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Synge's problem consists in to determine the dynamics of two point electrical charges interacting through their electromagnetic fields, without to take into account the radiation terms due to the self-forces in each charge. We discuss how this problem is related to the question on to establish initial conditions for the electromagnetic fields that are compatible with the two point charges system isolation, that is, the charges are free from the action of external forces. This problem stems from the existence of inter-temporal constraints for the charges trajectories, which implies that the relativistic Newton equations for the charges is not a system of ODEs, but rather a system of Functional Differential Equations (FDEs). We developed a new method to obtain global solutions that satisfies this system of FDEs and a given initial condition for the charges positions and velocities. This method allows the construction of a recursive numerical algorithm that only use integration methods for ODEs systems. Finally, we apply this algorithm to obtain numerical approximations for the quasi-circular solutions that are predicted in Synge's problem., Comment: 32 pages, 10 Figures, 2 Tables, Preprint Article. J. Phys. A: Math. Theor (2023)

3XMM J185246.6+003317 is a transient magnetar located in the vicinity of the supernova remnant Kes\,79. So far, observations have only set upper limits to its surface magnetic field and spindown, and there is no estimate for its mass and radius. Using ray-tracing modelling and Bayesian inference for the analysis of several light curves spanning a period of around three weeks, we have found that it may be one of the most massive neutron stars to date. In addition, our analysis suggests a multipolar magnetic field structure with a subcritical field strength and a carbon atmosphere composition. Due to the time-resolution limitation of the available light curves, we estimate the surface magnetic field and the mass to be $\log_{10} (B/{\rm G}) = 11.89^{+0.19}_{-0.93}$ and $M=2.09^{+0.16}_{-0.09}$~$M_{\odot}$ at $1\sigma$ confidence level, while the radius is estimated to be $R=12.02^{+1.44}_{-1.42}$ km at $2\sigma$ confidence level. They were verified by simulations, i.e., data injections with known model parameters, and their subsequent recovery. The best-fitting model has three small hot spots, two of them in the southern hemisphere. These are, however, just first estimates and conclusions, based on a simple ray-tracing model with anisotropic emission; we also estimate the impact of modelling on the parameter uncertainties and the relevant phenomena on which to focus in more precise analyses. We interpret the above best-fitting results as due to accretion of supernova layers/interstellar medium onto 3XMM J185246.6+003317 leading to burying and a subsequent re-emergence of the magnetic field, and a carbon atmosphere being formed possibly due to hydrogen/helium diffusive nuclear burning. Finally, we briefly discuss some consequences of our findings for superdense matter constraints., Comment: 14 pages, 5 figures, 4 tables. Accepted for publication in Journal of High Energy Astrophysics (JHEAP)

A scalar-tensor theory of gravity is considered wherein the gravitational coupling $G$ and the speed of light $c$ are admitted as space-time functions and combine to form the definition of the scalar field $\phi$. The varying $c$ participates in the definition of the variation of the matter part of the action; it is related to the effective stress-energy tensor which is a result of the requirement of symmetry under general coordinate transformations. The effect of the cosmological coupling $\Lambda$ is accommodated within a possible behaviour of $\phi$. We analyze the dynamics of $\phi$ in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential $V(\phi)$ and no particular assumption on the Hubble function. The phase space analysis is performed both with the linear stability theory and via the more general Lyapunov's method. Either method lead to the conclusion that the condition $\dot{G}/G=\sigma\left(\dot{c}/c\right)$ where $\sigma=3$ must hold for the rest of cosmic evolution after the system gets to the globally asymptotically stable fixed point and the dynamics of $\phi$ ceases. This result provides a physical foundation for the phenomenological model admitting $\left(G/G_{0}\right)=\left(c/c_{0}\right)^{3}$ used recently to interpret cosmological and astrophysical data. The thus co-varying couplings $G$ and $c$ impact the cosmic evolution after the dynamical system settles to equilibrium. This impact is investigated by constructing the generalized continuity equation in our scalar-tensor model and considering two possible regimes for the varying speed of light -- decreasing $c(a)$ and increasing $c(a)$ -- while solving our modified Friedmann equations. The solutions to the latter equations make room for radiation- and matter-dominated eras that progress to a dark-energy-type of accelerated expansion., Comment: 15 pages, 4 figures. v2: 19 pages, 6 figures; stability analysis expanded and generalized; discussion improved. v3: 27 pages, 6 figures; appendix added; abstract edited due to arXiv's policy; content matches the published version

In April 2020, the QUality Assessment and REProducibility for Instruments and Images in Light Microscopy (QUAREP-LiMi) initiative was formed. This initiative comprises imaging scientists from academia and industry who share a common interest in achieving a better understanding of the performance and limitations of microscopes and improved quality control (QC) in light microscopy. The ultimate goal of the QUAREP-LiMi initiative is to establish a set of common QC standards, guidelines, metadata models, and tools, including detailed protocols, with the ultimate aim of improving reproducible advances in scientific research. This White Paper 1) summarizes the major obstacles identified in the field that motivated the launch of the QUAREP-LiMi initiative; 2) identifies the urgent need to address these obstacles in a grassroots manner, through a community of stakeholders including, researchers, imaging scientists, bioimage analysts, bioimage informatics developers, corporate partners, funding agencies, standards organizations, scientific publishers, and observers of such; 3) outlines the current actions of the QUAREP-LiMi initiative, and 4) proposes future steps that can be taken to improve the dissemination and acceptance of the proposed guidelines to manage QC. To summarize, the principal goal of the QUAREP-LiMi initiative is to improve the overall quality and reproducibility of light microscope image data by introducing broadly accepted standard practices and accurately captured image data metrics., Comment: 17 pages, 3 figures, shortened abstract, Co-Lead Authors: Glyn Nelson and Ulrike Boehm, Corresponding author: Roland Nitschke

In this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible, some previous exposure to the language of differential geometry may be helpful. In this sense the work is aimed to late undergraduate or beginners graduate students interested in mathematical physics. To illustrate the development, we graphically present the eleven coordinate systems in which the Laplace operator is separable. We detail the development of the basis and the connection for the cylindrical and paraboloidal coordinate systems. We also present in [1] codes both in Maxima and Maple for the spherical orthonormal basis, which serves as a working model for calculations in other situations of interest. Also in [1] the codes to obtain the coordinate surfaces are given.

Fault-tolerant distributed systems offer high reliability because even if faults in their components occur, they do not exhibit erroneous behavior. Depending on the fault model adopted, hardware and software errors that do not result in a process crashing are usually not tolerated. To tolerate these rather common failures the usual solution is to adopt a stronger fault model, such as the arbitrary or Byzantine fault model. Algorithms created for this fault model, however, are considerably more complex and require more system resources than the ones developed for less strict fault models. One approach to reach a middle ground is the non-malicious arbitrary fault model. This model assumes it is possible to detect and filter faults with a given probability, if these faults are not created with malicious intent, allowing the isolation and mapping of these faults to benign faults. In this paper we describe how we incremented an implementation of active replication in the non-malicious fault model with a basic type of distributed validation, where a deviation from the expected algorithm behavior will make a process crash. We experimentally evaluate this implementation using a fault injection framework showing that it is feasible to extend the concept of non-malicious failures beyond hardware failures., Comment: 14 pages

A channel with continuous phase modulation and 1-bit ADC with oversampling is considered. Due to oversampling, higher-order modulations yield a higher achievable rate and this work presents a method to approach this with sophisticated coding. A tailored bit mapping is proposed where two bits can be detected reliably at high SNR and only the third bit suffers from an error floor. With this, a convolutional code is only applied to the third bit. Our experiments with a turbo receiver show that the proposed method corresponds to a lower BER in comparison to the case of conventional channel coding., Comment: 5 pages, 7 figures, Asilomar 2019

We propose a penalized pseudo-likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or countable infinite set of nodes. In the finite case, the underlying graph can be recovered with probability one, while in the countable infinite case, we can recover any finite sub-graph with probability one by allowing the candidate neighborhoods to grow as a function o(log n), with n the sample size. Our method requires minimal assumptions on the probability distribution, and contrary to other approaches in the literature, the usual positivity condition is not needed. We evaluate the performance of the estimator on simulated data, and we apply the methodology to a real dataset of stock index markets in different countries.

Continuous phase modulation (CPM) with 1-bit quantization at the receiver is promising in terms of energy and spectral efficiency. In this study, CPM waveforms with symbol durations significantly shorter than the inverse of the signal bandwidth are proposed, termed faster-than-Nyquist CPM. This configuration provides a better steering of zero-crossings as compared to conventional CPM. Numerical results confirm a superior performance in terms of BER in comparison with state-of-the-art methods, while having the same spectral efficiency and a lower oversampling factor. Moreover, the new waveform can be detected with low-complexity, which yields almost the same performance as using the BCJR algorithm., Comment: 5 pages, submitted to IEEE Wireless Communications Letters

On 27 Apr 2015, when 67P/C-G was at 1.76 au from the Sun and moving towards perihelion, the OSIRIS and VIRTIS-M instruments on Rosetta observed the evolving dust and gas coma during a complete rotation of the comet. We aim to characterize the dust, H2O and CO2 gas spatial distribution in the inner coma. To do this we performed a quantitative analysis of the release of dust and gas and compared the observed H2O production rate with the one calculated using a thermo-physical model. For this study we selected OSIRIS WAC images at 612 nm (dust) and VIRTIS-M image cubes at 612 nm, 2700 nm (H2O) and 4200 nm (CO2). We measured the average signal in a circular annulus, to study spatial variation around the comet, and in a sector of the annulus, to study temporal variation in the sunward direction with comet rotation, both at a fixed distance of 3.1 km from the comet centre. The spatial correlation between dust and water, both coming from the sun-lit side of the comet, shows that water is the main driver of dust activity in this time period. The spatial distribution of CO2 is not correlated with water and dust. There is no strong temporal correlation between the dust brightness and water production rate as the comet rotates. The dust brightness shows a peak at 0deg sub-solar longitude, which is not pronounced in the water production. At the same epoch, there is also a maximum in CO2 production. An excess of measured water production, with respect to the value calculated using a simple thermo-physical model, is observed when the head lobe and regions of the Southern hemisphere with strong seasonal variations are illuminated. A drastic decrease in dust production, when the water production (both measured and from the model) displays a maximum, happens when typical Northern consolidated regions are illuminated and the Southern hemisphere regions with strong seasonal variations are instead in shadow., Comment: 15 pages, accepted for publication in A&A

The southern hemisphere of comet 67P/Churyumov-Gerasimenko (67P) became observable by the Rosetta mission in March 2015, a few months before cometary southern vernal equinox. The Anhur region in the southern part of the comet's larger lobe was found to be highly eroded, enriched in volatiles, and highly active. We analyze high-resolution images of the Anhur region pre- and post-perihelion acquired by the OSIRIS imaging system on board the Rosetta mission. The Narrow Angle Camera is particularly useful for studying the evolution in Anhur in terms of morphological changes and color variations.}{Radiance factor images processed by the OSIRIS pipeline were coregistered, reprojected onto the 3D shape model of the comet, and corrected for the illumination conditions. We find a number of morphological changes in the Anhur region that are related to formation of new scarps; removal of dust coatings; localized resurfacing in some areas, including boulders displacements; and vanishing structures, which implies localized mass loss that we estimate to be higher than 50 million kg. The strongest changes took place in and nearby the Anhur canyon-like structure, where significant dust cover was removed, an entire structure vanished, and many boulders were rearranged. All such changes are potentially associated with one of the most intense outbursts registered by Rosetta during its observations, which occurred one day before perihelion passage. Moreover, in the niche at the foot of a new observed scarp, we also see evidence of water ice exposure that persisted for at least six months. The abundance of water ice, evaluated from a linear mixing model, is relatively high (> 20%). Our results confirm that the Anhur region is volatile-rich and probably is the area on 67P with the most pristine exposures near perihelion., Comment: 19 pages, 16 figures; accepted for publication in Astronomy and Astrophysics for the Rosetta 2 special number

In April 2016, the Rosetta spacecraft performed a low-altitude low-phase-angle flyby over the Imhotep-Khepry transition of 67P/Churyumov-Gerasimenko's nucleus. The OSIRIS/Narrow-Angle-Camera (NAC) acquired 112 images with mainly 3 broadband filters in the visible at a resolution of up to 0.53 m/px and for phase angles between 0.095{\deg} and 62{\deg}. Using those images, we have investigated the morphological and spectrophotometrical properties of this area. We assembled the images into coregistered color cubes. Using a 3D shape model, we produced the illumination conditions and georeference for each image. We projected the observations on a map to investigate its geomorphology. Observations were photometrically corrected using the Lommel-Seeliger disk law. Spectrophotometric analyses were performed on the coregistered color cubes. These data were used to estimate the local phase reddening. This region of the nucleus hosts numerous and varied types of terrains and features. We observe an association between a feature's nature, its reflectance, and its spectral slope. Fine material deposits exhibit an average reflectance and spectral slope, while terrains with diamictons, consolidated material, degraded outcrops, or features such as somber boulders, present a lower-than-average reflectance and higher-than-average spectral slope. Bright surfaces present here a spectral behavior consistent with terrains enriched in water-ice. We find a phase-reddening slope of 0.064{\pm}0.001{\%}/100nm/{\deg} at 2.7 au outbound, similarly to the one obtained at 2.3 au inbound during the February 2015 flyby. Identified as the source region of multiple jets and a host of water-ice material, the Imhotep-Khepry transition appeared in April 2016, close to the frost line, to further harbor several potential locations with exposed water-ice material among its numerous different morphological terrain units., Comment: 23 pages, 14 figures, 5 tables

We propose a cosmological scenario involving a scalar field, $\varphi$, that is a source of Dark Matter as well as of Dark Energy. Besides $\varphi$, the Lagrangian of the field theory envisaged in our scenario contains a second field $\chi$, for simplicity assumed to be a scalar, too. For fixed values of $\chi$, the potential term decays exponentially at large positive values of $\varphi$. While $\varphi$ is not coupled to Standard Model fields, $\chi$ is assumed to be coupled to them, and the Green functions of $\chi$ depend on the cosmological redshift in the expanding universe. We assume that the term in the Lagrangian coupling $\chi$ to $\varphi$ is such that, at redshifts $z$ larger than some critical redshift $z_c$, $\varphi$ is trapped near $\varphi=0$, and oscillations of $\varphi$ about $\varphi=0$ describing massive scalar particles give rise to Dark Matter. At redshifts below $z_c$, the field $\varphi$ is no longer trapped near the origin and starts to `roll' towards large field values. A homogenous component of $\varphi$ emerges that acts as Dark Energy. Within over-dense regions, such as galaxies and galaxy clusters, the redshifting of $\chi$ stops, and $\varphi$ therefore remains trapped near $\varphi=0$ as long as $z_c$ is smaller than the redshift when structures on galactic scales decouple from the Hubble flow. Thus, at the present time, $\varphi$ describes both Dark Energy and Dark Matter., Comment: 6 pages

The Rosetta space probe accompanied comet 67P/Churyumov-Gerasimenko for more than two years, obtaining an unprecedented amount of unique data of the comet nucleus and inner coma. This work focuses identifying the source regions of faint jets and outbursts and on studying the spectrophotometric properties of some outbursts. We use observations acquired with the OSIRIS/NAC camera during July-October 2015, that is, close to perihelion. More than 200 jets of different intensities were identified directly on the nucleus. Some of the more intense outbursts appear spectrally bluer than the comet dark terrain in the vivible-to-near-infrared region. We attribute this spectral behavior to icy grains mixed with the ejected dust. Some of the jets have an extremely short lifetime. They appear on the cometary surface during the color sequence observations, and vanish in less than some few minutes after reaching their peak. We also report a resolved dust plume observed in May 2016 at a resolution of 55 cm/pixel, which allowed us to estimate an optical depth of $\sim$0.65 and an ejected mass of $\sim$ 2200 kg. We present the results on the location, duration, and colors of active sources on the nucleus of 67P from the medium-resolution (i.e., 6-10 m/pixel) images acquired close to perihelion passage. The observed jets are mainly located close to boundaries between different morphological regions. Jets depart not only from cliffs, but also from smooth and dust-covered areas, from fractures, pits, or cavities that cast shadows and favor the recondensation of volatiles. This study shows that faint jets or outbursts continuously contribute to the cometary activity close to perihelion passage, and that these events are triggered by illumination conditions. Faint jets or outbursts are not associated with a particular terrain type or morphology., Comment: Accepted for publication on Astronomy and Astrophysics on 27 August 2018. 27 pages, 18 figures, 2 tables

We study cosmological perturbations in a model of unified dark matter and dark energy with a sharp transition in the late-time universe. The dark sector is described by a dark fluid which evolves from an early stage at redshifts $z > z_C$ when it behaves as cold dark matter (CDM) to a late time dark energy (DE) phase ($z < z_C$) when the equation of state parameter is $w = -1 + \epsilon$, with a constant $\epsilon$ which must be in the range $0 < \epsilon < 2/3$. We show that fluctuations in the dark energy phase suffer from an exponential instability, the mode functions growing both as a function of comoving momentum $k$ and of conformal time $\eta$. In order that this exponential instability does not lead to distortions of the energy density power spectrum on scales for which we have good observational results, the redshift $z_C$ of transition between the two phases is constrained to be so close to zero that the model is unable to explain the supernova data., Comment: 17 pages; 2 figures; v2: minor changes to match the published version

We directly measure twenty overhanging cliffs on the surface of comet 67P/Churyumov-Gerasimenko extracted from the latest shape model and estimate the minimum tensile strengths needed to support them against collapse under the comet's gravity. We find extremely low strengths of around one Pa or less (one to five Pa, when scaled to a metre length). The presence of eroded material at the base of most overhangs, as well as the observed collapse of two features and implied previous collapse of another, suggests that they are prone to failure and that true material strengths are close to these lower limits (although we only consider static stresses and not dynamic stress from, for example, cometary activity). Thus, a tensile strength of a few pascals is a good approximation for the tensile strength of 67P's nucleus material, which is in agreement with previous work. We find no particular trends in overhang properties with size, over the $\sim10-100$ m range studied here, or location on the nucleus. There are no obvious differences, in terms of strength, height or evidence of collapse, between the populations of overhangs on the two cometary lobes, suggesting that 67P is relatively homogenous in terms of tensile strength. Low material strengths are supportive of cometary formation as a primordial rubble pile or by collisional fragmentation of a small (tens of km) body., Comment: 13 pages, 11 figures. Accepted for publication in Astronomy & Astrophysics

On 3 July 2016, several instruments on board ESA's Rosetta spacecraft detected signs of an outburst event on comet 67P, at a heliocentric distance of 3.32 AU from the sun, outbound from perihelion. We here report on the inferred properties of the ejected dust and the surface change at the site of the outburst. The activity coincided with the local sunrise and continued over a time interval of 14 - 68 minutes. It left a 10m-sized icy patch on the surface. The ejected material comprised refractory grains of several hundred microns in size, and sub-micron-sized water ice grains. The high dust mass production rate is incompatible with the free sublimation of crystalline water ice under solar illumination as the only acceleration process. Additional energy stored near the surface must have increased the gas density. We suggest a pressurized sub-surface gas reservoir, or the crystallization of amorphous water ice as possible causes., Comment: 20 pages, 19 figures, 5 tables

Due to the emergent adoption of distributed systems when building applications, demand for reliability and availability has increased. These properties can be achieved through replication techniques using middleware algorithms that must be capable of tolerating faults. Certain faults such as arbitrary faults, however, may be more difficult to tolerate, resulting in more complex and resource intensive algorithms that end up being not so practical to use. We propose and experiment with the use of consistency validation techniques to harden a benign fault-tolerant Paxos, thus being able to detect and tolerate non-malicious arbitrary faults., Comment: 6 pages, fixed metadata

We collect observational evidence that supports the scheme of mass transfer on the nucleus of comet 67P/Churyumov-Gerasimenko. The obliquity of the rotation axis of 67P causes strong seasonal variations. During perihelion the southern hemisphere is four times more active than the north. Northern territories are widely covered by granular material that indicates back fall originating from the active south. Decimetre sized chunks contain water ice and their trajectories are influenced by an anti-solar force instigated by sublimation. OSIRIS observations suggest that up to 20 % of the particles directly return to the nucleus surface taking several hours of travel time. The back fall covered northern areas are active if illuminated but produce mainly water vapour. The decimetre chunks from the nucleus surface are too small to contain more volatile compounds such as CO 2 or CO. This causes a north-south dichotomy of the composition measurements in the coma. Active particles are trapped in the gravitational minimum of Hapi during northern winter. They are "shock frozen" and only reactivated when the comet approaches the sun after its aphelion passage. The insolation of the big cavity is enhanced by self-heating, i. e. reflection and IR radiation from the walls. This, together with the pristinity of the active back fall, explains the early observed activity of the Hapi region. Sobek may be a role model for the consolidated bottom of Hapi. Mass transfer in the case of 67P strongly influences the evolution of the nucleus and the interpretation of coma measurements., Comment: 17 pages, 20 figures

The Southern hemisphere of the 67P/Churyumov-Gerasimenko comet has become visible from Rosetta only since March 2015. It was illuminated during the perihelion passage and therefore it contains the regions that experienced the strongest heating and erosion rate, thus exposing the subsurface most pristine material. In this work we investigate, thanks to the OSIRIS images, the geomorphology, the spectrophotometry and some transient events of two Southern hemisphere regions: Anhur and part of Bes. Bes is dominated by outcropping consolidated terrain covered with fine particle deposits, while Anhur appears strongly eroded with elongated canyon-like structures, scarp retreats, different kinds of deposits, and degraded sequences of strata indicating a pervasive layering. We discovered a new 140 m long and 10 m high scarp formed in the Anhur/Bes boundary during/after the perihelion passage, close to the area where exposed CO$_2$ and H$_2$O ices were previously detected. Several jets have been observed originating from these regions, including the strong perihelion outburst, an active pit, and a faint optically thick dust plume. We identify several areas with a relatively bluer slope (i.e. a lower spectral slope value) than their surroundings, indicating a surface composition enriched with some water ice. These spectrally bluer areas are observed especially in talus and gravitational accumulation deposits where freshly exposed material had fallen from nearby scarps and cliffs. The investigated regions become spectrally redder beyond 2 au outbound when the dust mantle became thicker, masking the underlying ice-rich layers., Comment: 16 pages, 15 figures, published online on 24 May 2017 on Mon. Not. R. Astron. Soc. stx1275, https://doi.org/10.1093/mnras/stx1275

We present a statistical analysis of the distribution of large scale topographic features on comet 67P/Churyumov-Gerasimenko. We observe that the cumulative cliff height distribution across the surface follows a power law with a slope equal to -1.69 +- 0.02. When this distribution is studied independently for each region, we find a good correlation between the slope of the power law and the orbital erosion rate of the surface. For instance, the northern hemisphere topography is dominated by structures on the 100~m scale while the southern hemisphere topography, illuminated at perihelion, is dominated by 10~m scale terrain features. Our study suggest that the current size of a cliff is controlled not only by material cohesion but by the dominant erosional process in each region. This observation can be generalized to other comets, where we argue that primitive nuclei are characterized by the presence of large cliffs with a cumulative height power index equal to or above -1.5, while older, eroded cometary surfaces have a power index equal to or below -2.3. In effect, our model shows that a measure of the topography provides a quantitative assessment of a comet's erosional history, i.e. its evolutionary age.

Images of the nucleus and the coma (gas and dust) of comet 67P/Churyumov- Gerasimenko have been acquired by the OSIRIS (Optical, Spectroscopic, and Infrared Remote Imaging System) cameras since March 2014 using both the Wide Angle Camera (WAC) and the Narrow Angle Camera (NAC). We use images from the NAC camera to study a bright outburst observed in the southern hemisphere on July 29, 2015. The high spatial resolution of the NAC is needed to localize the source point of the outburst on the surface of the nucleus. The heliocentric distance is 1.25 au and the spacecraft-comet distance is 186 km. Aiming to better understand the physics that led to the outgassing, we used the Direct Simulation Monte Carlo (DSMC) method to study the gas flow close to the nucleus and the dust trajectories. The goal is to understand the mechanisms producing the outburst. We reproduce the opening angle of the outburst in the model and constrain the outgassing ratio between the outburst source and the local region. The outburst is in fact a combination of both gas and dust, in which the active surface is approximately 10 times more active than the average rate found in the surrounding areas. We need a number of dust particles 7.83 $\times$ 10$^{11}$ - 6.90 $\times$ 10$^{15}$ (radius 1.97 - 185 {\mu}m), which corresponds to a mass of dust 220 - 21 $\times$ 10$^{3}$kg., Comment: 8 pages, 9 figures

The ESA Rosetta spacecraft has been tracking its target, the Jupiter-family comet 67P/Churyumov-Gerasimenko, in close vicinity for over two years. It hosts the OSIRIS instruments: the Optical, Spectroscopic, and Infrared Remote Imaging System composed of two cameras, see e.g. Keller et al. (2007). In some imaging sequences dedicated to observe dust particles in the comet's coma, the two cameras took images at the same time. The aim of this work is to use these simultaneous double camera observations to calculate the dust particles' distance to the spacecraft. As the two cameras are mounted on the spacecraft with an offset of 70 cm, the distance of particles observed by both cameras can be determined by a shift of the particles' apparent trails on the images. This paper presents first results of the ongoing work, introducing the distance determination method for the OSIRIS instrument and the analysis of an example particle. We note that this method works for particles in the range of about 500 m - 6000 m from the spacecraft.

We develop an action principle to construct the dynamics that give rise to a minimal generalization of Einstein's equations, where the speed of light ($c$), the gravitational constant ($G$) and the cosmological constant ($\Lambda$) are allowed to vary. Our construction preserves general covariance of the theory, which yields a general dynamical constraint on $c$, $G$ and $\Lambda$. This action is general and can be applied to describe different cosmological solutions. We apply this formulation to the initial condition puzzles of the early universe and show that it generates a dynamical mechanism to obtain the homogeneous and flat universe we observe today. We rewrite the conditions necessary to solve the horizon and flatness problems in this framework, which does not necessarily lead to an accelerated expansion as in inflation. Then, we show how the dynamics of the scalar field that represents $c$ or $G$ (and $\Lambda$) can be used to solve the problems of the early universe cosmology by means of different ways to c-inflate the horizon in the early universe. By taking $\Lambda = 0$, we show that the dynamics of the scalar field representing $c$ can be described once a potential is given., Comment: 19 pages

The main purpose of this paper is to study \emph{$e$-separable spaces}, originally introduced by Kurepa as $K_0'$ spaces; we call a space $X$ $e$-separable iff $X$ has a dense set which is the union of countably many closed discrete sets. We primarily focus on the behaviour of $e$-separable spaces under products and the cardinal invariants that are naturally related to $e$-separable spaces. Our main results show that the statement "there is a product of at most $\mathfrak c$ many $e$-separable spaces that fails to be $e$-separable'" is equiconsistent with the existence of a weakly compact cardinal., Comment: 19 pages, improved results, submitted to Topology Proceedings

During its two years mission around comet 67P/Churyumov-Gerasimenko, ESA's Rosetta spacecraft had the unique opportunity to follow closely a comet in the most active part of its orbit. Many studies have presented the typical features associated to the activity of the nucleus, such as localized dust and gas jets. Here we report on series of more energetic transient events observed during the three months surrounding the comet's perihelion passage in August 2015. We detected and characterized 34 outbursts with the Rosetta cameras, one every 2.4 nucleus rotation. We identified 3 main dust plume morphologies associated to these events: a narrow jet, a broad fan, and more complex plumes featuring both previous types together. These plumes are comparable in scale and temporal variation to what has been observed on other comets. We present a map of the outbursts source locations, and discuss the associated topography. We find that the spatial distribution sources on the nucleus correlates well with morphological region boundaries, especially in areas marked by steep scarps or cliffs. Outbursts occur either in the early morning or shortly after the local noon, indicating two potential processes: Morning outbursts may be triggered by thermal stresses linked to the rapid change of temperature, afternoon events are most likely related to the diurnal or seasonal heat wave reaching volatiles buried under the first surface layer. In addition, we propose that some events can be the result of a completely different mechanism, in which most of the dust is released upon the collapse of a cliff., Comment: MNRAS (2016)

Since the orbital insertion of the Rosetta spacecraft, comet 67P/Churyumov-Gerasimenko (67P/C-G) has been mapped by OSIRIS camera and VIRTIS spectro-imager, producing a huge quantity of images and spectra of the comet's nucleus. The aim of this work is to search for the presence of H$_2$O on the nucleus which, in general, appears very dark and rich in dehydrated organic material. After selecting images of the bright spots which could be good candidates to search for H$_2$O ice, taken at high resolution by OSIRIS, we check for spectral cubes of the selected coordinates to identify these spots observed by VIRTIS. The selected OSIRIS images were processed with the OSIRIS standard pipeline and corrected for the illumination conditions for each pixel using the Lommel-Seeliger disk law. The spots with higher I/F were selected and then analysed spectrophotometrically and compared with the surrounding area. We selected 13 spots as good targets to be analysed by VIRTIS to search for the 2 micron absorption band of water ice in the VIRTIS spectral cubes. Out of the 13 selected bright spots, eight of them present positive H$_2$O ice detection on the VIRTIS data. A spectral analysis was performed and the approximate temperature of each spot was computed. The H$_2$O ice content was confirmed by modeling the spectra with mixing (areal and intimate) of H$_2$O ice and dark terrain, using Hapke's radiative transfer modeling. We also present a detailed analysis of the detected spots., Comment: paper in press in A&A, 13 pages, 6 figures

Beginning in March 2014, the OSIRIS (Optical, Spectroscopic, and Infrared Remote Imaging System) cameras began capturing images of the nucleus and coma (gas and dust) of comet 67P/Churyumov-Gerasimenko using both the wide angle camera (WAC) and the narrow angle camera (NAC). The many observations taken since July of 2014 have been used to study the morphology, location, and temporal variation of the comet's dust jets. We analyzed the dust monitoring observations shortly after the southern vernal equinox on May 30 and 31, 2015 with the WAC at the heliocentric distance Rh = 1.53 AU, where it is possible to observe that the jet rotates with the nucleus. We found that the decline of brightness as a function of the distance of the jet is much steeper than the background coma, which is a first indication of sublimation. We adapted a model of sublimation of icy aggregates and studied the effect as a function of the physical properties of the aggregates (composition and size). The major finding of this article was that through the sublimation of the aggregates of dirty grains (radius a between 5 microm and 50 microm) we were able to completely reproduce the radial brightness profile of a jet beyond 4 km from the nucleus. To reproduce the data we needed to inject a number of aggregates between 8.5 x $10^{13}$ and 8.5 x $10^{10}$ for a = 5 microm and 50 microm respectively, or an initial mass of $H_2O$ ice around 22kg., Comment: 11 pages, 7 figures, 3 tables, special issue "The ESLAB 50 Symposium - spacecraft at comets from 1P/Halley to 67P/Churyumov-Gerasimenko" in the Monthly Notices of the Royal Astronomical Society

We present OSIRIS/NAC observations of decimetre-sized, likely ice-containing aggregates ejected from a confined region on the surface of comet 67P/Churyumov-Gerasimenko. The images were obtained in January 2016 when the comet was at 2 AU from the Sun out-bound from perihelion. We measure the acceleration of individual aggregates through a two-hour image series. Approximately 50% of the aggregates are accelerated away from the nucleus, and 50% towards it, and likewise towards either horizontal direction. The accelerations are up to one order of magnitude stronger than local gravity, and are most simply explained by the combined effect of gas drag accelerating all aggregates upwards, and the recoil force from asymmetric outgassing, either from rotating aggregates with randomly oriented spin axes and sufficient thermal inertia to shift the temperature maximum away from an aggregate's subsolar region, or from aggregates with variable ice content. At least 10% of the aggregates will escape the gravity field of the nucleus and feed the comet's debris trail, while others may fall back to the surface and contribute to the deposits covering parts of the northern hemisphere. The rocket force plays a crucial role in pushing these aggregates back towards the surface. Our observations show the future back fall material in the process of ejection, and provide the first direct measurement of the acceleration of aggregates in the innermost coma (<2km) of a comet, where gas drag is still significant., Comment: 11 pages, 14 figures, accepted for publication in MNRAS

The Wide Angle Camera of the OSIRIS instrument on board the Rosetta spacecraft is equipped with several narrowband filters that are centered on the emission lines and bands of various fragment species. These are used to determine the evolution of the production and spatial distribution of the gas in the inner coma of comet 67P with time and heliocentric distance, here between 2.6 - 1.3 AU pre-perihelion. Our observations indicate that the emission observed in the OH, OI, CN, NH, and NH2 filters is mostly produced by dissociative electron impact excitation of different parent species. We conclude that CO2 rather than H2O is a significant source of the [OI] 630 nm emission. A strong plume-like feature observed in the in CN and [OI] filters is present throughout our observations. This plume is not present in OH emission and indicates a local enhancement of the CO2/H2O ratio by as much as a factor of 3. We observed a sudden decrease in intensity levels after March 2015, which we attribute to decreased electron temperatures in the first kilometers above the nucleus surface., Comment: 6 figures, 6 tables

For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then the second player picks a point $a_n\in A_n$; the second player is the winner if and only if $x\in\overline{\{a_n:n\in\omega\}}$. In this work, we study variations of this game in which the second player is allowed to choose finitely many points per inning rather than one, but in which the number of points they are allowed to choose in each inning has been fixed in advance. Surprisingly, if the number of points allowed per inning is the same throughout the play, then all of the games obtained in this fashion are distinct. We also show that a new game is obtained if the number of points the second player is allowed to pick increases at each inning.

The ESA Rosetta spacecraft, currently orbiting around comet 67P, has already provided in situ measurements of the dust grain properties from several instruments, particularly OSIRIS and GIADA. We propose adding value to those measurements by combining them with ground-based observations of the dust tail to monitor the overall, time-dependent dust-production rate and size distribution. To constrain the dust grain properties, we take Rosetta OSIRIS and GIADA results into account, and combine OSIRIS data during the approach phase (from late April to early June 2014) with a large data set of ground-based images that were acquired with the ESO Very Large Telescope (VLT) from February to November 2014. A Monte Carlo dust tail code has been applied to retrieve the dust parameters. Key properties of the grains (density, velocity, and size distribution) were obtained from Rosetta observations: these parameters were used as input of the code to considerably reduce the number of free parameters. In this way, the overall dust mass-loss rate and its dependence on the heliocentric distance could be obtained accurately. The dust parameters derived from the inner coma measurements by OSIRIS and GIADA and from distant imaging using VLT data are consistent, except for the power index of the size-distribution function, which is $\alpha$=--3, instead of $\alpha$=--2, for grains smaller than 1 mm. This is possibly linked to the presence of fluffy aggregates in the coma. The onset of cometary activity occurs at approximately 4.3 au, with a dust production rate of 0.5 kg/s, increasing up to 15 kg/s at 2.9 au. This implies a dust-to-gas mass ratio varying between 3.8 and 6.5 for the best-fit model when combined with water-production rates from the MIRO experiment., Comment: Accepted by Astronomy and Astrophysics (January 17th, 2016)

We analyze the physical properties and dynamical origin of a curved jet of comet 67P/Churyumov-Gerasimenko that was observed repeatedly in several nucleus rotations starting on May 30 and persisting until early August, 2015. We simulated the motion of dust grains ejected from the nucleus surface under the influence of the gravity and viscous drag effect of the expanding gas flow from the rotating nucleus. The formation of the curved jet is a combination of the size of the dust particles (~0.1-1 mm) and the location of the source region near the nucleus equator. This enhances the spiral feature of the collimated dust stream after the dust is accelerated to a terminal speed on the order of m/s., Comment: 5pages, 5 figures

Dust jets, i.e. fuzzy collimated streams of cometary material arising from the nucleus, have been observed in-situ on all comets since the Giotto mission flew by comet 1P/Halley in 1986. Yet their formation mechanism remains unknown. Several solutions have been proposed, from localized physical mechanisms on the surface/sub-surface (see review in Belton (2010)) to purely dynamical processes involving the focusing of gas flows by the local topography (Crifo et al. 2002). While the latter seems to be responsible for the larger features, high resolution imagery has shown that broad streams are composed of many smaller features (a few meters wide) that connect directly to the nucleus surface. We monitored these jets at high resolution and over several months to understand what are the physical processes driving their formation, and how this affects the surface. Using many images of the same areas with different viewing angles, we performed a 3-dimensional reconstruction of collimated jets, and linked them precisely to their sources on the nucleus. Results.We show here observational evidence that the Northern hemisphere jets of comet 67P arise from areas with sharp topographic changes and describe the physical processes involved. We propose a model in which active cliffs are the main source of jet-like features, and therefore the regions eroding the fastest on comets. We suggest that this is a common mechanism taking place on all comets., Comment: Accepted by Astronomy & Astrophysics on 4 December 2015

We report on the first major temporal morphological changes observed on the surface of the nucleus of comet 67P/Churyumov-Gerasimenko, in the smooth terrains of the Imhotep region. We use images of the OSIRIS cameras onboard Rosetta to follow the temporal changes from 24 May 2015 to 11 July 2015. The morphological changes observed on the surface are visible in the form of roundish features, which are growing in size from a given location in a preferential direction, at a rate of 5.6 - 8.1$\times$10$^{-5}$ m s$^{-1}$ during the observational period. The location where changes started and the contours of the expanding features are bluer than the surroundings, suggesting the presence of ices (H$_2$O and/or CO$_2$) exposed on the surface. However, sublimation of ices alone is not sufficient to explain the observed expanding features. No significant variations in the dust activity pattern are observed during the period of changes., Comment: 4 pages, 3 figures; Letter for Astronomy and Astrophysics: accepted

We study the link between gravitational slopes and the surface morphology on the nucleus of comet 67P/Churyumov-Gerasimenko and provide constraints on the mechanical properties of the cometary material. We computed the gravitational slopes for five regions on the nucleus that are representative of the different morphologies observed on the surface, using two shape models computed from OSIRIS images by the stereo-photoclinometry (SPC) and stereo-photogrammetry (SPG) techniques. We estimated the tensile, shear, and compressive strengths using different surface morphologies and mechanical considerations. The different regions show a similar general pattern in terms of the relation between gravitational slopes and terrain morphology: i) low-slope terrains (0-20 deg) are covered by a fine material and contain a few large ($>$10 m) and isolated boulders, ii) intermediate-slope terrains (20-45 deg) are mainly fallen consolidated materials and debris fields, with numerous intermediate-size boulders from $<$1 m to 10 m for the majority of them, and iii) high-slope terrains (45-90 deg) are cliffs that expose a consolidated material and do not show boulders or fine materials. The best range for the tensile strength of overhangs is 3-15 Pa (upper limit of 150 Pa), 4-30 Pa for the shear strength of fine surface materials and boulders, and 30-150 Pa for the compressive strength of overhangs (upper limit of 1500 Pa). The strength-to-gravity ratio is similar for 67P and weak rocks on Earth. As a result of the low compressive strength, the interior of the nucleus may have been compressed sufficiently to initiate diagenesis, which could have contributed to the formation of layers. Our value for the tensile strength is comparable to that of dust aggregates formed by gravitational instability and tends to favor a formation of comets by the accrection of pebbles at low velocities., Comment: 18 pages, 15 figures, 1 table; Astronomy and Astrophysics, in press

Given a connected region in two-dimensional space where events of a certain kind occur according to a certain time-varying density, we consider the problem of setting up a network of autonomous mobile agents to detect the occurrence of those events and possibly record them in as effective a manner as possible. We assume that agents can communicate with one another wirelessly within a fixed communication radius, and moreover that initially no agent has any information regarding the event density. We introduce a new distributed algorithm for agent control based on the notion of an execution mode, which essentially lets each agent roam the target region either at random or following its local view of a density-dependent gradient. Agents can switch back and forth between the two modes, and the precise manner of such changes depends on the setting of various parameters that can be adjusted as a function of the application at hand. We provide simulation results on some synthetic applications especially designed to highlight the algorithm's behavior relative to the possible execution modes.

The Rosetta mission of the European Space Agency has been orbiting the comet 67P/Churyumov-Gerasimenko (67P) since August 2014 and is now in its escort phase. A large complement of scientific experiments designed to complete the most detailed study of a comet ever attempted are onboard Rosetta. We present results for the photometric and spectrophotometric properties of the nucleus of 67P derived from the OSIRIS imaging system, which consists of a Wide Angle Camera (WAC) and a Narrow Angle Camera (NAC). The disk-averaged phase function of the nucleus of 67P shows a strong opposition surge with a G parameter value of -0.13$\pm$0.01 in the HG system formalism and an absolute magnitude $H_v(1,1,0)$ = 15.74$\pm$0.02 mag. The integrated spectrophotometry in 20 filters covering the 250-1000 nm wavelength range shows a red spectral behavior, without clear absorption bands except for a potential absorption centered at $\sim$ 290 nm that is possibly due to SO$_2$ ice. The nucleus shows strong phase reddening, with disk-averaged spectral slopes increasing from 11\%/(100 nm) to 16\%/(100 nm) in the 1.3$^{\circ}$--54$^{\circ}$ phase angle range. The geometric albedo of the comet is 6.5$\pm$0.2\% at 649 nm, with local variations of up to $\sim$ 16\% in the Hapi region. From the disk-resolved images we computed the spectral slope together with local spectrophotometry and identified three distinct groups of regions (blue, moderately red, and red). The Hapi region is the brightest, the bluest in term of spectral slope, and the most active surface on the comet. Local spectrophotometry shows an enhancement of the flux in the 700-750 nm that is associated with coma emissions., Comment: 18, pages, 14 figures, Astronomy and Astrophysics, in press

We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them., Comment: 28 pages

In this paper we study connections between topological games such as Rothberger, Menger and compact-open, and relate these games to properties involving covers by G_{\delta} subsets. The results include: (1) If Two has a winning strategy in the Menger game on a regular space X, then X is an Alster space. (2) If Two has a winning strategy in the Rothberger game on a topological space X, then the G_\delta-topology on X is Lindelof. (3) The Menger game and the compact-open game are (consistently) not dual., Comment: 13 pages; submitted

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to $\omega_1$-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba's "$\aleph_1$-Borel Conjecture" is equiconsistent with the existence of an inaccessible cardinal., Comment: 18 pages