Stability problems in randomly-excited dynamic systems.
Stability problems in randomly excited dynamic systems, discussing partial differential equations governing evolution of conditional probabilities and expectations
RANDOM PROCESS↗
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Chronology of ungrouped achondrites Northwest Africa 11119 and 7325/8486: implications for early evolution of a heterogeneous crust on a differentiated planetesimal
The chronology of ungrouped achondrites provides key insights into the timeline of igneous activity in the early Solar System. Two ungrouped achondrites – Northwest Africa (NWA) 11119 (andesite-dacite) and NWA 8486 and its pair NWA 7325 (olivine gabbro) – are the focus of this study, where their chronologies are investigated using multiple high-resolution techniques. Here we report the lead-lead (207Pb-206Pb) and manganese-chromium (53Mn-53Cr) systematics of NWA 11119, as well as the 207Pb-206Pb systematics of NWA 8486 alongside aluminum-magnesium (26Al-26Mg) systematics for NWA 7325. The U-corrected 207Pb-206Pb ages of NWA 11119 and the combined ages of NWA 7325/8486 are 4566.4 ± 0.8 Ma and 4563.8 ± 1.9 Ma, respectively. Additionally, we report the 53Mn-53Cr age of NWA 11119 to be 4564.4 ± 2.5 Ma and the 26Al-26Mg age of NWA 7325/8486 to be 4563.1 ± 0.3 Ma. The formation of NWA 11119 requires partial melting of a (likely chondritic) source reservoir leading to eruption of Si rich, alkali depleted magmas, while NWA 7325/8486 likely formed from a chemically fractionated reservoir with superchondritic Al/Mg. The clear geochemical and isotopic similarities of these achondrites, combined with the chronology reported here, is suggestive of formation of these two ungrouped achondrites on a common parent body which likely formed in the inner Solar System and experienced early differentiation under reducing conditions. If these achondrites did share a parent body, it would suggest that primary asteroids in the early Solar System commonly produced mineralogically and geochemically heterogeneous crusts. While mineralogical and geochemical heterogeneity is known to exist in the (mostly mafic) crust of asteroid Vesta, our findings show that even more significant crustal heterogeneity (representing felsic and mafic compositions) may exist on other asteroids.
Cartwright, Julia [University of Leicester, UK]↗
An Iron-Rain Model for Core Formation on Asteroid 4 Vesta
Asteroid 4 Vesta is differentiated into a crust, mantle, and core, as demonstrated by studies of the eucrite and diogenite meteorites and by data from NASA's Dawn spacecraft. Most models for the differentiation and thermal evolution of Vesta assume that the metal phase completely melts within 20 degrees of the eutectic temperature, well before the onset of silicate melting. In such a model, core formation initially happens by Darcy flow, but this is an inefficient process for liquid metal and solid silicate. However, the likely chemical composition of Vesta, similar to H chondrites with perhaps some CM or CV chondrite, has 13-16 weight percent S. For such compositions, metal-sulfide melting will not be complete until a temperature of at least 1350 degrees Centigrade. The silicate solidus for Vesta's composition is between 1100 and 1150 degrees Centigrade, and thus metal and silicate melting must have substantially overlapped in time on Vesta. In this chemically and physically more likely view of Vesta's evolution, metal sulfide drops will sink by Stokes flow through the partially molten silicate magma ocean in a process that can be envisioned as "iron rain". Measurements of eucrites show that moderately siderophile elements such as Ni, Mo, and W reached chemical equilibrium between the metal and silicate phases, which is an important test for any Vesta differentiation model. The equilibration time is a function of the initial metal grain size, which we take to be 25-45 microns based on recent measurements of H6 chondrites. For these sizes and reasonable silicate magma viscosities, equilibration occurs after a fall distance of just a few meters through the magma ocean. Although metal drops may grow in size by merger with other drops, which increases their settling velocities and decreases the total core formation time, the short equilibration distance ensures that the moderately siderophile elements will reach chemical equilibrium between metal and silicate before metal drop merger becomes important. In this model, there must be at least 30 percent melting of the silicate phase when metal melting is complete, corresponding to a crust thickness of at least 30 kilometers on Vesta, consistent with Dawn gravity observations. Greater degrees of silicate melting and a correspondingly thicker crust are possible if Vesta accreted sufficiently rapidly.
Kiefer, Walter S.↗
Kernel methods for evolution of generalized parton distributions
Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The dependence of GPDs on the factorization scale Q 2 allows one to connect hard exclusive processes involving GPDs at disparate energy and momentum scales, which is needed in global analyses of experimental data. Here, in this work, we explore how finite element methods can be used to construct fast and differentiable Q 2 evolution codes for GPDs in momentum space, which can be used in a machine learning framework. We show numerical benchmarks of the methods' accuracy, including a comparison to an existing evolution code from PARTONS/APFEL++, and provide a repository where the code can be accessed.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Synthesis of Experimental Data Describing the Partitioning of Moderately Volatile Elements in Major Rock Forming Minerals: Implications for the Moon
Highly volatile elements [condensation temperatures below about 700 K] and water are highly informative about lunar bulk composition (hence origin), differentiation and magmatic evolution, and the role of impacts in delivering volatiles to the Moon. Fractionation of volatile elements compared to moderately volatile and refractory elements are informative about high-temperature conditions that operated in the proto-lunar disk. Existing data show clearly that the Moon is depleted in volatile elements compared to the bulk silicate Earth. For example, K/Th is ~400-700 in the Moon compared to 2800-3000 in Earth. A complicating factor is that the abundances of the highly volatile elements in major lunar lithologies vary by approximately two orders of magnitude. Perhaps most interesting, H2O is not correlated with the concentration of volatile elements, indicating a decoupling of highly volatile elements from the even more volatile H2O. We contend that this decoupling could be a significant tracer of processes operating during lunar formation, differentiation, and bombardment, and the combination of analyzing both volatile elements and water is likely to provide significant insight into lunar geochemical history. This variation and lack of correlation raises the question: what were the relative contributions of crystallization in the magma ocean, subsequent mantle overturn, production of secondary magmas, and addition of volatiles by large impacts in producing this apparently large range in volatile abundances? This current study will produce new partitioning data relevant to the role and distribution of the volatile and non-volatile, yet geochemically significant elements (Co, Ni, Zn, Se, Rb, Sr, Mo, Ag, Cd, In, Sb, Ce, Yb, Tl, Pb, Bi) during the thermal and magmatic evolution of the Moon.
Vander Kaaden, Kathleen E.↗
Mathematical Analysis and Optimization of Infiltration Processes
A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants.
Chang, H.-C.↗
Phase equilibria of the magnesium sulfate-water system to 4 kbars
Magnesium sulfate is the most abundant salt in carbonaceous chondrites, and it may be important in the low-temperature igneous evolution and aqueous differentiation of icy satellites and large chondritic asteroids. Accordingly, we are investigating high-pressure phase equilibria in MgSO4-H2O solutions under pressures up to four kbars. An initial report was presented two years ago. This abstract summarizes our results to date including studies of solutions containing 15.3 percent, 17 percent, and 22 percent MgSO4. Briefly, these results demonstrate that increasing pressure causes the eutectic and peritectic compositions to shift to much lower concentrations of magnesium sulfate, and the existence of a new low-density phase of magnesium sulfate hydrate.
Hogenboom, D. L.↗
Analysis of ERS 1 synthetic aperture radar data of frozen lakes in northern Montana and implications for climate studies
Lakes that freeze each winter are good indicators of regional climate change if key parameters, such as freeze-up and breakup date and maximum ice thickness, are measured over a decade-scale time frame. Synthetic aperture radar (SAR) satellite data have proven to be especially useful for measurement of climatologically significant parameters characteristic of frozen lakes. In this paper, five lakes in Glacier National Park, Montana, have been studied both in the field and using Earth Remote-Sensing Satellite (ERS) 1 SAR data during the 1992-1993 winter. The lakes are characterized by clear ice, sometimes with tubular or rounded bubbles, and often with a layer of snow ice on top of the clear ice. They are also often snow covered. Freeze-up is detected quite easily using ERS 1 SAR data as soon as a thin layer of ice forms. The effect of snow ice on the backscatter is thought to be significant but is, as yet, undetermined. On the five lakes studied, relative backscatter was found to increase with ice thickness until a maximum was reached in February. Breakup, an often ill-defined occurrence, is difficult to detect because surface water causes the SAR signal to be absorbed, thus masking the ice below. Comparison of the bubble structure of thaw lakes in northern Alaska with lakes in northern Montana has shown that the ice structure is quite different, and this difference may contribute to differential SAR signature evolution in the lakes of the two areas.
Hall, Dorothy K.↗
Evolution of the Debris Cloud Generated by the Fengyun-1C Fragmentation Event
The cloud of cataloged debris produced in low earth orbit by the fragmentation of the Fengyun-1C spacecraft was propagated for 15 years, taking into account all relevant perturbations. Unfortunately, the cloud resulted to be very stable, not suffering substantial debris decay during the time span considered. The only significant short term evolution was the differential spreading of the orbital planes of the fragments, leading to the formation of a debris shell around the earth approximately 7-8 months after the breakup, and the perigee precession of the elliptical orbits. Both effects will render the shell more "isotropic" in the coming years. The immediate consequence of the Chinese anti-satellite test, carried out in an orbital regime populated by many important operational satellites, was to increase significantly the probability of collision with man-made debris. For the two Italian spacecraft launched in the first half of 2007, the collision probability with cataloged objects increased by 12% for AGILE, in equatorial orbit, and by 38% for COSMO-SkyMed 1, in sun-synchronous orbit.
Pardini, Carmen↗
Chemical Mapping of Vesta
Vesta s surface mineralogy and composition have been studied for decades via telescopic spectroscopy and laboratory analyses of the howardite, eucrite, and diogenite (HED) meteorites, which are thought to originate from Vesta. Visible and infrared reflectance measurements by Dawn have broadly confirmed the paradigm established by Earth-based work, strengthening the Vesta-HED connection. The Dawn mission has achieved a milestone by completing the first chemical measurements of a main-belt asteroid using nuclear spectroscopy. Dawn s Gamma Ray and Neutron Detector (GRaND) has globally mapped the composition of Vesta, including the portions of the northern hemisphere not illuminated by solar radiation. GRaND is sensitive to the composition of the bulk regolith to depths of several decimeters. Abundances and/or detection limits for specific elements and elemental ratios, such as H, Fe, Si, Fe/O, Fe/Si, and K, have been measured. Variations in the average atomic mass and neutron macroscopic absorption cross section have been characterized. The measurements constrain the relative proportions of HED whole-rock end-members, providing measurements of the pyroxene and plagioclase content of the regolith, thereby constraining the processes underlying Vesta s differentiation and crustal evolution. The spatial resolution of GRaND is sufficient to determine basin-average compositions of Veneneia and Rheasilvia, which may contain outcrops of Vesta s olivine-rich mantle. While the elemental composition of Vesta s regolith is similar to the meteorites, there are notable departures from HED whole-rock compositions. While these differences are not sufficient to topple the Vesta-HED paradigm, they provide insight into global-scale processes that have shaped Vesta s surface. Questions addressed by the analysis of GRaND data include: (i) Is Vesta the source of the Fe-rich mesosiderites? (ii) Are evolved, igneous lithologies present on Vesta s surface? (iii) What are the origins of exogenic materials found in Vesta s regolith? (iv) Is the vestan mantle exposed within the southern basins?
Prettyman, Thomas H.↗
Assessing the Behavior of Typically Lithophile Elements Under Highly Reducing Conditions Relevant to the Planet Mercury
With the data returned from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (lvtESSENGER) mission, there are now numerous constraints on the physical and chemical properties of Mercury, including its surface composition. The high S and low FeO contents observed from MESSENGER suggest a low oxygen fugacity of the present materials on the planet's surface. Most of our understanding of elemental partitioning behavior comes from observations made on terrestrial rocks, but Mercury's oxygen fugacity is far outside the conditions of those samples, estimated at approximately 3-7 log units below the Iron-Wustite (lW) oxygen buffer, several orders of magnitude more reducing than other terrestrial bodies we have data from. With limited oxygen available, lithophile elements may instead exhibit chalcophile, halophile, or siderophile behaviors. Furthermore, very few natural samples of rocks that formed under reducing conditions (e.g., enstatite chondrites, achondrites, aubrites) are available in our collections for examination of this change in geochemical affinity. Our goal is to determine the elemental partitioning behavior of typically lithophile elements at lower oxygen fugacity as a function of temperature and pressure. Experiments were conducted at I GPa in a 13 mm QUICKpress piston cylinder and at 4 GPa in an 880-ton multi-anvil press, at temperatures up to 1850 C. The composition of starting materials for the experiments were designed so the final run products contained metal, silicate melt, and sulfide melt phases. Oxygen fugacity was controlled in the experiments by adding silicon metal to the samples, in order to utilize the Si-Si02 buffer, which is approx. 5 log units more reducing than the IW buffer at our temperatures of interest. The target silicate melt composition was diopside (CaMgSi206) because measured surface compositions indicate partial melting of a pyroxene-rich mantle. The results of our experiments will aid in our understanding of the fate of elements during the differentiation and thermal evolution of Mercury and other highly reducing planetary bodies.
Rowland, Rick, II↗
Assessing the Behavior of Typically Lithophile Elements Under Highly Reducing Conditions Relevant to the Planet Mercury
With the data returned from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission, there are now numerous constraints on the physical and chemical properties of Mercury, including its surface composition. The high Sand low FeO contents observed from MESSENGER suggest a low oxygen fugacity of the present materials on the planet's surface. Most of our understanding of elemental partitioning behavior comes from observations made on terrestrial rocks, but Mercury's oxygen fugacity is far outside the conditions of those samples, estimated at approximately 3-7 log units below the Iron-Wtistite (lW) oxygen buffer, several orders of magnitude more reducing than other terrestrial bodies we have data from. With limited oxygen available, lithophile elements may instead exhibit chalcophile, halophile, or siderophile behaviors. Furthermore, very few natural samples of rocks that formed under reducing conditions (e.g., enstatite chondrites, achondrites, aubrites) are available in our collections for examination of this change in geochemical affinity. Our goal is to determine the elemental partitioning behavior of typically lithophile elements at lower oxygen fugacity as a function of temperature and pressure. Experiments were conducted at I GPa in a 13 mm QUICKpress piston cylinder and at 4 GPa in an 880-ton multianvil press, at temperatures up to 1850degC. The composition of starting materials for the experiments were designed so the final run products contained metal, silicate melt, and sulfide melt phases. Oxygen fugacity was controlled in the experiments by adding silicon metal to the samples, in order to utilize the Si-Si02 buffer, which is approximately 5 log units more reducing than the IW buffer at our temperatures of interest. The target silicate melt composition was diopside (CaMgSi206) because measured surface compositions indicate partial melting of a pyroxene-rich mantle. The results of our experiments will aid in our understanding of the fate of elements during the differentiation and thermal evolution of Mercury and other highly reducing planetary bodies.
Rowland, Rick, II↗
Geochemical Advances in Mercury Science Facilitated by a Landed Mission
The data from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft have revealed several surprising characteristics about the surface of Mercury, leading to its classification as a geochemical endmember among the terrestrial planets. Some of these features include elevated abundances of up to 3 wt% S, C enrichment as high as 4 wt% over the local mean in low reflectance materials (LRM), Na up to 5 wt% at high northern latitudes, and Fe abundances typically lower than 2 wt% [e.g., 1–4]. The S and Fe concentrations have been used to infer that Mercury’s igneous history evolved under highly reduced oxygen fugacity conditions between 2.6 and 7.3 log10 units below the iron-wüstite buffer [e.g., 5], which is more reducing than any other terrestrial planet in the solar system [e.g., 6]. This highly reduced nature has important consequences for the differentiation and thermal/magmatic evolution of Mercury. While the immense amount of data collected by MESSENGER revealed Mercury as a geochemical endmember, this new knowledge gained raised additional questions that necessitate continued exploration of the planet. Fortunately, BepiColombo launched in October of 2018, and this joint ESA/JAXA dual-orbiter spacecraft is the most ambitious effort yet attempted to explore Mercury [e.g., 7]. Looking beyond BepiColombo, there are major aspects of Mercury’s geochemical character and evolution for which significant knowledge gaps can be dramatically improved with data acquired from the planet’s surface via in situ landed science.
Vander Kaaden, K. E.↗
The Lunar Geophysical Network Mission
The National Academy’s current Planetary Decadal Survey (NRC, 2011) prioritizes a future Lunar Geophysical Network (LGN) mission to gather new information that will permit us to better determine how the overall composition and structure of the Moon inform us about the initial differentiation and subsequent evolution of terrestrial planets.
R C Weber↗
Landing on Mercury: A Geochemical Perspective
The data from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft have revealed several surprising characteristics about the surface of Mercury, leading to its classification as a geochemical endmember among the terrestrial planets. Some of these features include elevated abundances of up to 3 wt% S, as much as 4 wt% C enrichment in low-reflectance materials (LRM) over the local mean, Na up to 5 wt% at high northern latitudes, and Fe abundances typically lower than 2 wt% [e.g., 1–4]. The S and Fe concentrations have been used to infer that Mercury’s igneous history evolved under highly reduced oxygen fugacity conditions between 2.6 and 7.3 log(sub 10) units below the iron–wüstite buffer [e.g., 5], which is more reducing than any other terrestrial planet in the solar system [e.g., 6]. This highly reduced nature has important con-sequences for the differentiation and thermal/magmatic evolution of Mercury. While the immense amount of data collected by MESSENGER revealed Mercury as a geochemical endmember, this new knowledge raised additional questions that necessitate continued exploration of the planet. Indeed, the joint ESA–JAXA dual-orbiter BepiColombo mission, launched in October 2018, is the most ambitious effort yet attempted to explore Mercury [e.g., 7]. Direct in situ elemental and mineralogical measurements on Mercury’s surface, however, are essential for addressing the new science questions that have arisen since MESSENGER.
K E Vander Kaaden↗
Differential Exudation Creates Biogeochemically Distinct Microenvironments during Rhizosphere Evolution
Plant roots and associated microbes release a diverse range of functionally distinct exudates into the surrounding rhizosphere with direct impacts on soil carbon storage, nutrient availability, and contaminant dynamics. Yet mechanistic linkages between root exudation and emergent biogeochemical processes remain challenging to measure nondestructively, in real soil, over time. Here we used a novel combination of in situ microsensors with high-resolution mass spectrometry to measure, nondestructively, changing exudation and associated biogeochemical dynamics along single growing plant roots (Avena sativa). We found that metabolite and dissolved organic carbon (DOC) concentrations as well as microbial growth, redox potential (EH), and pH dynamics vary significantly among bulk soil, root tip, and more mature root zones. Surprisingly, the significant spike of rhizosphere DOC upon root tip emergence did not significantly correlate with any biogeochemical parameters. However, the presence of sugars significantly correlated with declines in EH following the arrival of the root tip, likely due to enhanced microbial oxygen demand. Similarly, the presence of organic acids significantly correlated to declines in pH upon root tip emergence. Altogether, our in situ measurements highlight how different exudates released along growing roots create functionally distinct soil microenvironments that evolve over time.
54 ENVIRONMENTAL SCIENCES↗
Plasticity and the evolution of group-level regulation of cellular differentiation in the volvocine algae
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Dinah R. Davison↗
Model of a rotating magnetic cloud
The possibility that magnetic clouds rotate while they propagate antisunward was investigated. Magnetic clouds are modeled as magnetic flux ropes which rotate rigidly about the axis of symmetry. An ideal magnetohydrodynamic model, in which the evolution of the magnetic structure is related to the time evolution of the angular frequency, is developed. A class of 'separable' magnetic fields is employed to reduce the problem to a nonlinear ordinary differential equation for the evolution function, and it is solved numerically. The corresponding effective potential gives rise to two modes of evolution--expansion and oscillation--depending on the energy and on the value of a dimensionless parameter, k. Parameter k depends on the gas pressure, the ratio of the magnetic field components, and the frequency of rotation. There is a critical value of k, k(sub c), above which the oscillatory regime disappears and the flux rope invariably expands, regardless of the energy. Below k(sub c) the energy determines whether the configuration is confined or unbounded. Rotation always helps expansion by lowering the potential barrier. A data example was studied and features which are interpreted as signatures of rotation are presented. The angular speed is comparable to the Alfven speed, and the core of the rotating cloud completes on average one full revolution every three days at 1 AU. The parameter k is calculated from observations, and it is found to be close to, but below, critical. Only three out of the nine clouds examined showed signatures of rotation. Theoretical analysis suggests that close to the Sun rotation effects may play a more important role in the evolution of magnetic clouds than 1 AU.
Farrugia, C. J.↗