Sublinear Higson corona and Lipschitz extensions

The purpose of the paper is to characterize the dimension of sublinear Higson corona $\nu_L(X)$ of $X$ in terms of Lipschitz extensions of functions: Theorem: Suppose $(X,d)$ is a proper metric space. The dimension of the sublinear Higson corona $\nu_L(X)$ of $X$ is the smallest integer $m\ge 0$ with the following property: Any norm-preserving asymptotically Lipschitz function $f'\colon A\to \R^{m+1}$, $A\subset X$, extends to a norm-preserving asymptotically Lipschitz function $g'\colon X\to \R^{m+1}$. One should compare it to the result of Dranishnikov \cite{Dr1} who characterized the dimension of the Higson corona $\nu(X)$ of $X$ is the smallest integer $n\ge 0$ such that $\R^{n+1}$ is an absolute extensor of $X$ in the asymptotic category \AAA (that means any proper asymptotically Lipschitz function $f\colon A\to \R^{n+1}$, $A$ closed in $X$, extends to a proper asymptotically Lipschitz function $f'\colon X\to \R^{n+1}$). \par In \cite{Dr1} Dranishnikov introduced the category \tilde \AAA whose objects are pointed proper metric spaces $X$ and morphisms are asymptotically Lipschitz functions $f\colon X\to Y$ such that there are constants $b,c > 0$ satisfying $|f(x)|\ge c\cdot |x|-b$ for all $x\in X$. We show $\dim(\nu_L(X))\leq n$ if and only if $\R^{n+1}$ is an absolute extensor of $X$ in the category \tilde\AAA. \par As an application we reprove the following result of Dranishnikov and Smith \cite{DRS}: Theorem: Suppose $(X,d)$ is a proper metric space of finite asymptotic Assouad-Nagata dimension \asdim_{AN}(X). If $X$ is cocompact and connected, then \asdim_{AN}(X) equals the dimension of the sublinear Higson corona $\nu_L(X)$ of $X$.Comment: 13 page

The thermal state and interior structure of Mars

©2018. American Geophysical UnionThe present‐day thermal state, interior structure, composition, and rheology of Mars can be constrained by comparing the results of thermal history calculations with geophysical, petrological, and geological observations. Using the largest‐to‐date set of 3‐D thermal evolution models, we find that a limited set of models can satisfy all available constraints simultaneously. These models require a core radius strictly larger than 1,800 km, a crust with an average thickness between 48.8 and 87.1 km containing more than half of the planet's bulk abundance of heat producing elements, and a dry mantle rheology. A strong pressure dependence of the viscosity leads to the formation of prominent mantle plumes producing melt underneath Tharsis up to the present time. Heat flow and core size estimates derived from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will increase the set of constraining data and help to confine the range of admissible models.DFG, 280637173, FOR 2440: Materie im Inneren von Planeten - Hochdruck-, Planeten- und Plasmaphysi

Compact maps and quasi-finite complexes

The simplest condition characterizing quasi-finite CW complexes $K$ is the implication $X\tau_h K\implies \beta(X)\tau K$ for all paracompact spaces $X$. Here are the main results of the paper: Theorem: If $\{K_s\}_{s\in S}$ is a family of pointed quasi-finite complexes, then their wedge $\bigvee\limits_{s\in S}K_s$ is quasi-finite. Theorem: If $K_1$ and $K_2$ are quasi-finite countable complexes, then their join $K_1\ast K_2$ is quasi-finite. Theorem: For every quasi-finite CW complex $K$ there is a family $\{K_s\}_{s\in S}$ of countable CW complexes such that $\bigvee\limits_{s\in S} K_s$ is quasi-finite and is equivalent, over the class of paracompact spaces, to $K$. Theorem: Two quasi-finite CW complexes $K$ and $L$ are equivalent over the class of paracompact spaces if and only if they are equivalent over the class of compact metric spaces. Quasi-finite CW complexes lead naturally to the concept of $X\tau {\mathcal F}$, where ${\mathcal F}$ is a family of maps between CW complexes. We generalize some well-known results of extension theory using that concept.Comment: 20 page

Deep space 2: The Mars Microprobe Mission

The Mars Microprobe Mission will be the second of the New Millennium Program's technology development missions to planetary bodies. The mission consists of two penetrators that weigh 2.4 kg each and are being carried as a piggyback payload on the Mars Polar Lander cruise ring. The spacecraft arrive at Mars on December 3, 1999. The two identical penetrators will impact the surface at similar to 190 m/s and penetrate up to 0.6 m. They will land within 1 to 10 km of each other and similar to 50 km from the Polar Lander on the south polar layered terrain. The primary objective of the mission is to demonstrate technologies that will enable future science missions and, in particular, network science missions. A secondary goal is to acquire science data. A subsurface evolved water experiment and a thermal conductivity experiment will estimate the water content and thermal properties of the regolith. The atmospheric density, pressure, and temperature will be derived using descent deceleration data. Impact accelerometer data will be used to determine the depth of penetration, the hardness of the regolith, and the presence or absence of 1.0 cm scale layers

Volcanic and Tectonic Constraints on the Evolution of Venus

Surface geologic features form a detailed record of Venus’ evolution. Venus displays a profusion of volcanic and tectonics features, including both familiar and exotic forms. One challenge to assessing the role of these features in Venus’ evolution is that there are too few impact craters to permit age dates for specific features or regions. Similarly, without surface water, erosion is limited and cannot be used to evaluate age. These same observations indicate Venus has, on average, a very young surface (150–1000 Ma), with the most recent surface deformation and volcanism largely preserved on the surface except where covered by limited impact ejecta. In contrast, most geologic activity on Mars, the Moon, and Mercury occurred in the 1st billion years. Earth’s geologic processes are almost all a result of plate tectonics. Venus’ lacks such a network of connected, large scale plates, leaving the nature of Venus’ dominant geodynamic process up for debate. In this review article, we describe Venus’ key volcanic and tectonic features, models for their origin, and possible links to evolution. We also present current knowledge of the composition and thickness of the crust, lithospheric thickness, and heat flow given their critical role in shaping surface geology and interior evolution. Given Venus’ hot lithosphere, abundant activity and potential analogues of continents, roll-back subduction, and microplates, it may provide insights into early Earth, prior to the onset of true plate tectonics. We explore similarities and differences between Venus and the Proterozoic or Archean Earth. Finally, we describe the future measurements needed to advance our understanding of volcanism, tectonism, and the evolution of Venus

SEIS: Insight's Seismic Experiment for Internal Structure of Mars.

By the end of 2018, 42 years after the landing of the two Viking seismometers on Mars, InSight will deploy onto Mars' surface the SEIS (Seismic Experiment for Internal Structure) instrument; a six-axes seismometer equipped with both a long-period three-axes Very Broad Band (VBB) instrument and a three-axes short-period (SP) instrument. These six sensors will cover a broad range of the seismic bandwidth, from 0.01 Hz to 50 Hz, with possible extension to longer periods. Data will be transmitted in the form of three continuous VBB components at 2 sample per second (sps), an estimation of the short period energy content from the SP at 1 sps and a continuous compound VBB/SP vertical axis at 10 sps. The continuous streams will be augmented by requested event data with sample rates from 20 to 100 sps. SEIS will improve upon the existing resolution of Viking's Mars seismic monitoring by a factor of ∼ 2500 at 1 Hz and ∼ 200 000 at 0.1 Hz. An additional major improvement is that, contrary to Viking, the seismometers will be deployed via a robotic arm directly onto Mars' surface and will be protected against temperature and wind by highly efficient thermal and wind shielding. Based on existing knowledge of Mars, it is reasonable to infer a moment magnitude detection threshold of M w ∼ 3 at 40 ∘ epicentral distance and a potential to detect several tens of quakes and about five impacts per year. In this paper, we first describe the science goals of the experiment and the rationale used to define its requirements. We then provide a detailed description of the hardware, from the sensors to the deployment system and associated performance, including transfer functions of the seismic sensors and temperature sensors. We conclude by describing the experiment ground segment, including data processing services, outreach and education networks and provide a description of the format to be used for future data distribution.Electronic supplementary materialThe online version of this article (10.1007/s11214-018-0574-6) contains supplementary material, which is available to authorized users

Using the inertia of spacecraft during landing to penetrate regoliths of the Solar System

The high inertia, i.e. high mass and low speed, of a landing spacecraft has the potential to drive a penetrometer into the subsurface without the need for a dedicated deployment mechanism, e.g., during Huygens landing on Titan. Such a method could complement focused subsurface exploration missions, particularly in the low gravity environments of comets and asteroids, as it is conducive to conducting surveys and to the deployment of sensor networks. We make full-scale laboratory simulations of a landing spacecraft with a penetrometer attached to its base plate. The tip design is based on that used in terrestrial Cone Penetration Testing (CPT) with a large enough shaft diameter to house instruments for analysing pristine subsurface material. Penetrometer measurements are made in a variety of regolith analogue materials and target compaction states. For comparison a copy of the ACC-E penetrometer from the Huygens mission to Titan is used. A test rig at the Open University is used and is operated over a range of speeds from 0.9 to 3 m s−1 and under two gravitational accelerations. The penetrometer was found to be sensitive to the target’s compaction state with a high degree of repeatability. The penetrometer measurements also produced unique pressure profile shapes for each material. Measurements in limestone powder produced an exponential increase in pressure with depth possibly due to increasing compaction with depth. Measurements in sand produced an almost linear increase in pressure with depth. Iron powder produced significantly higher pressures than sand presumably due to the rough surface of the grains increasing the grain-grain friction. Impacts into foamglas produced with both ACC-E and the large penetrometer produced an initial increase in pressure followed by a leveling off as expected in a consolidated material. Measurements in sand suggest that the pressure on the tip is not significantly dependent on speed over the range tested, which suggests bearing strength equations could be applied to impact penetrometry in sand-like regoliths. In terms of performance we find the inertia of a landing spacecraft, with a mass of 100 kg, is adequate to penetrate regoliths expected on the surface of Solar System bodies. Limestone powder, an analogue for a dusty surface, offered very little resistance allowing full penetration of the target container. Both iron powder, representing a stronger coarse grained regolith, and foamglas, representing a consolidated comet crust, could be penetrated to similar depths of around two to three tip diameters. Speed tests suggest a linear dependence of penetration depth on impact speed

First Atmospheric Results from InSight APSS

NASA’s Mars InSight Spacecraft landed on Nov 26, 2018 (Ls=295°) in Elysium Planitia (~4.5°N, 136°E). InSight’s main scientific purpose is to investigate the interior structure and heat flux from Mars, but it is also equipped with instrumentation that can serve as a very capable meteorological station. To remove unwanted environmental noise from the seis- mic signals, InSight carries a very precise pressure sensor (PS) and the first magnetometer (IFG) to the surface of Mars. Additionally, to aid in removing the atmospheric pressure-induced seismic noise, and to identify periods when wind-induced seismic noise may reduce sensitivity, InSight also carries a pair of Wind and Air temperature sensors (TWINS). These three sensors comprise the Auxiliary Payload Sensor Suite (APSS) [1]. Complementing this are a radiometer in the HP3 suite to measure surface radiance, the seismic measurements of SEIS which can record interesting atmospheric phenomena, and the InSight cameras to image clouds and dust devils and estimate atmospheric opacity from dust or clouds. The Lander also carried accelerometers that can be used to reconstruct the at- mospheric structure during descent. We will discuss results drawn from atmospheric measurements on board InSight from the first months of operation, high- lighting the new perspectives permitted by the novel high-frequency, and continuous nature of the InSight data acquisition. Details on pre-landing scientific perspectives for atmospheric science with InSight are found in [2]

Efecto del sustrato carbonoso en la nucleación de nanopartículas de Sn para ánodos en baterías de ion-litio : Experimentos y modelado computacional

En este trabajo hemos estudiado la nucleación de nanopartículas de estaño usando tres diferentes materiales carbonosos como soporte, para obtener los correspondientes compósitos Sn/C. Los materiales carbonosos estudiados fueron: escamas de grafito comercial, nanotubos de carbono (de pared múltiple y 100 nm diámetro) y carbono amorfo (super P ®). La síntesis de las nanopartículas metálicas fue realizada utilizando el método de reducción química a partir de SnCl2 y NaBH4. Los materiales resultantes fueron caracterizados estructuralmente mediante microscopía electrónica de transmisión (TEM) y de barrido (SEM), así como también utilizando la técnica de EDS (“Energy Dispersive Scanning”) de la cual se puede obtener la composición de los compósitos de manera semi cuantitativa. El área superficial específica para los materiales compósitos obtenidos fue determinada mediante la adsorción de N2 y utilizando la teoría BET. Las propiedades electróquímicas de los materiales sintetizados fueron caracterizadas utilizando las técnicas de voltametría cíclica y espectroscopía de impedancia. Se evaluó el desempeño de estos compósitos como ánodos en baterías de ion-litio. Se realizaron estudios de carga y descarga para determinar la capacidad y ciclabilidad de los mismos. De esta manera fue posible determinar que todos los compósitos Sn/C obtenidos presentan un mejor desempeño, en cuanto a capacidad, que el ánodo de grafito que se utiliza comercialmente. Se encontró que el sustrato carbonoso tiene un efecto importante en el desempeño del electrodo, resultando el de mejores propiedades el compósito obtenido a partir de carbono amorfo, lo cual está relacionado con las características estructurales del soporte carbonoso y la correspondiente influencia en el proceso de nucleación y crecimiento de las nanopartículas metálicas. Se modeló computacionalmente el sistema bajo estudio con el objeto de racionalizar las tendencias observadas experimentalmente. Se determinaron los valores para la energía de adsorción de un solo átomo de Sn sobre los distintos soportes carbonosos. Estos valores pueden usarse como referencia en relación con la fuerza impulsora termodinámica para la nucleación de Sn, y resultaron ser el factor clave para comprender las diferencias entre los diferentes materiales carbonosos estudiados.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada