Gromov-Hausdorff-like distance function defined in the aspect of Riemannian submanifold theory

In this paper, we discuss how a Gromov-Hausdorff-like distance function over the space of all isometric classes of compact $C^k$-Riemannian manifolds should be defined in the aspect of the Riemannan submanifold theory, where $k\geq 1$. The most important fact in this discussion is as follows. The Hausdorff distance function between two spheres of mutually distinct radii isometrically embedded into the hypebolic space of curvature $c$ converges to zero as $c\to-\infty$. The key in the construction of the Gromov-Hausdorff-like distance function given in this paper is to define the distance of two $C^{k+1}$-isometric embeddings of distinct compact $C^k$-Riemannian manifolds into a higher dimensional Riemannian manifold by using the Hausdorff distance function in the tangent bundle of order $k+1$ equipped with the Sasaki metric. Furthermore, we show that the convergence of a sequence of compact Riemannian manifolds with respect to this distance function coincides with the convergence in the sense of R. S. Hamilton.Comment: 14 page

Scientific rationale for Uranus and Neptune <i>in situ</i> explorations

The ice giants Uranus and Neptune are the least understood class of planets in our solar system but the most frequently observed type of exoplanets. Presumed to have a small rocky core, a deep interior comprising ∼70% heavy elements surrounded by a more dilute outer envelope of H2 and He, Uranus and Neptune are fundamentally different from the better-explored gas giants Jupiter and Saturn. Because of the lack of dedicated exploration missions, our knowledge of the composition and atmospheric processes of these distant worlds is primarily derived from remote sensing from Earth-based observatories and space telescopes. As a result, Uranus's and Neptune's physical and atmospheric properties remain poorly constrained and their roles in the evolution of the Solar System not well understood. Exploration of an ice giant system is therefore a high-priority science objective as these systems (including the magnetosphere, satellites, rings, atmosphere, and interior) challenge our understanding of planetary formation and evolution. Here we describe the main scientific goals to be addressed by a future in situ exploration of an ice giant. An atmospheric entry probe targeting the 10-bar level, about 5 scale heights beneath the tropopause, would yield insight into two broad themes: i) the formation history of the ice giants and, in a broader extent, that of the Solar System, and ii) the processes at play in planetary atmospheres. The probe would descend under parachute to measure composition, structure, and dynamics, with data returned to Earth using a Carrier Relay Spacecraft as a relay station. In addition, possible mission concepts and partnerships are presented, and a strawman ice-giant probe payload is described. An ice-giant atmospheric probe could represent a significant ESA contribution to a future NASA ice-giant flagship mission

The photochemical fractionation of nitrogen isotopologues in Titan’s atmosphere

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SPECIFIC CONTRIBUTIONS OF SIMS AND XPS TO STUDIES OF THERMAL OXIDE FILM

Le SIMS donne des informations spécifiques sur la diffusion d'un traceur dans un film d'oxyde en cours de croissance et sur la distribution d'impuretés en faibles concentrations dans le film. L'état de valence de ces dopants peut être déterminé par XPS, permettant ainsi d'expliciter leur influence sur les processus de diffusion.SIMS give specific informations on the diffusion of a tracer in growing oxide films and the depth distribution of impurities in low concentrations in the films. The valency of these dopants can be determined by XPS, thus permitting to explain their influence on diffusion processes

The photochemical production of aromatics in the atmosphere of Titan

International audienceThe photochemical processes at work in the atmosphere of Titan are very complex and lead to a great variety of compounds with aerosols as an end-product. One of the most complex molecules detected so far is benzene (C6H6). In the present work, we have updated and improved the chemistry of aromatics in order to better understand the main chemical pathways leading to the production of benzene and determine what other aromatics could be produced efficiently in the atmosphere. This new chemical scheme has been incorporated in our 1D photochemical model corresponding to mean conditions. We confirm the importance of ionic chemistry for benzene production in the upper atmosphere and we have found that excited benzene is an important intermediate in benzene production due to the exothermicity of many production reactions. Among the 24 aromatics included in the model, neutral aromatics like toluene (C6H5CH3) and ethylbenzene (C6H5C2H5) are relatively abundant, suggesting in particular that toluene could be detectable in the infrared, and eventually microwave wavelength ranges. However, we obtained large uncertainties on model results highlighting the need for more experiments and theoretical studies to improve the chemistry of aromatics

The photochemical production of aromatics in the atmosphere of Titan

International audienceThe photochemical processes at work in the atmosphere of Titan are very complex and lead to a great variety of compounds with aerosols as an end-product. One of the most complex molecules detected so far is benzene (C6H6). In the present work, we have updated and improved the chemistry of aromatics in order to better understand the main chemical pathways leading to the production of benzene and determine what other aromatics could be produced efficiently in the atmosphere. This new chemical scheme has been incorporated in our 1D photochemical model corresponding to mean conditions. We confirm the importance of ionic chemistry for benzene production in the upper atmosphere and we have found that excited benzene is an important intermediate in benzene production due to the exothermicity of many production reactions. Among the 24 aromatics included in the model, neutral aromatics like toluene (C6H5CH3) and ethylbenzene (C6H5C2H5) are relatively abundant, suggesting in particular that toluene could be detectable in the infrared, and eventually microwave wavelength ranges. However, we obtained large uncertainties on model results highlighting the need for more experiments and theoretical studies to improve the chemistry of aromatics.List of reactions (with rate constants) and references used in the present model.List of photodissociations and references used in the present model.For each reaction included in the model, the integrated column rate scaled to the surface (in cm-2 s-1) and the mean altitude (in km) of the production are given.In the three following files, we list the key reactions at 300 km, 500 km and 1000 km of altitude for all species in the present model

1D-coupled photochemical model of neutrals, cations and anions in the atmosphere of Titan

Many models with different characteristics have been published so far to study the chemical processes at work in Titan's atmosphere. Some models focus on neutral species in the stratosphere or ionic species in the ionosphere, but few of them couple all the species throughout the whole atmosphere. Very few of these emphasize the importance of uncertainties in the chemical scheme and study their propagation in the model.We have developed a new 1D-photochemical model of Titan's atmosphere coupling neutral species with positive and negative ions from the lower atmosphere up to the ionosphere and have compared our results with observations to have a comprehensive view of the chemical processes driving the composition of the stratosphere and ionosphere of Titan. We have updated the neutral, positive ion and negative ion chemistry and have improved the description of N2 photodissociation by introducing high resolution N2 absorption cross sections. We performed for the first time an uncertainty propagation study in a fully coupled ion-neutral model.We determine how uncertainties on rate constants on both neutral and ionic reactions influence the model results and pinpoint the key reactions responsible for this behavior. We find very good agreement between our model results and observations in both the stratosphere and in the ionosphere for most neutral compounds. Our results are also in good agreement with an average INMS mass spectrum and specific flybys in the dayside suggesting that our chemical model (for both neutral and ions) provides a good approximation of Titan's atmospheric chemistry as a whole. Our uncertainty propagation study highlights the difficulty to interpret the INMS mass spectra for masses 14, 31, 41 and we identified the key reactions responsible for these ambiguities.Despite an overall improvement in the chemical model, disagreement for some specific compounds (HC3N, C2H5CN, C2H4) highlights the role that certain physical processes could play (meridional dynamics or sticking on aerosols). We find that some critical key reactions are important for many compounds including both neutrals and ions and should be studied in priority to lower the remaining model uncertainties. Extensive studies for some specific processes (including photolyses) are required

The photochemical fractionation of oxygen isotopologues in Titan’s atmosphere

The origin of CO and the external source of H2O in the atmosphere of Titan is still a matter of debate. We investigated the chemical fractionation of oxygen isotopologues in order to give new constraints on the origin of oxygen species. We created a new chemical scheme and we developed a 1-D time-dependent photochemical model to compute the mole fraction profiles of various oxygen isotopologues. We show that the photochemical fractionation of oxygen isotopologues is quite low. Observations of C18O and CO18O are compatible with both an external origin or an internal origin of CO considering that the various sources of oxygen have a cometary 16O/18O ratio (16O/18O ≈ 500). Improvement of the measurements of the 16O/18O ratio in both Enceladus' plumes and atmospheric CO2 could give a valuable constraint on the origin of oxygen in Titan's atmosphere

One dimension photochemical models in global mean conditions in question: Application to Titan

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