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The concept of a Solar System, a fundamental Copernican construct, started to gain a footing in the seventeenth century. Although the cosmological debates around the Copernican system are the subject of a vast literature, the role of images in firming the concept of the Copernican Solar System has received scant attention. This paper addresses the emergence and early development of Solar System maps and diagrams, focusing on images produced by Andreas Cellarius, Christiaan Huygens (especially), William Whiston, and James Ferguson between the mid-seventeenth century and the mid-eighteenth century that ultimately turned the Solar System into a cartographic object depicted to scale, in a manner akin to that of terrestrial maps. This paper also shows that while these images were originally produced with the aim of sustaining particular claims and arguments about Copernicanism, the plurality of inhabited worlds, and Newtonianism, they gained a life of their own, codifying a set of visual conventions that have been used to this day to represent the Solar System and its scale. [ABSTRACT FROM AUTHOR]

This article traces the conceptual origins of Newton's draft scholia to Propositions IV through IX of Book III of the Principia to a manuscript booklet of observational data. By coordinating passages marked by dog-eared pages in Newton's books with his correspondence and working papers, it is possible to date these references to a time when he was still actively working on the Principia itself. This provides the basis for a new interpretation of Newton's uses of Egyptian and Graeco-Roman antiquity to counter rival histories of astronomy and philosophy influenced by Descartes. [ABSTRACT FROM AUTHOR]

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature , rather than in mathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, contradictory in their definition, and thus absolutely impossible. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the part–whole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are mentis fictiones , i.e., (well-founded) fictions usable in mathematics, but possibly contrary to the Leibnizian principle of the harmony of things and not necessarily idealizing anything in rerum natura. Unlike infinite wholes, infinitesimals—as well as imaginary roots and other well-founded fictions—may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality. [ABSTRACT FROM AUTHOR]

In this article, we have investigated the effect of using a real feed on the performance of one-dimensional binary Huygens metasurfaces (BHMS). The designed structure has variable periods and each unit-cell consists of two dipoles with different lengths. Floquet theory and local constant period assumption are used to design these metasurfaces. The simulation results show the high efficiency of the designed structure and its beam squint capability. The results in this article make it possible to use this type of metasurface in real applications under the illumination of real feed sources. [ABSTRACT FROM AUTHOR]

In recent years there has been a shift of interest in the Nanophotonics community moving from using metallic/plasmonic materials to using high‐index dielectric materials for the construction of metasurfaces. Although high‐index dielectrics hold many advantages over their plasmonic counterparts, the selection of materials that exhibit high‐index properties, have low loss, and are complemetary metal‐oxide‐semiconductor (CMOS) compatible that also operate in the visible regime is extremely challenging. In this work, a high‐index dielectric material using silicon rich nitride (SRN) is proposed and experimentally demonstrated as a platform for solving this problem. While SRN has been used before for diffractive lenses and structural colors, here its applicability for Huygens‐type metasurfaces is focused upon. Specifically, a Huygens metasurface that operates in the visible range around a wavelength of 575 nm is theoretically and experimentally demonstrated, and the capabilities of spatially controlling the phase of this metasurface are further demonstrated by designing and fabricating a Huygens meta hologram. The study also shows that the refractive index can be controlled by the interplay between SiH4 and NH3 during the plasma‐enhanced chemical vapor deposition (PECVD) process. [ABSTRACT FROM AUTHOR]

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converging series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz's various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers the question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. [ABSTRACT FROM AUTHOR]

In this article, a new transmitarray (TA) antenna is designed and fabricated based on Huygens metasurfaces (HMSs). An analytical method has been used to achieve the distribution of surface parameters equivalent to HMS. In this method, the required equations for computing the surface parameters are derived using ray tracing, generalized sheet transition conditions, and two conditions of local power consumption and local impedance equalization. In order to implement these surface parameters, wire and loop unit cells are utilized, which are exposed to the radiation transversely. The array of these unit cells offers high aperture efficiency broadband TA antennas in low aperture profile. The fabricated TA antenna with a low aperture thickness of $0.2\lambda $ exhibits the bandwidth, sidelobe level (SLL), and cross-polarization level of 14%, −19 dB, and −19 dB, respectively. In addition, the high aperture efficiency of 65% is reached with this TA, which shows great improvement in comparison to previous works. [ABSTRACT FROM AUTHOR]

The consensus today is that both Newton and Leibniz created calculus independently. Yet, this was not so clear at the beginning of the eighteenth century. A bitter controversy took place at that time, which came to be known as the 'calculus war', probably the greatest clash in the history of science. While it is accepted that the debate started when Fatio de Duillier publicly accused Leibniz of plagiarism in 1699, earlier evidence of its origins can be found in an exchange of letters between Leibniz and Huygens. [ABSTRACT FROM AUTHOR]

River valleys have been observed on Titan at all latitudes by the Cassini‐Huygens mission. Just like water on Earth, liquid methane carves into the substrate to form a complex network of rivers, particularly stunning in the images acquired near the equator by the Huygens probe. To better understand the processes at work that form these landscapes, one needs an accurate digital terrain model (DTM) of this region. The first and to date the only existing DTM of the Huygens landing site was produced by the U.S. Geological Survey (USGS) from high‐resolution images acquired by the DISR (Descent Imager/Spectral Radiometer) cameras on board the Huygens probe and using the SOCET SET photogrammetric software. However, this DTM displays inconsistencies, primarily due to nonoptimal viewing geometries and to the poor quality of the original data, unsuitable for photogrammetric reconstruction. We investigate a new approach, benefiting from a recent reprocessing of the DISR images correcting both the radiometric and geometric distortions. For the DTM reconstruction, we use MicMac, a photogrammetry software based on automatic open‐source shape‐from‐motion algorithms. To overcome challenges such as data quality and image complexity (unusual geometric configuration), we developed a specific pipeline that we detailed and documented in this article. In particular, we take advantage of geomorphic considerations to assess ambiguity on the internal calibration and the global orientation of the stereo model. Besides the novelty in this approach, the resulting DTM obtained offers the best spatial sampling of Titan's surface available and a significant improvement over the previous results. Key Points: We create a new digital terrain model (DTM) of the Huygens landing site that offers the best available resolution of river valleys on TitanThe complexity of the data set requires a tailor‐made reconstruction procedure that is detailedThe workflow uses reprocessed Huygens/DISR images and an automated shape‐from‐motion algorithm to improve an earlier DTM [ABSTRACT FROM AUTHOR]

The elastodynamic geometrical theory of diffraction (GTD) has proved to be useful in ultrasonic nondestructive testing (NDT) and utilizes the so-called diffraction coefficients obtained by solving canonical problems, such as diffraction from a half-plane or an infinite wedge. Consequently, applying GTD as a ray method leads to several limitations notably when the scatterer contour cannot be locally approximated by a straight infinite line: when the contour has a singularity (for instance, at a corner of a rectangular scatterer), the GTD field is, therefore, spatially nonuniform. In particular, defects encountered in ultrasonic NDT have contours of complex shape and finite length. Incremental models represent an alternative to standard GTD in the view of overcoming its limitations. Two elastodynamic incremental models have been developed to better take into consideration the finite length and shape of the defect contour and provide a more physical representation of the edge diffracted field: the first one is an extension to elastodynamics of the incremental theory of diffraction (ITD) previously developed in electromagnetism, while the second one relies on the Huygens principle. These two methods have been tested numerically, showing that they predict a spatially continuous scattered field and their experimental validation is presented in a 3-D configuration. [ABSTRACT FROM AUTHOR]

Electrically thin and effectively 2-D material composites, metasurfaces, have been widely exploited for the manipulation of electromagnetic waves. For many applications, it is desired to transform incident waves of a specific frequency range keeping the metasurface invisible at other frequencies. Such a frequency-selective response can be achieved based on subwavelength Huygens’ inclusions. However, their fabrication requires sophisticated processes due to the 3-D geometry. Here, we propose a planar Huygens’ meta-atom with the goal to open a way to realize broadband invisible metasurfaces with topologies suitable for the conventional printed circuit board fabrication technology. We synthesize and analyze, both numerically and experimentally, three different metasurfaces capable of polarization and amplitude transformations of incident waves. [ABSTRACT FROM AUTHOR]

The article deals with selected aspects of two well-known publications on the multiplicity of worlds and extraterrestrial life that emerged at the end of the 17th century. These are Entretiens sur la pluralité des mondes (1686) by Bernard de Fontenelle and Cosmotheoros (1698) by Christiaan Huygens. In the first part, the article focuses primarily on how both authors understand the position of man in an inhabited and unbounded universe. Fontenelle and Huygens provide in their texts a convincing refutation of the often repeated notion that the idea of the infinite universe awakened terror and fears in early modern intellectuals. Actually, for them, the unbounded universe meant a celebration of reason that is able to emancipate itself from a geocentric superstition and anthropocentrism. At the same time, in the spirit of the early Enlightenment, it was also a celebration of the cosmic universality of reason. In its second part, the article deals with so-called cognitive passions: especially with fear, amazement and curiosity. The analysis of Huygens' and Fontenelles' works confirms and deepens some points of Lorraine Daston's research. It turns out that at the end of the 17th century, fear and admiration were clearly understood as manifestations of ignorance and backwardness, although in the previous philosophical tradition they were associated with piety and the beginning of philosophy. Compared to it, traditionally condemned curiosity has become a legitimate, even desirable, characteristics of a true scientist. [ABSTRACT FROM AUTHOR]

The history of the introduction of exotic therapeutic drugs in early modern Europe is usually rife with legend and obscurity and Peruvian bark is a case in point. The famous antimalarial drug entered the European medical market around 1640, yet it took decades before the bark was firmly established in pharmaceutical practice. This article argues that the history of Peruvian bark can only be understood as the interplay of its trajectories in science, commerce, and society. Modern research has mostly focused on the first of these, largely due to the abundance of medico-historical data. While appreciating these findings, this article proposes to integrate the medical trajectory in a richer narrative, by drawing particular attention to the acculturation of the bark in commerce and society. Although the evidence we have for these two trajectories is still sketchy and disproportionate, it can nevertheless help us to make sense of sources that have not yet been an obvious focus of research. Starting from an apparently isolated occurrence of the drug in a letter, this article focuses on Paris as the location where medical and public appreciation of the bark took shape, by exploring several contexts of knowledge circulation and medical practice there. These contexts provide a new window on the early circulation of knowledge of the bark, at a time when its eventual acceptance was by no means certain. [ABSTRACT FROM AUTHOR]

We compare measurements made by two impact penetrometers of different sizes and with different tip shapes to further understand penetrometer design for performing penetrometry on an asteroid. To this end we re-visit the interpretation of data from the Huygens’ penetrometer, ACC-E, that impacted Titan’s surface. In addition we investigate the potential of a spacecraft fitted with a penetrometer to bounce using a test rig, built at The Open University (UK). Analysis of ACC-E laboratory data, obtained from impacts into ∼4 mm diameter gravel, was found to produce an unusual decrease in resistance with depth (force–depth gradient) which was also seen in the Huygens’ ACC-E data from Titan and originally interpreted as a wet or moist sand. The downward trend could also be reproduced in a hybrid Discrete Element Model (DEM) if it was assumed that the near surface particles are more readily mobilised than those deeper in the target. With regard to penetrometer design penetration resistance was found to be sensitive to the ratio of particle to tip diameter. A clear trend was observed with a conical tip penetrometer, X-PEN, of decreasing force–depth gradients with increasing particle sizes most likely due to a transformation from a bulk displacement of material by the penetrating tip to more local interactions. ACC-E, which has a hemispherical tip, was found to produce a wider range of force–depth gradients than X-PEN, which had a conical tip, possibly due to difficulties dislodging jammed particles. Both penetrometers were able to determine particle diameter and mass after post-processing of the data. Laboratory simulations of landings with the test rig suggest that a large impact penetrometer under certain circumstances could absorb a significant amount of the elastic energy of the spacecraft possibly aiding landing. Alternatively a small impact penetrometer would allow the spacecraft to bounce freely off the surface to make a measurement at another location. [ABSTRACT FROM AUTHOR]

The Tercentenary of the publication of Jacob Bernoulli's Ars Conjectandi ( The Art of Conjecturing) provides an opportunity to look at the origins of mathematical probability from Jacob Bernoulli's point of view. Bernoulli gave a mathematically rigorous proof of what has come to be called the weak law of large numbers, relevant to discovering ratios of unknown factors through sampling. The Art of Conjecturing was a bridge between the mathematics of expectation in games of chance as found in Huygens's On Reckoning in Games of Chance and mathematical probability as found in Abraham De Moivre's The Doctrine of Chances. This paper looks at the conceptual context as well as the mathematics of Bernoulli's book. [ABSTRACT FROM AUTHOR]

On the 300th anniversary of the publication of Jacob Bernoulli's Ars Conjectandi, the book is revisited in historical context and seen in a new light. Bernoulli's announced goal of extending the application of probability from games to civil life was frustrated by the a priori difficulty of specifying equally likely cases. The great approximation theorem Bernoulli proved and suggested could lead to empirical applications was impractical for all but unrealistically large sample sizes, but it was immensely influential in the development of the mathematics of probability. [ABSTRACT FROM AUTHOR]

Constantijn Huygens (1596-1687) was a notable Dutch statesman who penned over 75,000 lines of verse in eight languages. He made visits to England on no less than seven occasions and wrote a significant body of poetry, primarily in Dutch, but also in Latin, and very occasionally in French and English, during these visits. In this article, a detailed account is given of the poetry, which Huygens wrote in England. It provides a case-study of someone writing Dutch, and indeed Latin, verse in England in the early-modern period. Furthermore, during a time when the fortunes of Britain and the Northern Netherlands were very closely linked, it illustrates how a Dutchman responded in verse to aspects of English social and cultural life, and events such as the execution of Charles I, and the Great Fire of London of 1666. [ABSTRACT FROM AUTHOR]

Abstract: The Surface Science Package (SSP) was one of six instruments flown onboard the Huygens probe to Titan, the largest moon of Saturn, in the framework of the NASA/ESA/ASI Cassini–Huygens mission (). The SSP operated throughout the probe''s descent and after landing on Titan on 14th January 2005. This paper reviews scientific results from the Surface Science Package, and also reports previously unpublished flight data which illustrate the performance of the measurement systems in the Titan environment. This review provides some lessons learned that may be useful for further detailed analysis of the Huygens mission data, and for payloads for future missions to Titan, in which there has been recent interest (e.g., the Titan Saturn System Mission (TSSM) (), TANDEM () or the Titan Mare Explorer (TiME) Discovery-class proposal ()), as well as for planetary probe missions more generally. [Copyright &y& Elsevier]

In this article, I provide a detailed analysis of the poems on the Lord's Supper by the Dutch statesman and man of letters, Constantijn Huygens (1596–1687). Between 1642 and 1684, he wrote eighteen poems on this subject, sixteen in Dutch and two in Latin. The type of poem varies from pithy epigrams to sonnets, through to longer poems over fifty lines in length, replete with well-conceived poetic tropes. To date, these poems have received little scholarly attention. Huygens was a lifelong member of the Reformed church and his poetry considers themes which are central to Reformed theology, such as human sin, divine grace and human gratitude. In his poetry, he recognises that he is a sinner and that it is not sufficient merely to ask for divine forgiveness, and then sin again. He acknowledges the need to intend to change his ways, but also recognises that he can only do this with divine assistance. Huygens published most of these poems and although such a public acknowledgement of sin may seem strange to us, there is a sense in which he was performing a public act of confession, to make common cause with his fellow believers, and also perhaps to encourage them to do the same. Much of the poetry considers the ontology and efficacy of the Lord's Supper. As well as exploring familiar tropes such as the sacrament as a feast and a pledge for God's promises, Huygens also asks about the very nature of the bread and wine of the sacrament. We might expect him to ascribe little or no value to the elements themselves, beyond, to use Brian Gerrish's phrase, ‘presenting what they represent’. poetry. However, at some points, the language Huygens uses to refer to the elements, such as ‘holy bread’ and ‘healing dew’, suggests something more is at stake. Some may dismiss such phrases as mere lyrical flourish, but I argue that they point to a central tension inherent within Reformed eucharistic theology between sign and signified and, furthermore, that this poetry offers us the opportunity to explore that tension. Huygens’ poems bear comparison with the best English-language religious poetry of the seventeenth century, and remind us that poetry as well as prose can offer us valuable theological insight. [ABSTRACT FROM PUBLISHER]

Abstract: The Huygens absorbing boundary conditions (ABCs) are promising new implementations of operator ABCs. They have certain advantageous features which are lacked in other operator ABCs. Under certain conditions and with the Huygens ABCs, the transmitted wave depends solely upon the second derivative with respect to time or upon the double integral of the incident wave. For such cases and for problems with a Dirichlet boundary condition, the overall reflection is not unique. Two new examples of the Huygens ABCs are given for such cases. For each example and with a FDTD scheme the newly derived reflection is less than that which has been studied by Bérenger [J.-P. Bérenger, On the Huygens absorbing boundary conditions for electromagnetics, J. Comput. Phys. 226 (2007) 354–378]. [Copyright &y& Elsevier]

Huygens is known among Physics introductory teaching for his study on refraction through a wave model. Didactic books honor him by giving his name to a principle. But in his masterpiece, Treatise on Light, it is possible to notice much more: his inventiveness in defending an alternative wave model of light in opposition to the corpuscular model. This work attempts to highlight Huygens' reasoning, showing that, despite having been published more than three hundred years ago, the work is written in a relatively accessible language. [ABSTRACT FROM AUTHOR]

Abstract: Scattering properties of large (N>2000) aggregates of monomers as found in Titan’s atmosphere during the descent of the Cassini/Huygens probe are numerically calculated. We extend our previous quantitative analysis of small aggregates (N≤256) to verify the obtained conclusions. To calculate the light scattering of such big non-spherical aggregates we use the DDSCAT code based on the discrete dipole approximation (DDA) technique introduced by . The orientation averaged single-scattering phase function as well as the degree of linear polarization is calculated. Clusters with up to 2048 monomers are investigated in the optical wavelength range. We conclude that (a) the applied mathematical aggregation mechanism plays only a minor role, and it is sufficient to test particles formed by diffusion limited aggregation (DLA) with different cluster parameters; (b) the aggregate “fluffiness” can be qualitatively derived from polarization data; (c) for a fixed number of monomers the scattering function of intensity is sensitive to the size parameter of the aggregates (e.g. to the effective cluster density); (d) consequently, characterization of aggregates by their number of monomers only is generally insufficient and more detail cluster descriptions are needed; (e) even when an aggregate is described more explicitly significant intensity variations can be observed for “identical” model particles over the whole range of scattering angles, particular for large fluffy aggregates; (j) random generation averaging should be added to the standard orientation averaging procedure. Finally, we discuss our results in respect of the conclusions of the paper. [ABSTRACT FROM AUTHOR]

Abstract: In 2005, the Huygens probe, designed by Thales Alenia Space, France, successfully completed its entry and descent in Titan''s atmosphere. In the frame of the Aurora Exploration Program, ESA has initiated industrial studies for the ExoMars mission. The Thales Alenia Space France-led consortium was awarded the contract for the design, development and manufacturing of the Entry and Descent System under Thales Alenia Space—Italy mission prime. Huygens and ExoMars constitute major European milestones in the field of atmospheric entry and descent. Eight out of the ten bodies larger than Mercury in the Solar System have a significant atmosphere to descent in, either to reach a solid surface, or to explore the atmosphere itself. The gained experience in Entry Descent and Landing design will enhance European industry capability to contribute to future planetary exploration missions. This paper assesses the different environments and conditions that Entry Descent and Landing Systems will meet. It discusses how Europe''s Huygens and ExoMars experience will apply in such environments and identifies the critical technologies needed to complement it. It concludes on the elements of a roadmap for the related technological development. [Copyright &y& Elsevier]

In this essay, I attempt to assess Henk de Regt and Dennis Dieks recent pragmatic and contextual account of scientific understanding on the basis of an important historical case-study: understanding in Newton’s theory of universal gravitation and Huygens’ reception of universal gravitation. It will be shown that de Regt and Dieks’ Criterion for the Intelligibility of a Theory (CIT), which stipulates that the appropriate combination of scientists’ skills and intelligibility-enhancing theoretical virtues is a condition for scientific understanding, is too strong. On the basis of this case-study, it will be shown that scientists can understand each others’ positions qualitatively and quantitatively, despite their endorsement of different worldviews and despite their convictions as what counts as a proper explanation. [ABSTRACT FROM AUTHOR]

Abstract: The Huygens Probe data provided a direct measurement of CH4, temperature, and pressure in Titan''s atmosphere. This data can be used to compare to the Voyager data in which the effects of CH4, temperature, and pressure were mixed together. Comparison with Huygens data indicates that values of the surface relative humidity of CH4 at the Voyager ingress and egress were between 20% and 45%, and values above 60% are inconsistent with this comparison. The most parsimonious explanation for the Voyager data is that the temperature and CH4 surface humidity at the Voyager ingress and egress profiles were identical to the Huygens values; a surface temperature of 93.65±0.25K, and a surface relative humidity of 43%. Thus, it is likely that these values have characterized the equatorial region of Titan from 1980 until 2005. The small reduction of 1K, between the tropopause temperatures of the Voyager profiles and the tropopause temperature of the Huygens profile is explainable by a change in the antigreenhouse flux from the stratosphere from 0.13 to 0.1 of the total average solar flux. This could result from a small seasonal change in the optical properties of the stratospheric haze. [Copyright &y& Elsevier]

The first century of telescopic astronomy can be divided into two periods. During the first, from 1609 to ca. 1640, observations were made with a simple “Dutch” or “Galilean” telescope with a concave eyepiece. Galileo made all his discoveries with this instrument. Its limited field of view, however, made magnifications of more than about 20 impractical, and therefore this instrument’s limit had been reached within a few years. During the second period, ca. 1640–ca. 1700, the simple astronomical telescope came into use, almost immediately augmented with a field lens and an erector lens (the latter used only for terrestrial purposes). Magnifications were increased by increasing the focal lengths of objectives, and this quickly led to very long telescopes, often used without a tube. The astronomical discoveries made possible by this form of the instrument were, however, made with instruments of relatively modest lengths. By the end of the century, very long telescopes fell out of use, while shorter ones were adapted for measurements. Further discoveries became possible only with the reflecting telescope in the second half of the eighteenth century. [ABSTRACT FROM AUTHOR]

Abstract: The descent imager/spectral radiometer (DISR) onboard the Huygens probe investigated the radiation balance inside Titan''s atmosphere and took hundreds of images and spectra of the ground during the descent. The scattering of the aerosols in the atmosphere and the absorption by methane strongly influence the irradiation reaching the surface and the signals received by the various instruments. The physical properties of the surface can only be assessed after the influence of the atmosphere has been taken into account and properly removed. In the broadband visible images (660 to 1000nm) the contrast of surface features is strongly reduced by the aerosol scattering. Calculations show that for an image taken from an altitude of 14.5km, the corrected contrast is about three times higher than in the raw image. Spectral information of the surface by the imaging spectrometers in the visible and near infrared range can only be retrieved in the methane absorption windows. Intensity ratios from the methane windows can be used to make false color maps. The elevated bright ‘land’ terrain is redder than the flat dark ‘lake bed’ terrain. The reflectance spectra of the land and lake bed area in the IR are derived, as well as the reflectance phase function in the limited range from to phase angle. An absorption feature at 1.55 m which may be attributed tentatively to water ice is found in the lake bed, but not in the land area. Otherwise the surface exhibits a featureless blue slope in the near-IR region (0.9–). Brightness profiles perpendicular to the coast line show that the bottoms of the channels of the large scale flow pattern become darker the further they are away from the land area. This could be interpreted as sedimentation of the bright land material transported by the rivers into the lake bed area. The river beds in the deeply incised valleys need not to be covered by dark material. Their roughly 10% brightness decrease could be caused by the illumination as illustrated by a model calculation. The size distribution of cobbles seen in the images after landing is in agreement with a single major flooding of the area with a flow speed of about . [Copyright &y& Elsevier]

Abstract: The descent imager/spectral radiometer (DISR) instrument aboard the Huygens probe into the atmosphere of Titan measured the brightness of sunlight using a complement of spectrometers, photometers, and cameras that covered the spectral range from 350 to 1600nm, looked both upward and downward, and made measurements at altitudes from 150km to the surface. Measurements from the upward-looking visible and infrared spectrometers are described in Tomasko et al. [2008a. Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan''s atmosphere. Planet. Space Sci., this volume]. Here, we very briefly review the measurements by the violet photometers, the downward-looking visible and infrared spectrometers, and the upward-looking solar aureole (SA) camera. Taken together, the DISR measurements constrain the vertical distribution and wavelength dependence of opacity, single-scattering albedo, and phase function of the aerosols in Titan''s atmosphere. Comparison of the inferred aerosol properties with computations of scattering from fractal aggregate particles indicates the size and shape of the aerosols. We find that the aggregates require monomers of radius 0.05μm or smaller and that the number of monomers in the loose aggregates is roughly 3000 above 60km. The single-scattering albedo of the aerosols above 140km altitude is similar to that predicted for some tholins measured in laboratory experiments, although we find that the single-scattering albedo of the aerosols increases with depth into the atmosphere between 140 and 80km altitude, possibly due to condensation of other gases on the haze particles. The number density of aerosols is about 5/cm3 at 80km altitude, and decreases with a scale height of 65km to higher altitudes. The aerosol opacity above 80km varies as the wavelength to the −2.34 power between 350 and 1600nm. Between 80 and 30km the cumulative aerosol opacity increases linearly with increasing depth in the atmosphere. The total aerosol opacity in this altitude range varies as the wavelength to the −1.41 power. The single-scattering phase function of the aerosols in this region is also consistent with the fractal particles found above 60km. In the lower 30km of the atmosphere, the wavelength dependence of the aerosol opacity varies as the wavelength to the −0.97 power, much less than at higher altitudes. This suggests that the aerosols here grow to still larger sizes, possibly by incorporation of methane into the aerosols. Here the cumulative opacity also increases linearly with depth, but at some wavelengths the rate is slightly different than above 30km altitude. For purely fractal particles in the lowest few km, the intensity looking upward opposite to the azimuth of the sun decreases with increasing zenith angle faster than the observations in red light if the single-scattering albedo is assumed constant with altitude at these low altitudes. This discrepancy can be decreased if the single-scattering albedo decreases with altitude in this region. A possible explanation is that the brightest aerosols near 30km altitude contain significant amounts of methane, and that the decreasing albedo at lower altitudes may reflect the evaporation of some of the methane as the aerosols fall into dryer layers of the atmosphere. An alternative explanation is that there may be spherical particles in the bottom few kilometers of the atmosphere. [Copyright &y& Elsevier]

Abstract: In the frame of fractal modeling of tholin aggregates we made a systematic analysis of their optical properties. Ballistic particle–cluster aggregation (BPCA) and diffusion-limited aggregation (DLA) of spherical primary particles (monomers) identical in material composition were considered. Aggregates composed of identical particles (monodisperse cluster), as well as of size-distributed particles (polydisperse cluster), were simulated. To calculate the light-scattering models, the code based on the superposition T-matrix method is used. Orientationally averaged properties of light scattering by model particles were extracted, and the normalized phase function and the degree of linear polarization were calculated as functions of scattering angle. We concluded that: (a) aggregation mechanism as well as specific internal structure of the clusters play only a minor role, and for the future it is not necessary to investigate aggregates of different types; (b) the intensity is very sensitive both to the size parameter of forming particles x and to the size parameter of the aggregates X; (c) characterization of the aggregates by the number of monomers is insufficient to retrieve physical properties of aggregates from optical measurement; and (d) it is very desirable to include into the analysis polarization data calculated for the different clusters. [Copyright &y& Elsevier]

Abstract: The recent measurements of the vertical distribution and optical properties of haze aerosols as well as of the absorption coefficients for methane at long paths and cold temperatures by the Huygens entry probe of Titan permit the computation of the solar heating rate on Titan with greater certainty than heretofore. We use the haze model derived from the Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., See, C., 2008a. A model of Titan''s aerosols based on measurements made inside the atmosphere. Planet. Space Sci., this issue, doi:10.1016/j.pss.2007.11.019] to evaluate the variation in solar heating rate with altitude and solar zenith angle in Titan''s atmosphere. We find the disk-averaged solar energy deposition profile to be in remarkably good agreement with earlier estimates using very different aerosol distributions and optical properties. We also evaluated the radiative cooling rate using measurements of the thermal emission spectrum by the Cassini Composite Infrared Spectrometer (CIRS) around the latitude of the Huygens site. The thermal flux was calculated as a function of altitude using temperature, gas, and haze profiles derived from Huygens and Cassini/CIRS data. We find that the cooling rate profile is in good agreement with the solar heating profile averaged over the planet if the haze structure is assumed the same at all latitudes. We also computed the solar energy deposition profile at the 10°S latitude of the probe-landing site averaged over one Titan day. We find that some 80% of the sunlight that strikes the top of the atmosphere at this latitude is absorbed in all, with 60% of the incident solar energy absorbed below 150km, 40% below 80km, and 11% at the surface at the time of the Huygens landing near the beginning of summer in the southern hemisphere. We compare the radiative cooling rate with the solar heating rate near the Huygens landing site averaging over all longitudes. At this location, we find that the solar heating rate exceeds the radiative cooling rate by a maximum of 0.5K/Titan day near 120km altitude and decreases strongly above and below this altitude. Since there is no evidence that the temperature structure at this latitude is changing, the general circulation must redistribute this heat to higher latitudes. [Copyright &y& Elsevier]

Abstract: New low-temperature methane absorption coefficients pertinent to the Titan environment are presented as derived from the Huygens DISR spectral measurements combined with the in-situ measurements of the methane gas abundance profile measured by the Huygens Gas Chromatograph/Mass Spectrometer (GCMS). The visible and near-infrared spectrometers of the descent imager/spectral radiometer (DISR) instrument on the Huygens probe looked upward and downward covering wavelengths from 480 to 1620nm at altitudes from 150km to the surface during the descent to Titan''s surface. The measurements at continuum wavelengths were used to determine the vertical distribution, single-scattering albedos, and phase functions of the aerosols. The gas chromatograph/mass spectrometer (GCMS) instrument on the probe measured the methane mixing ratio throughout the descent. The DISR measurements are the first direct measurements of the absorbing properties of methane gas made in the atmosphere of Titan at the pathlengths, pressures, and temperatures that occur there. Here we use the DISR spectral measurements to determine the relative methane absorptions at different wavelengths along the path from the probe to the sun throughout the descent. These transmissions as functions of methane path length are fit by exponential sums and used in a haze radiative transfer model to compare the results to the spectra measured by DISR. We also compare the recent laboratory measurements of methane absorption at low temperatures [Irwin et al., 2006. Improved near-infrared methane band models and k-distribution parameters from 2000 to 9500cm−1 and implications for interpretation of outer planet spectra. Icarus 181, 309–319] with the DISR measurements. We find that the strong bands formed at low pressures on Titan act as if they have roughly half the absorption predicted by the laboratory measurements, while the weak absorption regions absorb considerably more than suggested by some extrapolations of warm measurements to the cold Titan temperatures. We give factors as a function of wavelength that can be used with the published methane coefficients between 830 and 1620nm to give agreement with the DISR measurements. We also give exponential sum coefficients for methane absorptions that fit the DISR observations. We find the DISR observations of the weaker methane bands shortward of 830nm agree with the methane coefficients given by Karkoschka [1994. Spectrophotometry of the jovian planets and Titan at 300- to 1000-nm wavelength: the methane spectrum. Icarus 111, 174–192]. Finally, we discuss the implications of our results for computations of methane absorption in the atmospheres of the outer planets. [Copyright &y& Elsevier]

Abstract: Laboratory spectra of methane–nitrogen mixtures have been recorded in the near-infrared range (1.0–1.65μm) in conditions similar to Titan''s near surface, to facilitate the interpretation of the DISR/DLIS (DISR—Descent Imager/Spectral Radiometer) spectra taken during the last phase of the descent of the Huygens Probe, when the surface was illuminated by a surface-science lamp. We used a 0.03cm−1 spectral resolution, adequate to resolve the lines at high pressure (∼1.5bar). By comparing the laboratory spectra with synthetic calculations in the well-studied ν 2+2ν 3 band (7515–7620cm−1), we determine a methane absorption column density of 178±20cmatm and a temperature of 118±10K in our experiment. From this, we derive the methane absorption coefficients over 1.0–1.65μm with a 0.03cm−1 sampling, allowing for the extrapolation of the results to any other methane column density under the relevant pressure and temperature conditions. We then revisit the calibration and analysis of the Titan “lamp-on” DLIS spectra. We infer a 5.1±0.8% methane-mixing ratio in the first 25m of Titan''s atmosphere. The CH4 mixing ratio measured 90s after landing from a distance of 45cm is found to be 0.92±0.25 times this value, thus showing no post-landing outgassing of methane in excess of ∼20%. Finally, we determine the surface reflectivity as seen between 25m and 45cm and find that the 1500nm absorption band is deeper in the post-landing spectrum as compared to pre-landing. [Copyright &y& Elsevier]

Abstract: The Huygens probe returned scientific measurements from the atmosphere and surface of Titan on 14 January 2005. Knowledge of the trajectory of Huygens is necessary for scientific analysis of those measurements. We use measurements from the Huygens Atmospheric Structure Instrument (HASI) to reconstruct the trajectory of Huygens during its mission. The HASI Accelerometer subsystem measured the axial acceleration of the probe with errors of 3E−6ms−2, the most accurate measurements ever made by an atmospheric structure instrument on another planetary body. The atmosphere was detected at an altitude of 1498km. Measurements of the normal acceleration of the probe, which are important for determining the probe''s attitude during hypersonic entry, were significantly less accurate and limited by transverse sensitivity of the piezo sensors. Peak acceleration of 121.2ms−2 occurred at 234.9km altitude. The parachute deployment sequence started at 157.1km and a speed of 342.1ms−1. Direct measurements of pressure and temperature began shortly afterwards. The measured accelerations and equations of motion have been used to reconstruct the trajectory prior to parachute deployment. Measured pressures and temperatures, together with the equation of hydrostatic equilibrium and the equation of state, have been used to reconstruct the trajectory after parachute deployment. Uncertainties in the entry state of Huygens at the top of the atmosphere are significant, but can be reduced by requiring that the trajectory and atmospheric properties be continuous at parachute deployment. [Copyright &y& Elsevier]

Abstract: We have calculated the condensation and evaporation of ternary CH4–N2–C2H6 liquid drops and solid CH4 hail as they fall through Titan''s lower atmosphere to determine the likelihood that precipitation reaches the ground. Assuming the humidity profile determined by the Huygens probe, binary liquid CH4/N2 condensate grows in the region from ∼8 to 15km in Titan''s atmosphere because the combined humidity of CH4 and N2 exceeds saturation. These drops evaporate below ∼8km. We determine the fate of 10μm seeds composed of ethane, which is expected to provide condensation sites. In addition, we study the fate of already formed raindrops with radii of 1–4.75mm falling out of the growth region. High (50%) and low (0%) ethane relative humidities (RH) are considered in the calculation. We find that drops with radii ∼3mm and smaller dropping from 8km reach the ground in compositional equilibrium with the atmosphere in the high ethane RH case as a result of the stabilizing influence of the ethane, and evaporate in the atmosphere in the low ethane RH case. Large drops (>∼3mm) reach the surface large and cold because the latent heat loss due to the evaporation of methane cools the drop and slows the evaporation rate. Pure methane hail hits the ground if its radius is initially more than 4mm at 16km above the surface and sublimates in the atmosphere if its radius is smaller. [Copyright &y& Elsevier]

Abstract: We have developed a new method to analyse in situ observations of atmospheric variables of state: the reconstruction of the vertical temperature profile from pressure measurements accompanied by rough knowledge of the atmospheric composition and the aerodynamical response properties of the descent vehicle. We can use the method to construct the temperature profile when no direct measurements are available, as well as to analyse the consistency between data from different instruments. We applied the method to the Huygens measurements of Titan''s atmosphere, determining the aerodynamical drag properties from radar altimeter data. We discovered that the temperature profile computed in this manner differs from the profile from the temperature sensor (TEM) of the probe by up to 5% in the altitude range of 0–60km, and up to 10% at higher altitudes due to increased noise. The method gives a tropopause altitude of about 50km and a surface temperature of about 98K, in contrast to the TEM temperature measurements. Our error analysis shows that these differences are caused by the known discrepancy in the Huygens altimeter data, with the estimates made by the reconstruction algorithm contributing only 1–2% of error. [Copyright &y& Elsevier]

Abstract: This study aims at interpreting the zonal and meridional wind in Titan''s troposphere measured by the Huygens probe by means of a general circulation model. The numerical simulation elucidates the relative importance of the seasonal variation in the Hadley circulation and Saturn''s gravitational tide in affecting the actual wind profile. The observed reversal of the zonal wind at two altitudes in the lower troposphere can be reproduced with this model only if the near-surface temperature profile is asymmetric about the equator and substantial seasonal redistribution of angular momentum by the variable Hadley circulation takes place. The meridional wind near the surface is mainly caused by the meridional pressure gradient and is thus a manifestation of the Hadley circulation. Southward meridional wind in the PBL (planetary boundary layer) is consistent with the near-surface temperature at the equator being lower than at mid southern latitudes. Even small changes in the radiative heating profile in the troposphere can substantially affect the mean zonal and meridional wind including their direction. Saturn''s gravitational tide is rather weak at the Huygens site due to the proximity to the equator, and does not clearly manifest itself in the instantaneous vertical profile of wind. Nevertheless, the simulated descent trajectory is more consistent with the observation if the tide is present. Because of a different force balance in Titan''s atmosphere from terrestrial conditions, PBL-specific wind systems like on Earth are unlikely to exist on Titan. [Copyright &y& Elsevier]

Abstract: It is possible to determine the mean molecular mass of a planetary atmosphere using pressure and temperature measurements made by an entry probe descending at terminal velocity. The descent trajectory of an entry probe can be determined from pressure, temperature, and mean molecular mass data. This technique offers redundancy for large entry probes in the event of a mass spectrometer failure and increases the potential scientific yield of small entry probes that do not carry mass spectrometers. This technique is demonstrated on Huygens atmospheric structure instrument (HASI) data from Titan. Accurate knowledge of entry probe and parachute drag coefficients is required for this technique to be useful. [Copyright &y& Elsevier]

Abstract: The signal strength of the Huygens Probe Channel B transmission to the Cassini Orbiter was monitored during the Probe descent through Titan''s atmosphere on 14 January 2005. A model of the Probe motion during the mission was constructed to include Probe spin, coning motion and tilt caused by varying wind speeds. This simple model is sufficient to reproduce the most prominent features seen in the signal level measurements. It provides estimates of the coning and tilt angles as well as the direction of the Huygens coordinate axes over extended time intervals in the mission. [Copyright &y& Elsevier]

Abstract: A new absorbing boundary condition (ABC) is presented for the solution of Maxwell equations in unbounded spaces. Called the Huygens ABC, this condition is a generalization of two previously published ABCs, namely the multiple absorbing surfaces (MAS) and the re-radiating boundary condition (rRBC). The properties of the Huygens ABC are derived theoretically in continuous spaces and in the finite-difference (FDTD) discretized space. A solution is proposed to render the Huygens ABC effective for the absorption of evanescent waves. Numerical experiments with the FDTD method show that the effectiveness of the Huygens ABC is close to that of the PML ABC in some realistic problems of numerical electromagnetics. It is also shown in the paper that a combination of the Huygens ABC with the PML ABC is very well suited to the solution of some particular problems. [Copyright &y& Elsevier]

This paper outlines the method of measurement and analysis of the thermal conductivity instrument (THP) that has successfully returned measurements from the atmosphere of Saturn’s moon Titan during the descent of the Huygens probe on 14th January 2005. The technique is validated by analysing laboratory calibration data gathered by our instrument in three pure gases (nitrogen, methane, and ethane) over Titan’s temperature range (90 to 180 K). Calibration results show errors <1% compared to reference values when processed using this method. Details included here along with references should serve as a useful guide for interpreting data from thermal conductivity instruments for space or other stand alone applications for fluids over various pressure and temperature ranges. Our calibration only verifies measurements over Titan conditions, although [4] suggests that the validity of this method extends up to 400 atmospheres and 800°C. [ABSTRACT FROM AUTHOR]

Abstract: With Huygens’ descent into Titan’s atmosphere drawing nearer, the composition and state of Titan’s surface remained largely unknown. The idea of a global ocean on Titan has become less popular over the last decade, though the possibility of lakes and seas has remained, and recently [Campbell, D.B., Black, G.J., Carter, L.M., Ostro, S.J. Radar evidence for liquid surfaces on Titan. Science 302, 431–434, 2003] reported radar evidence for liquid surfaces. Ground truth for the existence of an ocean, sea or lake on Titan or, more precisely, a liquid surface at the specific impact point of the Huygens probe, came from the sensors of the Huygens Surface Science Package (SSP). The state of the surface material can be derived on impact using the onboard accelerometers. In the case of an impact into a liquid the SSP sensors would have been able to measure not only density but also acoustic properties, permittivity, refractive index and thermal properties. In this work, we describe possible ways of constraining the composition of a liquid surface on Titan by combining various measurements made by SSP. [Copyright &y& Elsevier]

An aspect of the long history of the struggle to quantify motion is briefly traced through three extended problem sets suitable for use in first year calculus courses. The sketch culminates with an application of simple mathematics to one of the most current problems in the theory of the universe. [ABSTRACT FROM AUTHOR]

Abstract: During the descent of the Huygens probe in January 2005, its Descent Imager/Spectral Radiometer (DISR) will take the first close up images of Titan''s surface. The shading imposed by the illumination of a planetary surface contains information on its topography. For planetary bodies without an optically thick atmosphere, the light can be assumed to stem from a point source. In this case, methods are available in order to estimate the shape of surface features from shading. The situation is quite different for Titan, as its atmosphere is optically thick at optical wavelengths. The sun is visible from the surface, but the illumination is dominated by diffuse radiance. In order to investigate the characteristics of shading under Titan''s sky and to assess methods to retrieve the shape, different digital terrain models (DTMs) are used to simulate images according to different types of illumination. For an idealized DTM, the shape is retrieved from the shading in the simulated images. Deriving the shape from shading under Titan''s sky using existing methods is only possible if the topography is relatively flat, i.e. in the absence of steep slopes. [Copyright &y& Elsevier]

The Cassini Ion and Neutral Mass Spectrometer (INMS) investigation will determine the mass composition and number densities of neutral species and low-energy ions in key regions of the Saturn system. The primary focus of the INMS investigation is on the composition and structure of Titan’s upper atmosphere and its interaction with Saturn’s magnetospheric plasma. Of particular interest is the high-altitude region, between 900 and 1000 km, where the methane and nitrogen photochemistry is initiated that leads to the creation of complex hydrocarbons and nitriles that may eventually precipitate onto the moon’s surface to form hydrocarbon-nitrile lakes or oceans. The investigation is also focused on the neutral and plasma environments of Saturn’s ring system and icy moons and on the identification of positive ions and neutral species in Saturn’s inner magnetosphere. Measurement of material sputtered from the satellites and the rings by magnetospheric charged particle and micrometeorite bombardment is expected to provide information about the formation of the giant neutral cloud of water molecules and water products that surrounds Saturn out to a distance of ~12 planetary radii and about the genesis and evolution of the rings.The INMS instrument consists of a closed ion source and an open ion source, various focusing lenses, an electrostatic quadrupole switching lens, a radio frequency quadrupole mass analyzer, two secondary electron multiplier detectors, and the associated supporting electronics and power supply systems. The INMS will be operated in three different modes: a closed source neutral mode, for the measurement of non-reactive neutrals such as N2 and CH4; an open source neutral mode, for reactive neutrals such as atomic nitrogen; and an open source ion mode, for positive ions with energies less than 100 eV. Instrument sensitivity is greatest in the first mode, because the ram pressure of the inflowing gas can be used to enhance the density of the sampled non-reactive neutrals in the closed source antechamber. In this mode, neutral species with concentrations on the order of =104 cm-3 will be detected (compared with =105 cm-3 in the open source neutral mode). For ions the detection threshold is on the order of 10-2 cm-3 at Titan relative velocity (6 km sec-1). The INMS instrument has a mass range of 1-99 Daltons and a mass resolutionM/?Mof 100 at 10% of the mass peak height, which will allow detection of heavier hydrocarbon species and of possible cyclic hydrocarbons such as C6H6.The INMS instrument was built by a team of engineers and scientists working at NASA’s Goddard Space Flight Center (Planetary Atmospheres Laboratory) and the University of Michigan (Space Physics Research Laboratory). INMS development and fabrication were directed by Dr. Hasso B. Niemann (Goddard Space Flight Center). The instrument is operated by a Science Team, which is also responsible for data analysis and distribution. The INMS Science Team is led by Dr. J. Hunter Waite, Jr. (University of Michigan). [ABSTRACT FROM AUTHOR]

In January 2005, the Huygens probe will descent through Titan''s atmosphere and the Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking observations at various spectral ranges and spatial resolutions. One of the subinstruments, the Upward Looking Visible Spectrometer (ULVS), measures the total downward radiation flux including the direct solar beam and also, with a shadow bar over the Sun, the diffuse downward flux. The intensity of the direct solar beam and thus the optical depth can be calculated from the difference of these two measurements. But 10° wide shadow bar also obscures the Solar Aureole Imager (SA) and therefore removes a considerable fraction of the diffuse downward radiation. This fraction can be estimated taking into account the brightness distribution of the SA which is estimated with the Titan Inverse Radiation Model (TIRM). Input to the model are a first guess of the optical depth in dependence on the altitude calculated directly from ULVS measurements and data from another DISR subinstrument, the Solar Aureole Imager SA imager. By assimilating the sparse SA data, TIRM yields a consistent estimate of the scattering phase function and the complete radiance field in dependence on the altitude. By iteratively correcting the initial optical depth estimation using the resultant radiance field and passing it again to TIRM, the model is used to simultaneously solve for optical depths and scattering phase functions. [Copyright &y& Elsevier]

The Huygens descent through Titan''s atmosphere in January 2005 will provide invaluable information about Titan''s atmospheric composition and aerosol properties. The Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking radiation observations at various spectral ranges and spatial resolutions. To prepare the DISR data interpretation we have developed a new model for radiation transfer in Titan''s atmosphere. The model solves for the full three-dimensional polarized radiation field in spherical geometry. However, the atmosphere itself is assumed to be spherically symmetric. The model is initialized with a fast-to-compute plane–parallel solution based on the doubling and adding algorithm that incorporates a spherical correction for the incoming direct solar beam. The full three-dimensional problem is then solved using the characteristics method combined with the Picard iterative approximation as described in Rozanov et al. (J. Quant. Spectrosc. Radiat. Transfer 69 (2001) 491). Aerosol scattering properties are calculated with a new microphysical model. In this formulation, aerosols are assumed to be fractal aggregates and include methane gas absorption embedded into the extinction coefficient. The resulting radiance of the model atmosphere''s internal field is presented for two prescribed DISR wavelengths. [Copyright &y& Elsevier]

The photochemical flow reactor , Icarus 147, 282–291) has been modified to minimize the incorporation of oxygen and other impurities in the photoproducts. A mixture of gases that approximate their mixing ratios on Titan (N2, CH4, H2, C2H2, C2H4, and HC3N) (0.98, 0.018, 0.002, 3.5 × 10−4, 3 × 10−4, 1.7 × 10−5, respectively) was irradiated in the flow photochemical reactor using a 185-nm source to give a Titan haze analog as a solid product. X-ray photoelectron spectroscopy (XPS) gave a composition of 93.3% C, 5.3% N, and 1.4% O. Of the 93.3% carbon, high-resolution XPS revealed that 81.2% was present as C&z.sbnd;H, C&z.sbnd;C, and C&z.dbnd6;C groups, 12.1% may be C&z.sbnd;O, C&z.sbnd;N, C&z.dbnd6;N, &z.sbnd;C&z.tbnd6;N, and/or C&z.tbnd6;N groups, 5.3% as a &z.sbnd;C&z.tbnd6;N group. The peak for N was symmetrical and was assigned to the &z.sbnd;C&z.tbnd6;N while that for oxygen was assigned to the C&z.dbnd6;O and/or the C&z.sbnd;O group. Some of these assignments were confirmed by FTIR spectroscopy. The polymeric product had a C:N ratio of 17.6, which is significantly greater than that for Titan haze analogs prepared in discharge reactions. When the polymer was exposed to air for seven days the oxygen content increased by 6% along with an increase in the infrared absorption at 1710 cm−1 assigned to the C&z.dbnd6;O group of a ketone. The oxidation is attributed to the reaction of oxygen with free radicals trapped in the polymer matrix. It is proposed that the photochemical initiation of Titan haze formation from compounds formed from starting materials formed high in Titan’s atmosphere is a more plausible model than haze formed in reactions initiated by solely by discharges. These data will be helpful in the interpretation of the data returned from the Huygens probe of the Cassini mission. [Copyright &y& Elsevier]

During the descent of the Huygens probe through Titan''s atmosphere in January 2005, the Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking measurements at various spectral ranges and spatial resolutions. This internal radiation density could be estimated by radiative transfer calculations for Titan''s atmosphere. However, to do this, the optical properties—i.e. volume extinction coefficient, single scattering albedo and scattering phase function—have to be prescribed at every altitude, and these are apriori not known. Herein, an inverse approach is investigated, which retrieves the single scattering albedo and the phase function of the aerosols from DISR observations. The method uses data from a DISR subinstrument, the Solar Aureole imager (SA), to estimate the optical properties of the atmospheric layer between two successive observation altitudes. A unique solution for one layer can in principle be calculated directly from a linear system of equations, but due to the sparseness of the data and the unavoidable noise in the measurements, the inverse problem is ill-posed. The problem is stabilized by the regularization method requiring smoothness of the resultant solution. A consistent set of solutions for all layers is obtained by iterating several times downward and upward through the layers. The method is tested in a simulated radiation density scenario for Titan, which is based on a microphysical aerosol model for the haze layer. Within this scenario, the expected coverage of SA data allows a reconstruction of the angular dependence of the scattering phase function with an explained variance better than 90%. [Copyright &y& Elsevier]

In this study, the high-efficiency phase control Si metasurfaces are investigated based on aperiodic nanoarrays unlike widely-used period structures, the aperiodicity of which providing additional freedom to improve metasurfaces' performance. Firstly, the phase control mechanism of Huygens nanoblocks is demonstrated, particularly the internal electromagnetic resonances and the manipulation of effective electrical/magnetic polarizabilities. Then, a group of high-transmission Si nanoblocks with 2π phase control is sought by sweeping the geometrical parameters. Finally, several metasurfaces, such as grating and parabolic lens, are numerically realized by the nanostructures with high efficiency. The conversion efficiency of the grating reaches 80%, and the focusing conversion efficiency of the metalens is 99.3%. The results show that the high-efficiency phase control metasurfaces can be realized based on aperiodic nanoarrays, i.e., additional design freedom. [ABSTRACT FROM AUTHOR]