Mathematical modeling of heat transfer process in a variable domain

In this paper, a brief review and generalization of studies on the heat transfer and heat conduction problem in a variable domain are presented. The equations of the process, where the boundary displacement velocity is the control, are obtained taking into account heat inflow. This article was submitted by the authors in English.     

Conversations with Rep. Ken Calvert. Interview by Frank Sietzen Jr

Rep. Calvert, chair of the House aeronautics and space subcommittee of the Science Committee, answers questions related to priorities for space in the current congressional session: the Vision for Space Exploration, development of the Crew Exploration Vehicle (CEV) and other heavy-lift launch vehicles, entrepreneurial alliances in the space transportation industry, the U.S. aerospace industry, space tourism, entrepreneurs and NASA, U.S. aeronautics research, a service mission to the Hubble Space Telescope, and priority military space programs.     

ExoMars 2016 Schiaparelli Module Trajectory and Atmospheric Profiles Reconstruction

On 19^th October 2016 Schiaparelli module of the ExoMars 2016 mission flew through the Mars atmosphere. After successful entry and descent under parachute, the module failed the last part of the descent and crashed on the Mars surface. Nevertheless the data transmitted in real-time by Schiaparelli during the entry and descent, together with the entry state vector as initial condition, have been used to reconstruct both the trajectory and the profiles of atmospheric density, pressure and temperature along the traversed path.The available data-set is only a small sub-set of the whole data acquired by Schiaparelli, with a limited data rate (8 kbps) and a large gap during the entry because of the plasma blackout on the communications.This paper presents the work done by the AMELIA (Atmospheric Mars Entry and Landing Investigations and Analysis) team in the exploitation of the available inertial and radar data. First a reference trajectory is derived by direct integration of the inertial measurements and a strategy to overcome the entry data gap is proposed. First-order covariance analysis is used to estimate the uncertainties on all the derived parameters. Then a refined trajectory is computed incorporating the measurements provided by the on-board radar altimeter.The derived trajectory is consistent with the events reported in the telemetry and also with the impact point identified on the high-resolution images of the landing site.Finally, atmospheric profiles are computed tacking into account the aerodynamic properties of the module. Derived profiles result in good agreement with both atmospheric models and available remote sensing observations.     

The Delivery of Water During Terrestrial Planet Formation

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. Here we review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, and the delivery efficiency is very low, such that it may be difficult to deliver even a single Earth ocean of water this way. The most promising route for water delivery is the accretion of material from beyond the snow line, similar to carbonaceous chondrites, that is scattered into the terrestrial planet region as the planets are growing. Two main scenarios are discussed in detail. First is the classical scenario in which the giant planets begin roughly in their final locations and the disk of planetesimals and embryos in the terrestrial planet region extends all the way into the outer asteroid belt region. Second is the Grand Tack scenario, where early inward and outward migration of the giant planets implants material from beyond the snow line into the asteroid belt and terrestrial planet region, where it can be accreted by the growing planets. Sufficient water is delivered to the terrestrial planets in both scenarios. While the Grand Tack scenario provides a better fit to most constraints, namely the small mass of Mars, planets may form too fast in the nominal case discussed here. This discrepancy may be reduced as a wider range of initial conditions is explored. Finally, we discuss several more recent models that may have important implications for water delivery to the terrestrial planets.     

Order out of Randomness: Self-Organization Processes in Astrophysics

Self-organization is a property of dissipative nonlinear processes that are governed by a global driving force and a local positive feedback mechanism, which creates regular geometric and/or temporal patterns, and decreases the entropy locally, in contrast to random processes. Here we investigate for the first time a comprehensive number of (17) self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous “order out of randomness”, during the evolution from an initially disordered system to an ordered quasi-stationary system, mostly by quasi-periodic limit-cycle dynamics, but also by harmonic (mechanical or gyromagnetic) resonances. The global driving force can be due to gravity, electromagnetic forces, mechanical forces (e.g., rotation or differential rotation), thermal pressure, or acceleration of nonthermal particles, while the positive feedback mechanism is often an instability, such as the magneto-rotational (Balbus-Hawley) instability, the convective (Rayleigh-Bénard) instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or a loss-cone instability. Physical models of astrophysical self-organization processes require hydrodynamic, magneto-hydrodynamic (MHD), plasma, or N-body simulations. Analytical formulations of self-organizing systems generally involve coupled differential equations with limit-cycle solutions of the Lotka-Volterra or Hopf-bifurcation type.     

Abundances,Ionization States,Temperatures, and FIP in Solar Energetic Particles

The relative abundances of chemical elements and isotopes have been our most effective tool in identifying and understanding the physical processes that control populations of energetic particles. The early surprise in solar energetic particles (SEPs) was 1000-fold enhancements in \({}^{3}\mbox{He}/{}^{4}\mbox{He}\) from resonant wave-particle interactions in the small “impulsive” SEP events that emit electron beams that produce type III radio bursts. Further studies found enhancements in Fe/O, then extreme enhancements in element abundances that increase with mass-to-charge ratio \(A/Q\), rising by a factor of 1000 from He to Au or Pb arising in magnetic reconnection regions on open field lines in solar jets. In contrast, in the largest SEP events, the “gradual” events, acceleration occurs at shock waves driven out from the Sun by fast, wide coronal mass ejections (CMEs). Averaging many events provides a measure of solar coronal abundances, but \(A/Q\)-dependent scattering during transport causes variations with time; thus if Fe scatters less than O, Fe/O is enhanced early and depleted later. To complicate matters, shock waves often reaccelerate impulsive suprathermal ions left over or trapped above active regions that have spawned many impulsive events. Direct measurements of ionization states \(Q\) show coronal temperatures of 1–2 MK for most gradual events, but impulsive events often show stripping by matter traversal after acceleration. Direct measurements of \(Q\) are difficult and often unavailable. Since both impulsive and gradual SEP events have abundance enhancements that vary as powers of \(A/Q\), we can use abundances to deduce the probable \(Q\)-values and the source plasma temperatures during acceleration, ≈3 MK for impulsive SEPs. This new technique also allows multiple spacecraft to measure temperature variations across the face of a shock wave, measurements otherwise unavailable and provides a new understanding of abundance variations in the element He. Comparing coronal abundances from SEPs and from the slow solar wind as a function of the first ionization potential (FIP) of the elements, remaining differences are for the elements C, P, and S. The theory of the fractionation of ions by Alfvén waves shows that C, P, and S are suppressed because of wave resonances during chromospheric transport on closed magnetic loops but not on open magnetic fields that supply the solar wind. Shock waves can accelerate ions from closed coronal loops that easily escape as SEPs, while the solar wind must emerge on open fields.     

Imaging Plasma Density Structures in the Soft X-Rays Generated by Solar Wind Charge Exchange with Neutrals

Both heliophysics and planetary physics seek to understand the complex nature of the solar wind’s interaction with solar system obstacles like Earth’s magnetosphere, the ionospheres of Venus and Mars, and comets. Studies with this objective are frequently conducted with the help of single or multipoint in situ electromagnetic field and particle observations, guided by the predictions of both local and global numerical simulations, and placed in context by observations from far and extreme ultraviolet (FUV, EUV), hard X-ray, and energetic neutral atom imagers (ENA). Each proposed interaction mechanism (e.g., steady or transient magnetic reconnection, local or global magnetic reconnection, ion pick-up, or the Kelvin-Helmholtz instability) generates diagnostic plasma density structures. The significance of each mechanism to the overall interaction (as measured in terms of atmospheric/ionospheric loss at comets, Venus, and Mars or global magnetospheric/ionospheric convection at Earth) remains to be determined but can be evaluated on the basis of how often the density signatures that it generates are observed as a function of solar wind conditions. This paper reviews efforts to image the diagnostic plasma density structures in the soft (low energy, 0.1–2.0 keV) X-rays produced when high charge state solar wind ions exchange electrons with the exospheric neutrals surrounding solar system obstacles.The introduction notes that theory, local, and global simulations predict the characteristics of plasma boundaries such the bow shock and magnetopause (including location, density gradient, and motion) and regions such as the magnetosheath (including density and width) as a function of location, solar wind conditions, and the particular mechanism operating. In situ measurements confirm the existence of time- and spatial-dependent plasma density structures like the bow shock, magnetosheath, and magnetopause/ionopause at Venus, Mars, comets, and the Earth. However, in situ measurements rarely suffice to determine the global extent of these density structures or their global variation as a function of solar wind conditions, except in the form of empirical studies based on observations from many different times and solar wind conditions. Remote sensing observations provide global information about auroral ovals (FUV and hard X-ray), the terrestrial plasmasphere (EUV), and the terrestrial ring current (ENA). ENA instruments with low energy thresholds (\(\sim1~\mbox{keV}\)) have recently been used to obtain important information concerning the magnetosheaths of Venus, Mars, and the Earth. Recent technological developments make these magnetosheaths valuable potential targets for high-cadence wide-field-of-view soft X-ray imagers.Section 2 describes proposed dayside interaction mechanisms, including reconnection, the Kelvin-Helmholtz instability, and other processes in greater detail with an emphasis on the plasma density structures that they generate. It focuses upon the questions that remain as yet unanswered, such as the significance of each proposed interaction mode, which can be determined from its occurrence pattern as a function of location and solar wind conditions. Section 3 outlines the physics underlying the charge exchange generation of soft X-rays. Section 4 lists the background sources (helium focusing cone, planetary, and cosmic) of soft X-rays from which the charge exchange emissions generated by solar wind exchange must be distinguished. With the help of simulations employing state-of-the-art magnetohydrodynamic models for the solar wind-magnetosphere interaction, models for Earth’s exosphere, and knowledge concerning these background emissions, Sect. 5 demonstrates that boundaries and regions such as the bow shock, magnetosheath, magnetopause, and cusps can readily be identified in images of charge exchange emissions. Section 6 reviews observations by (generally narrow) field of view (FOV) astrophysical telescopes that confirm the presence of these emissions at the intensities predicted by the simulations. Section 7 describes the design of a notional wide FOV “lobster-eye” telescope capable of imaging the global interactions and shows how it might be used to extract information concerning the global interaction of the solar wind with solar system obstacles. The conclusion outlines prospects for missions employing such wide FOV imagers.     

Impact of Distance Determinations on Galactic Structure. I. Young and Intermediate-Age Tracers

Here we discuss impacts of distance determinations on the Galactic disk traced by relatively young objects. The Galactic disk, \(\sim40~\mbox{kpc}\) in diameter, is a cross-road of studies on the methods of measuring distances, interstellar extinction, evolution of galaxies, and other subjects of interest in astronomy. A proper treatment of interstellar extinction is, for example, crucial for estimating distances to stars in the disk outside the small range of the solar neighborhood. We’ll review the current status of relevant studies and discuss some new approaches to the extinction law. When the extinction law is reasonably constrained, distance indicators found in today and future surveys are telling us stellar distribution and more throughout the Galactic disk. Among several useful distance indicators, the focus of this review is Cepheids and open clusters (especially contact binaries in clusters). These tracers are particularly useful for addressing the metallicity gradient of the Galactic disk, an important feature for which comparison between observations and theoretical models can reveal the evolution of the disk.     

Water Reservoirs in Small Planetary Bodies: Meteorites,Asteroids, and Comets

Asteroids and comets are the remnants of the swarm of planetesimals from which the planets ultimately formed, and they retain records of processes that operated prior to and during planet formation. They are also likely the sources of most of the water and other volatiles accreted by Earth. In this review, we discuss the nature and probable origins of asteroids and comets based on data from remote observations, in situ measurements by spacecraft, and laboratory analyses of meteorites derived from asteroids. The asteroidal parent bodies of meteorites formed \(\leq 4\) Ma after Solar System formation while there was still a gas disk present. It seems increasingly likely that the parent bodies of meteorites spectroscopically linked with the E-, S-, M- and V-type asteroids formed sunward of Jupiter’s orbit, while those associated with C- and, possibly, D-type asteroids formed further out, beyond Jupiter but probably not beyond Saturn’s orbit. Comets formed further from the Sun than any of the meteorite parent bodies, and retain much higher abundances of interstellar material. CI and CM group meteorites are probably related to the most common C-type asteroids, and based on isotopic evidence they, rather than comets, are the most likely sources of the H and N accreted by the terrestrial planets. However, comets may have been major sources of the noble gases accreted by Earth and Venus. Possible constraints that these observations can place on models of giant planet formation and migration are explored.