI [9]. The Al-26-Mg-26 and Mn-53-Cr-53 studies for a feldspathic lithology [10] and the Mn-53-Cr-53 for olivine- and pyroxene-dominant lithologies [11] in ureilites revealed that they crystallized approx.5.4 Ma after CAI, i.e., at 4563.8+/-0.5 Ma relative to D.Orbigny. In this report, we present Sm-Nd isotopic data for a relatively fresh ureilite, Novo Urei, a rare ureilite fall (1886). We compare these data to Sm-Nd data for other ureilites, and discuss Novo Urei's petrogenesis

Shih, C.-Y.↗
NASA NTRS2011

Experimental Shock Transformation of Gypsum to Anhydrite: A New Low Pressure Regime Shock Indicator

The shock behavior of gypsum is important in understanding the Cretaceous/Paleogene event and other terrestrial impacts that contain evaporite sediments in their targets (e.g., Mars Exploration Rover Spirit detected sulfate at Gusev crater, [1]). Most interest focuses on issues of devolatilization to quantify the production of SO2 to better understand its role in generating a temporary atmosphere and its effects on climate and biota [2,3]. Kondo and Ahrens [4] measured induced radiation emitted from single crystal gypsum shocked to 30 and 40 GPa. They observed greybody emission spectra corresponding to temperatures in the range of 3,000 to 4,000 K that are a factor of 2 to 10 times greater than calculated pressure-density energy equation of state temperatures (Hugoniot) and are high enough to melt gypsum. Chen et al. [5] reported results of shock experiments on anhydrite, gypsum, and mixtures of these phases with silica. Their observations indicated little or no devolatilization of anhydrite shocked to 42 GPa and that the fraction of sulfur, by mass, that degassed is approx.10(exp -2) of theoretical prediction. In another report of shock experiments on calcite, anhydrite, and gypsum, Badjukov et al. [6] observed only intensive plastic deformation in anhydrite shock loaded at 63 GPa, and gypsum converted to anhydrite when shock loaded at 56 GPa but have not experimentally shocked gypsum in a step-wise manner to constrain possible incipient transformation effects. Schmitt and Hornemann [7] shock loaded anhydrite and quartz to a peak pressure of 60 GPa and report the platy anhydrite grains were completely pseudomorphed by small crystallized anhydrite grains. However, no evidence of interaction between the two phases could be observed and they suggested that recrystallization of anhydrite grains is the result of a solid-state transformation. They concluded that significant decomposition of anhydrite requires shock pressures higher than 60 GPa. Gupta et al. [8] reanalyzed the calcite and anhydrite shock wave experiments of Yang [9] using improved equations of state of porous materials and vaporized products. They determined the pressures for incipient and complete vaporization to be 32.5 and 122 GPa for anhydrite GPa which is a factor of 2 to 3 lower than reported earlier by Yang [9]. These studies are not in agreement regarding the onset of sulfate decomposition and documentation of shock effects in gypsum is incomplete.

Bell, Mary S.↗
NASA NTRS2012

Evidence from Olivine-Hosted Melt Inclusions that the Martian Mantle has a Chondritic D/H Ratio and that Some Young Basalts have Assimilated Old Crust

Magmatic degassing of volatile elements affects the climate and near-surface environment of Mars. Telescopic and meteorite studies have revealed that the Martian atmosphere and near-surface materials have D/H ratios ~5-6 times terrestrial values [e.g., 1, 2]. Such high D/H ratios are interpreted to result from the preferential loss of H relative to heavier D from the Martian atmosphere, assuming that the original Martian water inventory had a D/H ratio similar to terrestrial values and to H in primitive meteorites [e.g., 1, 3]. However, the primordial Martian D/H ratio has, until now, not been well constrained. The uncertainty over the Martian primordial D/H ratio has arisen both from the scarcity of primitive Martian meteorites and as a result of contamination by terrestrial and, perhaps, Martian surface waters that obscure the signature of the Martian mantle. This study reports a comprehensive dataset of magmatic volatiles and D/H ratios in Martian primary magmas based on low-contamination, in situ ion microprobe analyses of olivine-hosted melt inclusions from both depleted [Yamato 980459 (Y98)] and enriched [Larkman Nunatak 06319 (LAR06)] Martian basaltic meteorites. Analyses of these primitive melts provide definitive evidence that the Martian mantle has retained a primordial D/H ratio and that young Martian basalts have assimilated old Martian crust.

Usui, Tomohiro↗
NASA NTRS2011

Microphysical, Macrophysical and Radiative Signatures of Volcanic Aerosols in Trade Wind Cumulus Observed by the A-Train

Increased aerosol concentrations can raise planetary albedo not only by reflecting sunlight and increasing cloud albedo, but also by changing cloud amount. However, detecting aerosol effect on cloud amount has been elusive to both observations and modeling due to potential buffering mechanisms and convolution of meteorology. Here through a natural experiment provided by long-tem1 degassing of a low-lying volcano and use of A-Train satellite observations, we show modifications of trade cumulus cloud fields including decreased droplet size, decreased precipitation efficiency and increased cloud amount are associated with volcanic aerosols. In addition we find significantly higher cloud tops for polluted clouds. We demonstrate that the observed microphysical and macrophysical changes cannot be explained by synoptic meteorology or the orographic effect of the Hawaiian Islands. The "total shortwave aerosol forcin", resulting from direct and indirect forcings including both cloud albedo and cloud amount. is almost an order of magnitude higher than aerosol direct forcing alone. Furthermore, the precipitation reduction associated with enhanced aerosol leads to large changes in the energetics of air-sea exchange and trade wind boundary layer. Our results represent the first observational evidence of large-scale increase of cloud amount due to aerosols in a trade cumulus regime, which can be used to constrain the representation of aerosol-cloud interactions in climate models. The findings also have implications for volcano-climate interactions and climate mitigation research.

Yuan, T.↗
NASA NTRS2012

Spacesuit Portable Life Support System Breadboard (PLSS 1.0) Development and Test Results

A multi-year effort has been carried out at the Johnson Space Center to develop an advanced EVA PLSS design intended to further the current state of the art by increasing operational flexibility, reducing consumables, and increasing robustness. This multi-year effort has culminated in the construction and operation of PLSS 1.0, a test rig that simulates full functionality of the advanced PLSS design. PLSS 1.0 integrates commercial off-the-shelf hardware with prototype technology development components, including the primary and secondary oxygen regulators, ventilation loop fan, Rapid Cycle Amine (RCA) swingbed, and Spacesuit Water Membrane Evaporator (SWME). PLSS 1.0 was tested from June 17th through September 30th, 2011. Testing accumulated 233 hours over 45 days, while executing 119 test points. An additional 164 hours of operational time were accrued during the test series, bringing the total operational time for PLSS 1.0 testing to 397 hours. Specific PLSS 1.0 test objectives assessed during this testing include: (1) Confirming prototype components perform in a system level test as they have performed during component level testing, (2) Identifying unexpected system-level interactions (3) Operating PLSS 1.0 in nominal steady-state EVA modes to baseline subsystem performance with respect to metabolic rate, ventilation loop pressure and flow rate, and environmental conditions (4) Simulating nominal transient EVA operational scenarios (5) Simulating contingency EVA operational scenarios (6) Further evaluating prototype technology development components Successful testing of the PLSS 1.0 provided a large database of test results that characterize system level and component performance. With the exception of several minor anomalies, the PLSS 1.0 test rig performed as expected. Documented anomalies and observations include: (1) Ventilation loop fan controller issues at high fan speeds (near 70,000 rpm, whereas the fan speed during nominal operations would be closer to 35,000 rpm) (2) RCA performance at boundary conditions, including carbon dioxide and water vapor saturation events, as well as reduced vacuum quality (3) SWME valve anomalies (4 documented cases where the SWME failed to respond to a control signal or physically jammed, preventing SWME control) (4) Reduction of SWME hollow fiber hydrophobicity and significant reduction of the SWME degassing capability after significant accumulated test time.

Watts, Carly A.↗
NASA NTRS2013

Evidence for a "Wet" Early Moon

The Moon was thought to have lost its volatiles during impact(s) of a Mars-size planetesimal with the proto Earth [1] and during degassing of an early planet-wide magma ocean [2]. This view of an anhydrous Moon, however, has been challenged by recent discoveries of water on its surface [3-5] and in lunar volcanics [6-10] and regoliths [11]. Indigenous water is suggested to be heterogeneously distributed in the lunar interior and some parts of lunar mantle may contain as much water as Earth's upper mantle [6,10]. This water is thought to have been brought in part through solar wind implantation [3-5,8,11] and meteorite/cometary impacts [3,4,8,12] after the formation of the primary crust. Here we measured water in primary products of the Lunar Magma Ocean (LMO) thereby by-passing the processes of later addition of water to the Moon through impact events or during mantle overturn as suggested by previous studies (e.g., [8,12]). So far, ferroan anorthosite (FAN) is the only available lithology that is believed to be a primary product of the LMO [2]. It is generally accepted that plagioclase, after crystallization, floated in the LMO and formed FAN as the original crust [2]. Therefore, any indigenous water preserved in FAN was partitioned from the LMO. These data can be used to estimate the water content of the magma ocean at the time of plagioclase crystallization, as well as that of the mare magma source regions.

Hui, Hejiu↗
NASA NTRS2013

Sheet Membrane Spacesuit Water Membrane Evaporator

A document describes a sheet membrane spacesuit water membrane evaporator (SWME), which allows for the use of one common water tank that can supply cooling water to the astronaut and to the evaporator. Test data showed that heat rejection performance dropped only 6 percent after being subjected to highly contaminated water. It also exhibited robustness with respect to freezing and Martian atmospheric simulation testing. Water was allowed to freeze in the water channels during testing that simulated a water loop failure and vapor backpressure valve failure. Upon closing the backpressure valve and energizing the pump, the ice eventually thawed and water began to flow with no apparent damage to the sheet membrane. The membrane evaporator also serves to de-gas the water loop from entrained gases, thereby eliminating the need for special degassing equipment such as is needed by the current spacesuit system. As water flows through the three annular water channels, water evaporates with the vapor flowing across the hydrophobic, porous sheet membrane to the vacuum side of the membrane. The rate at which water evaporates, and therefore, the rate at which the flowing water is cooled, is a function of the difference between the water saturation pressure on the water side of the membrane, and the pressure on the vacuum side of the membrane. The primary theory is that the hydrophobic sheet membrane retains water, but permits vapor pass-through when the vapor side pressure is less than the water saturation pressure. This results in evaporative cooling of the remaining water.

Bue, Grant↗
NASA NTRS2013

Preliminary Interpretations of Atmospheric Stable Isotopes and Argon from Mars Science Laboratory (SAM)

Given the broad agreement between C, H, and O isotopic ratios in the modern atmosphere and the ALH 84001 meteorite, it is possible that these reservoirs were established after early atmospheric loss prior to 4 Ga. The preservation of these signals over this long period of history can be explained in several slightly different ways: 1) C, O, and H have remained static in the atmosphere and have not exchanged with the surface over the past 4 Ga; 2) C, O, and H in the atmosphere have potentially varied widely over history but have been continually buffered by larger reservoirs in the crust which have remained unchanged over the past 4 Ga. This second possibility allows for potentially large variations in atmospheric pressure to occur as CO2 is recycled back into the atmosphere from crustal reservoirs or degassed from the mantle.

Jones, J. H.↗
NASA NTRS2013

Carbonate Mineral Formation on Mars: Clues from Stable Isotope Variation Seen in Cryogenic Laboratory Studies of Carbonate Salts

The geologic history of water on the planet Mars is intimately connected to the formation of carbonate minerals through atmospheric CO2 and its control of the climate history of Mars. Carbonate mineral formation under modern martian atmospheric conditions could be a critical factor in controlling the martian climate in a means similar to the rock weathering cycle on Earth. The combination of evidence for liquid water on the martian surface and cold surface conditions suggest fluid freezing could be very common on the surface of Mars. Cryogenic calcite forms readily when a rise in pH occurs as a result of carbon dioxide degassing quickly from freezing Ca-bicarbonate-rich water solutions. This is a process that has been observed in some terrestrial settings such as arctic permafrost cave deposits, lakebeds of the Dry Valleys of Antarctica, and in aufeis (river icings) from rivers of N.E. Alaska. We report here the results of a series of laboratory experiments that were conducted to simulate potential cryogenic carbonate formation on the planet Mars. These results indicate that carbonates grown under martian conditions (controlled atmospheric pressure and temperature) show enrichments from starting bicarbonate fluids in both carbon and oxygen isotopes beyond equilibrium values with average delta13C(DIC-CARB) values of ~20.5%0 which exceed the expected equilibrium fractionation factor of [10(sup 3) ln alpha = ~13%0] at 0 degC. Oxygen isotopes showed a smaller enrichment with delta18O(H2O-CARB) values of ~35.5%0, slightly exceeding the equilibrium fractionation factor of [10(sup 3) ln alpha = ~34%0 ] at 0degC. Large kinetic carbon isotope effects during carbonate precipitation could substantially affect the carbon isotope evolution of CO2 on Mars allowing for more efficient removal of 13C from the Noachian atmosphere enriched by atmospheric loss. This mechanism would be consistent with the observations of large carbon isotope variations in martian materials despite the relative paucity of carbonate minerals in the martian crust.

Socki, Richard↗
NASA NTRS2014

Core-Mantle Partitioning of Volatile Elements and the Origin of Volatile Elements in Earth and Moon

Depletions of volatile siderophile elements (VSE; Ga, Ge, In, As, Sb, Sn, Bi, Zn, Cu, Cd) in mantles of Earth and Moon, constrain the origin of volatile elements in these bodies, and the overall depletion of volatile elements in Moon relative to Earth. A satisfactory explanation has remained elusive [1,2]. We examine the depletions of VSE in Earth and Moon and quantify the amount of depletion due to core formation and volatility of potential building blocks. We calculate the composition of the Earth's PUM during continuous accretion scenarios with constant and variable fO2. Results suggest that the VSE can be explained by a rather simple scenario of continuous accretion leading to a high PT metal-silicate equilibrium scenario that establishes the siderophile element content of Earth's PUM near the end of accretion [3]. Core formation models for the Moon explain most VSE, but calculated contents of In, Sn, and Zn (all with Tc < 750 K) are all still too high after core formation, and must therefore require an additional process to explain the depletions in the lunar mantle. We discuss possible processes including magmatic degassing, evaporation, condensation, and vapor-liquid fractionation in the lunar disk.

Righter, Kevin↗
NASA NTRS2014

Rotating Balances Used for Fluid Pump Testing

Marshall Space Flight Center has developed and demonstrated two direct read force and moment balances for sensing and resolving the hydrodynamic loads on rotating fluid machinery. These rotating balances consist of a series of stainless steel flexures instrumented with semiconductor type, unidirectional strain gauges arranged into six bridges, then sealed and waterproofed, for use fully submerged in degassed water at rotational speeds up to six thousand revolutions per minute. The balances are used to measure the forces and moments due to the onset and presence of cavitation or other hydrodynamic phenomena on subscale replicas of rocket engine turbomachinery, principally axial pumps (inducers) designed specifically to operate in a cavitating environment. The balances are inserted into the drive assembly with power to and signal from the sensors routed through the drive shaft and out through an air-cooled twenty-channel slip ring. High frequency data - balance forces and moments as well as extensive, flush-mounted pressures around the rotating component periphery - are acquired via a high-speed analog to digital data acquisition system while the test rig conditions are varied continuously. The data acquisition and correction process is described, including the in-situ verifications that are performed to quantify and correct for known system effects such as mechanical imbalance, "added mass," buoyancy, mechanical resonance, and electrical bias. Examples of four types of cavitation oscillations for two typical inducers are described in the laboratory (pressure) and rotating (force) frames: 1) attached, symmetric cavitation, 2) rotating cavitation, 3) attached, asymmetric cavitation, and 4) cavitation surge. Rotating and asymmetric cavitation generate a corresponding unbalanced radial force on the rotating assembly while cavitation surge generates an axial force. Attached, symmetric cavitation induces no measurable force. The frequency of the forces can be determined a priori from the pressure environment while the magnitude of the hydrodynamic force is proportional to the pressure unsteadiness.

Skelley, Stephen↗
NASA NTRS2014

Martian Cryogenic Carbonate Formation: Stable Isotope Variations Observed in Laboratory Studies

The history of water on Mars is tied to the formation of carbonates through atmospheric CO2 and its control of the climate history of the planet. Carbonate mineral formation under modern martian atmospheric conditions could be a critical factor in controlling the martian climate in a means similar to the rock weathering cycle on Earth. The combination of evidence for liquid water on the martian surface and cold surface conditions suggest fluid freezing could be very common on the surface of Mars. Cryogenic calcite forms easily from freezing solutions when carbon dioxide degasses quickly from Ca-bicarbonate-rich water, a process that has been observed in some terrestrial settings such as arctic permafrost cave deposits, lake beds of the Dry Valleys of Antarctica, and in aufeis (river icings) from rivers of N.E. Alaska. A series of laboratory experiments were conducted that simulated cryogenic carbonate formation on Mars in order to understand their isotopic systematics. The results indicate that carbonates grown under martian conditions show variable enrichments from starting bicarbonate fluids in both carbon and oxygen isotopes beyond equilibrium values.

Socki, Richard A.↗