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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Absolute properties of the eclipsing binary system AQ Serpentis: A stringent test of convective core overshooting in stellar evolution models
We report differential photometric observations and radial-velocity measurements of the detached, 1.69 day period, double-lined eclipsing binary AQ Ser. Accurate masses and radii for the components are determined to better than 1.8% and 1.1%, respectively, and are M {sub 1} = 1.417 ± 0.021 M {sub ☉}, M {sub 2} = 1.346 ± 0.024 M {sub ☉}, R {sub 1} = 2.451 ± 0.027 R {sub ☉}, and R {sub 2} = 2.281 ± 0.014 R {sub ☉}. The temperatures are 6340 ± 100 K (spectral type F6) and 6430 ± 100 K (F5), respectively. Both stars are considerably evolved, such that predictions from stellar evolution theory are particularly sensitive to the degree of extra mixing above the convective core (overshoot). The component masses are different enough to exclude a location in the H-R diagram past the point of central hydrogen exhaustion, which implies the need for extra mixing. Moreover, we find that current main-sequence models are unable to match the observed properties at a single age even when allowing the unknown metallicity, mixing length parameter, and convective overshooting parameter to vary freely and independently for the two components. The age of the more massive star appears systematically younger. AQ Ser and other similarly evolved eclipsing binaries showing the same discrepancy highlight an outstanding and largely overlooked problem with the description of overshooting in current stellar theory.
79 ASTRONOMY AND ASTROPHYSICS↗
Asymmetric evolution of magnetic reconnection in collisionless accretion disk
An evolution of a magnetic reconnection in a collisionless accretion disk is investigated using a 2.5 dimensional hybrid code simulation. In astrophysical disks, magnetorotational instability (MRI) is considered to play an important role by generating turbulence in the disk and contributes to an effective angular momentum transport through a turbulent viscosity. Magnetic reconnection, on the other hand, also plays an important role on the evolution of the disk through a dissipation of a magnetic field enhanced by a dynamo effect of MRI. In this study, we developed a hybrid code to calculate an evolution of a differentially rotating system. With this code, we first confirmed a linear growth of MRI. We also investigated a behavior of a particular structure of a current sheet, which would exist in the turbulence in the disk. From the calculation of the magnetic reconnection, we found an asymmetric structure in the out-of-plane magnetic field during the evolution of reconnection, which can be understood by a coupling of the Hall effect and the differential rotation. We also found a migration of X-point whose direction is determined only by an initial sign of J{sub 0}×Ω{sub 0}, where J{sub 0} is the initial current density in the neutral sheet and Ω{sub 0} is the rotational vector of the background Keplerian rotation. Associated with the migration of X-point, we also found a significant enhancement of the perpendicular magnetic field compared to an ordinary MRI. MRI-Magnetic reconnection coupling and the resulting magnetic field enhancement can be an effective process to sustain a strong turbulence in the accretion disk and to a transport of angular momentum.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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]↗
Elemental Composition of Analogs to Mars Return Samples Studied with X-Ray Fluorescence Imaging at NSLS-II
In 2020, NASA will launch out into the first step of what may be an ambitious, multi-mission campaign with the goal to bring back for analysis in laboratories here to Earth a collection of rock, regolith, and atmosphere samples from Mars. It is the main objective of this endeavor to determine whether or not Mars was ever host to ancient microbial life. Finding evidence for extinct (or extant) life on Mars has the potential to fundamentally alter our view of the origin and evolution of life. It would provide proof for Earth being just one amongst others regarding the question of biological activity in the Solar System. Furthermore, returned Martian samples would provide a rich repository of information on the history of planetary accretion and differentiation, geochronology, atmospheric evolution, and the paleo-environmental history of Mars, adding tremendous additional value to such a mission beyond the issue of extraterrestrial life. Here the potential knowledge to be obtained by such a collection of samples will equal or exceed that of the Apollo lunar sample archive, which even today yields new insights on the history of the Solar System, over 40 years after they were returned to Earth.
36 MATERIALS SCIENCE↗
The influence of differential irradiation and circulation on the thermal evolution of gas giant planets. I. Upper limits from radiative equilibrium
As a planet ages, it cools and its radius shrinks at a rate set by the efficiency with which heat is transported from the interior out to space. The bottleneck for this transport is at the boundary between the convective interior and the radiative atmosphere; the opacity there sets the global cooling rate. Models of planetary evolution are often one dimensional (1D), such that the radiative-convective boundary (RCB) is defined by a single temperature, pressure, and opacity. In reality the spatially inhomogeneous stellar heating pattern and circulation in the atmosphere could deform the RCB, allowing heat from the interior to escape more efficiently through regions with lower opacity. We present an analysis of the degree to which the RCB could be deformed and the resultant change in the evolutionary cooling rate. In this initial work we calculate the upper limit for this effect by comparing an atmospheric structure in local radiative equilibrium to its 1D equivalent. We find that the cooling through an uneven RCB could be enhanced over cooling through a uniform RCB by as much as 10%-50%. We also show that the deformation of the RCB (and the enhancement of the cooling rate) increases with a greater incident stellar flux or a lower inner entropy. Our results indicate that this mechanism could significantly change a planet's thermal evolution, causing it to cool and shrink more quickly than would otherwise be expected. This may exacerbate the well-known difficulty in explaining the very large radii observed for some hot Jupiters.
79 ASTRONOMY AND ASTROPHYSICS↗
Comparison of momentum transport models for numerical relativity
The main problems of nonvacuum numerical relativity, compact binary mergers and stellar collapse, involve hydromagnetic instabilities and turbulent flows, so that kinetic energy at small scales leads to mean effects at large scale that drive the secular evolution. Notable among these effects is momentum transport. We investigate two models of this transport effect, a relativistic Navier-Stokes system and a turbulent mean stress model, that are similar to all of the prescriptions that have been attempted to date for treating subgrid effects on binary neutron star mergers and their aftermath. Our investigation involves both stability analysis and numerical experimentation on star and disk systems. We also begin the investigation of the effects of particle and heat transport on postmerger simulations. Here, we find that correct handling of turbulent heating is crucial for avoiding unphysical instabilities. Given such appropriate handling, the evolution of a differentially rotating star and the accretion rate of a disk are reassuringly insensitive to the choice of prescription. However, disk outflows can be sensitive to the choice of method, even for the same effective viscous strength. We also consider the effects of eddy diffusion in the evolution of an accretion disk and show that it can interestingly affect the composition of outflows.
79 ASTRONOMY AND ASTROPHYSICS↗
Observational constraints on finite scale factor singularities
We discuss the combined constraints on a Finite Scale Factor Singularity (FSF) universe evolution scenario, which come from the shift parameter R, baryon acoustic oscillations (BAO) A, and from the type Ia supernovae. We show that observations allow existence of such singularities in the 2 × 10{sup 9} years in future (at 1σ CL) which is much farther than a Sudden Future Singularity (SFS), and that at the present moment of the cosmic evolution, one cannot differentiate between cosmological scenario which allow finite scale factor singularities and the standard ΛCDM dark energy models. We also show that there is an allowed value of m = 2/3 within 1σ CL, which corresponds to a dust-filled Einstein-de-Sitter universe limit of the early time evolution and so it is pasted into a standard early-time scenario.
79 ASTRONOMY AND ASTROPHYSICS↗
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.↗
Paleomagnetic Evidence for a Partially Differentiated Ordinary Chondrite Parent Asteroid
Abstract The textures and accretion ages of chondrites have been used to argue that their parent asteroids never differentiated. Without a core, undifferentiated planetesimals could not have generated magnetic fields through dynamo activity, so chondrites are not expected to have experienced such fields. However, the magnetic remanence carried by the CV chondrites is consistent with dynamo‐generated fields, hinting that partially differentiated asteroids consisting of an unmelted crust atop a differentiated interior may exist. Here, we test this hypothesis by applying synchrotron X‐ray microscopy to metallic veins in the slowly cooled H6 chondrite Portales Valley. The magnetic remanence carried by nanostructures in these veins indicates that this meteorite recorded a magnetic field over a period of tens to hundreds of years at ∼100 Myr after solar system formation. These properties are inconsistent with external field sources such as the nebula, solar wind, or impacts, but are consistent with dynamo‐generated fields, indicating that the H chondrite parent body contained an advecting metallic core and was therefore partially differentiated. We calculate the thermal evolution of the chondritic portions of partially differentiated asteroids that form through incremental accretion across 10 5 to 10 6 years, finding this can agree with the measured ages and cooling rates of multiple H chondrites. We also predict that the cores of these bodies could have been partially liquid and feasibly generating a dynamo at 100 Myr after solar system formation. These observations contribute to a growing body of evidence supporting a spectrum of internal differentiation within some asteroids with primitive surfaces.
Bryson, J. F. J.↗
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.↗
The theory of nonclassical relaxation oscillations in singularly perturbed delay systems
Some special classes of relaxation systems are introduced, with one slow and one fast variable, in which the evolution of the slow component x(t) in time is described by an ordinary differential equation, while the evolution of the fast component y(t) is described by a Volterra-type differential equation with delay y(t−h), h=const>0, and with a small parameter ε>0 multiplying the time derivative. Questions relating to the existence and stability of impulse-type periodic solutions, in which the x-component converges pointwise to a discontinuous function as ε→0 and the y-component is shaped like a δ-function, are investigated. The results obtained are illustrated by several examples from ecology and laser theory. Bibliography: 11 titles. (paper)
97 MATHEMATICS AND COMPUTING↗
FUNDAMENTAL PARAMETERS AND CHEMICAL COMPOSITION OF ARCTURUS
We derive a self-consistent set of atmospheric parameters and abundances of 17 elements for the red giant star Arcturus: T{sub eff} = 4286 {+-} 30 K, log g = 1.66 {+-} 0.05, and [Fe/H] = -0.52 {+-} 0.04. The effective temperature was determined using model atmosphere fits to the observed spectral energy distribution from the blue to the mid-infrared (0.44 to 10 {mu}m). The surface gravity was calculated using the trigonometric parallax of the star and stellar evolution models. A differential abundance analysis relative to the solar spectrum allowed us to derive iron abundances from equivalent width measurements of 37 Fe I and 9 Fe II lines, unblended in the spectra of both Arcturus and the Sun; the [Fe/H] value adopted is derived from Fe I lines. We also determine the mass, radius, and age of Arcturus: M = 1.08 {+-} 0.06 M{sub Sun }, R = 25.4 {+-} 0.2 R{sub Sun }, and {tau} = 7.1{sup +1.5}{sub -1.2} Gyr. Finally, abundances of the following elements are measured from an equivalent width analysis of atomic features: C, O, Na, Mg, Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, and Zn. We find the chemical composition of Arcturus typical of that of a local thick-disk star, consistent with its kinematics.
79 ASTRONOMY AND ASTROPHYSICS↗
EVOLUTION OF ROTATIONAL VELOCITIES OF A-TYPE STARS
The equatorial velocity of A-type stars undergoes an acceleration in the first third of the main sequence (MS) stage, but the velocity decreases as if the stars were not undergoing any redistribution of angular momentum in the external layers in the last stage of the MS phase. Our calculations show that the acceleration and the decrease of the equatorial velocity can be reproduced by the evolution of the differential rotation zero-age MS model with the angular momentum transport caused by hydrodynamic instabilities during the MS stage. The acceleration results from the fact that the angular momentum stored in the interiors of the stars is transported outward. In the last stage, the core and the radiative envelope are uncoupling, and the rotation of the envelope is a quasi-solid rotation; the uncoupling and the expansion of the envelope indicate that the decrease of the equatorial velocity approximately follows the slope for the change in the equatorial velocity of the model without any redistribution of angular momentum. When the fractional age 0.3 {approx}< t/t{sub MS} {approx}< 0.5, the equatorial velocity remains almost constant for stars whose central density increases with age in the early stage of the MS phase, while the velocity decreases with age for stars whose central density decreases with age in the early stage of the MS phase.
79 ASTRONOMY AND ASTROPHYSICS↗
A diminutive perinate European Enantiornithes reveals an asynchronous ossification pattern in early birds
Fossils of juvenile Mesozoic birds provide insight into the early evolution of avian development, however such fossils are rare. The analysis of the ossification sequence in these early-branching birds has the potential to address important questions about their comparative developmental biology and to help understand their morphological evolution and ecological differentiation. Here we report on an early juvenile enantiornithine specimen from the Early Cretaceous of Europe, which sheds new light on the osteogenesis in this most species-rich clade of Mesozoic birds. Consisting of a nearly complete skeleton, it is amongst the smallest known Mesozoic avian fossils representing post-hatching stages of development. Finally, comparisons between this new specimen and other known early juvenile enantiornithines support a clade-wide asynchronous pattern of osteogenesis in the sternum and the vertebral column, and strongly indicate that the hatchlings of these phylogenetically basal birds varied greatly in size and tempo of skeletal maturation.
59 BASIC BIOLOGICAL SCIENCES↗
An extended trajectory-mechanics approach for calculating two-phase flow paths
A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.
58 GEOSCIENCES↗