A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.     

Daytime Ionosphere Retrieval Algorithm for the Ionospheric Connection Explorer (ICON)

The NASA Ionospheric Connection Explorer Extreme Ultraviolet spectrograph, ICON EUV, will measure altitude profiles of the daytime extreme-ultraviolet (EUV) OII emission near 83.4 and 61.7 nm that are used to determine density profiles and state parameters of the ionosphere. This paper describes the algorithm concept and approach to inverting these measured OII emission profiles to derive the associated \(\mathrm{O}^{+}\) density profile from 150–450 km as a proxy for the electron content in the F-region of the ionosphere. The algorithm incorporates a bias evaluation and feedback step, developed at the U.S. Naval Research Laboratory using data from the Special Sensor Ultraviolet Limb Imager (SSULI) and the Remote Atmospheric and Ionospheric Detection System (RAIDS) missions, that is able to effectively mitigate the effects of systematic instrument calibration errors and inaccuracies in the original photon source within the forward model. Results are presented from end-to-end simulations that convolved simulated airglow profiles with the expected instrument measurement response to produce profiles that were inverted with the algorithm to return data products for comparison to truth. Simulations of measurements over a representative ICON orbit show the algorithm is able to reproduce hmF2 values to better than 5 km accuracy, and NmF2 to better than 12% accuracy over a 12-second integration, and demonstrate that the ICON EUV instrument and daytime ionosphere algorithm can meet the ICON science objectives which require 20 km vertical resolution in hmF2 and 18% precision in NmF2.     

Planned Products of the Mars Structure Service for the InSight Mission to Mars

Space Science Reviews - The InSight lander will deliver geophysical instruments to Mars in 2018, including seismometers installed directly on the surface (Seismic Experiment for Interior Structure,...     

From Initial Models of Seismicity,Structure and Noise to Synthetic Seismograms for Mars

The InSight mission will land a single seismic station on Mars in November 2018, and the resultant seismicity catalog will be a key component for studies aiming to understand the interior structure of the planet. Here, we present a preliminary version of the web services that will be used to distribute the event and station metadata in practice, employing synthetic seismograms generated for Mars using a catalog of expected seismicity. Our seismicity catalog consists of 120 events with double-couple source mechanisms only. We also provide Green’s functions databases for a total of 16 structural models, which are constructed to reflect one-dimensional thin (30 km) and thick (80 km) Martian crust with varying seismic wave speeds and densities, combined with two different profiles for temperature and composition for the mantle. Both the Green’s functions databases and the precomputed seismograms are accessible online. These new utilities allow the researchers to either download the precomputed synthetic waveforms directly, or produce customized data sets using any desired source mechanism and event distribution via our servers.

     

Extended Pile Driving Model to Predict the Penetration of the Insight/HP<Superscript>3</Superscript> Mole into the Martian Soil

The NASA InSight mission will provide an opportunity for soil investigations using the penetration data of the heat flow probe built by the German Aerospace Center DLR. The Heat flow and Physical Properties Probe (HP³) will penetrate 3 to 5 meter into the Martian subsurface to investigate the planetary heat flow. The measurement of the penetration rate during the insertion of the HP³ will be used to determine the physical properties of the soil at the landing site. For this purpose, numerical simulations of the penetration process were performed to get a better understanding of the soil properties influencing the penetration performance of HP³. A pile driving model has been developed considering all masses of the hammering mechanism of HP³. By cumulative application of individual stroke cycles it is now able to describe the penetration of the Mole into the Martian soil as a function of time, assuming that the soil parameters of the material through which it penetrates are known. We are using calibrated materials similar to those expected to be encountered by the InSight/HP³ Mole when it will be operated on the surface of Mars after the landing of the InSight spacecraft. We consider various possible scenarios, among them a more or less homogeneous material down to a depth of 3–5 m as well as a layered ground, consisting of layers with different soil parameters. Finally we describe some experimental tests performed with the latest prototype of the InSight Mole at DLR Bremen and compare the measured penetration performance in sand with our modeling results. Furthermore, results from a 3D DEM simulation are presented to get a better understanding of the soil response.     

Range Correction Computations for Weapons Dropped from Aircraft

A general set of equations is developed from which the effects of initial condition perturbations upon weapon impact point are readily evaluated. Data are presented to illustrate the accuracy with which predictions can be made. Results obtained from the actual ballistic equations, from the time-varying perturbation equations, and from a time-invariant approximation of the perturbation equations are compared. It is shown that reasonable impact point predictive accuracy can be provited for fairly large changes in initial conditions.     

UV spectral lines from coronal transients

We investigated the UV emission expected from solar coronal transients, selecting some spectral lines which will be observed with the UVCS spectrocoronagraph onboard the SOHO spacecraft. The line intensities were calculated starting from a representative, simplified model of coronal transient. We discuss how the considered intensities depend on the physical parameters of the examined structures. This work is aimed to give a contribution in defining and preparing the future observations of coronal transients and coronal mass ejections by the UVCS/SOHO.     

Automated VOR Ground Check Techniques

Field conversions of many conventional VOR and VORTAC facilities to remote maintenance monitoring, which includes provisions for automated VOR ground check procedures, has been under way in the United States since 1982. A question that has arisen as a result of this effort concerns the minimum number of ground-check points that must be used in order that the bearing-error function can be resolved into its octantal as well as its quadrantal and "duantal" components. Some fundamental considerations relating to that question are examined here.     

Stars and Stellar Systems at z > 5: Implications for Structure Formation and Nucleosynthesis

Enough UV radiation was generated before z = 5 to have ionized the intergalactic medium. If this comes from stars (probably aggregated in systems of subgalactic scale), one straightforwardly calculates that the associated nucleosynthesis would be sufficient to produce a universal abundance of order 1 percent of solar. The first pre-galaxies may eventually be detectable by their direct UV emission, with characteristic spectral features at Lyman alpha; high-z supernovae may also be detectable. Other probes of the IGM beyond z = 5, and of the epochs of reheating and reionization, are discussed, along with possible links between the diffusion of pregalactic metals and the origin of magnetic fields.     

Interior Evolution of Mercury

The interior evolution of Mercury—the innermost planet in the solar system, with its exceptional high density—is poorly known. Our current knowledge of Mercury is based on observations from Mariner 10’s three flybys. That knowledge includes the important discoveries of a weak, active magnetic field and a system of lobate scarps that suggests limited radial contraction of the planet during the last 4 billion years. We review existing models of Mercury’s interior evolution and further present new 2D and 3D convection models that consider both a strongly temperature-dependent viscosity and core cooling. These studies provide a framework for understanding the basic characteristics of the planet’s internal evolution as well as the role of the amount and distribution of radiogenic heat production, mantle viscosity, and sulfur content of the core have had on the history of Mercury’s interior. The existence of a dynamo-generated magnetic field suggests a growing inner core, as model calculations show that a thermally driven dynamo for Mercury is unlikely. Thermal evolution models suggest a range of possible upper limits for the sulfur content in the core. For large sulfur contents the model cores would be entirely fluid. The observation of limited planetary contraction (∼1–2 km)—if confirmed by future missions—may provide a lower limit for the core sulfur content. For smaller sulfur contents, the planetary contraction obtained after the end of the heavy bombardment due to inner core growth is larger than the observed value. Due to the present poor knowledge of various parameters, for example, the mantle rheology, the thermal conductivity of mantle and crust, and the amount and distribution of radiogenic heat production, it is not possible to constrain the core sulfur content nor the present state of the mantle. Therefore, it is difficult to robustly predict whether or not the mantle is conductive or in the convective regime. For instance, in the case of very inefficient planetary cooling—for example, as a consequence of a strong thermal insulation by a low conductivity crust and a stiff Newtonian mantle rheology—the predicted sulfur content can be as low as 1 wt% to match current estimates of planetary contraction, making deep mantle convection likely. Efficient cooling—for example, caused by the growth of a crust strongly in enriched in radiogenic elements—requires more than 6.5 wt% S. These latter models also predict a transition from a convective to a conductive mantle during the planet’s history. Data from future missions to Mercury will aid considerably our understanding of the evolution of its interior.