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Complex architectures for wireless communications, digital electronics and space-based navigation interlink several oscillator-based devices such as clocks, transponders and synthesizers. Estimators characterizing their stability are critical for addressing the impact of random fluctuations (noise) on the overall system performance. Manufacturers typically specify this as an Allan/Hadamard Variance (AVAR/HVAR) profile in the _integration_ time domain, yet, stochastic processes governing the noise take place in the _Fourier_ frequency domain in the shape of a Power Spectral Density (PSD) function. Both are second-moment measures of the time series, however, it is only possible to translate unambiguously from the PSD to the AVAR/HVAR, not vice versa, except in the case of a single noise type, which is severely limiting in real-life applications. This note elaborates an analytical method to generate an approximated PSD expressed as a set of power-laws defined in specific intervals in the frequency domain, starting from an AVAR/HVAR expressed a set of power-laws in the time domain. The proposed algorithm is straightforward to implement, applicable to all noise types (and combinations thereof) and can be self-validated by reconstructing the corresponding AVAR/HVAR by direct calculus. We also report on its limitations of and analytical expressions of the continuous version of this algorithm. Coupling with well-established algorithms relying on the PSD for power-law noise generation, the ensuing method encompasses the capability for generating multi-colored noise in end-to-end simulations, as demonstrated hereby for NASA's Deep Space Atomic Clock., Comment: 18 pages, 9 figures

2D materials with high charge carrier mobility and tunable electronic band gaps have attracted intense research effort for their potential use as active components in nanoelectronics. 2D-conjugated polymers (2DCP) constitute a promising sub-class due to the fact that the electronic band structure can be manipulated by varying the molecular building blocks, while at the same time preserving the key features of 2D materials such as Dirac cones and high charge mobility. The major challenge for their use in technological applications is to fabricate mesoscale ordered 2DCP networks since current synthetic routes yield only small domains with a high density of defects. Here we demonstrate the synthesis of a mesoscale ordered 2DCP with semiconducting properties and Dirac cone structures via Ullmann coupling on Au(111). This material has been obtained by combining rigid azatriangulene precursors and a hot dosing approach which favours molecular diffusion and reduces the formation of voids in the network. These results open opportunities for the synthesis of 2DCP Dirac cone materials and their integration into devices., Comment: 21 pages, 3 figures

The NASA Discovery-class mission VERITAS, selected in June 2021, will be launched towards Venus after 2027. In addition to the science instrumentation that will build global foundational geophysical datasets, VERITAS proposed to conduct a technology demonstration for the Deep Space Atomic Clock (DSAC-2). A first DSAC successfully operated in low-Earth orbit for more than two years, demonstrated the trapped ion atomic clock technology, and established a new level of performance for clocks in space. DSAC-2 would have further improvements in size, power, and performance. It would host a $1\times{10}^{-13}$ grade USO to produce a frequency output with short-term stability of less than $2\times{10}^{-13}/\sqrt\tau$ (where $\tau$ is the averaging time). However, due to funding shortfalls, DSAC-2, had to be canceled. The initially foreseen presence of an atomic clock on board the probe, however, raised the question whether this kind of instrumentation could be useful not only for navigation and time transfer but also for fundamental physics tests. In this work, we consider the DSAC-2 atomic clock and VERITAS mission as a specific example to measure possible discrepancies in the redshift predicted by General Relativity by using an atomic clock onboard an interplanetary spacecraft. In particular we investigate the possibility of measuring possible violations of the Local Lorentz Invariance and Local Position Invariance principles. We perform accurate simulations of the experiment during the VERITAS cruise phase. We consider different parametrizations of the possible violations of the General Relativity, different operational conditions, and several different assumptions on the expected measurement performance. Our analysis shows the scientific value of atomic clocks like DSAC-2 hosted onboard interplanetary spacecraft., Comment: 15 pages, 9 figures

The increasing precision of spacecraft radiometric tracking data experienced in the last number of years, coupled with the huge amount of data collected and the long baselines of the available datasets, has made the direct observation of Solar System dynamics possible, and in particular relativistic effects, through the measurement of some key parameters as the post-Newtonian parameters, the Nordtvedt parameter "eta" and the graviton mass. In this work we investigate the potentialities of the datasets provided by the most promising past, present and future interplanetary missions to draw a realistic picture of the knowledge that can be reached in the next 10-15 years. To this aim, we update the semi-analytical model originally developed for the BepiColombo mission, to take into account planet-planet relativistic interactions and eccentricity-induced effects and validate it against well-established numerical models to assess the precision of the retrieval of the parameters of interest. Before the analysis of the results we give a review of some of the hypotheses and constrained analysis schemes that have been proposed until now to overcome geometrical weaknessess and model degeneracies, proving that these strategies introduce model inconsistencies. Finally we apply our semi-analytical model to perform a covariance analysis on three samples of interplanetary missions: 1) those for which data are available now (e.g. Cassini, MESSENGER, MRO, Juno), 2) in the next years (BepiColombo) and 3) still to be launched as JUICE and VERITAS (this latter is waiting for the approval)., Comment: 18 pages, 5 figures

The validity of General Relativity, after 100 years, is supported by solid experimental evidence. However, there is a lot of interest in pushing the limits of precision by other experiments. Here we focus our attention on the equivalence principle, in particular the strong form. The results of ground experiments and lunar laser ranging have provided the best upper limit on the Nordtvedt parameter {\eta} that models deviations from the strong equivalence principle. Its uncertainty is currently {\sigma}[{\eta}] =4.4 $\times$ $10^{-4}$. In the first part of this paper we will describe the experiment, to measure {\eta}, that will be done by the future mission BepiColombo. The expected precision on {\eta} is $\approx$ $10^{-5}$. In the second part we will consider the ranging between the Earth and a spacecraft orbiting near the Sun-Earth Lagrangian points to get an independent measurement of {\eta}. In this case, we forecast a constraint similar to that achieved by lunar laser ranging., Comment: 11 pages, 2 figures

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depends on our "knowledge" about solar system: ephemerides, number of bodies (planets, satellites and asteroids) and their masses. In this paper we describe a semi-analytic model used to perform a covariance analysis to quantify the effects, on the relativity experiment, due to the uncertainties of solar system bodies parameters. In particular, our attention is focused on the Nordtvedt parameter $\eta$ used to parametrize the strong equivalence principle violation. After our analysis we estimated $\sigma[\eta]\lessapprox 4.5\times 10^{-5}$ which is about 1~order of magnitude larger than the "ideal" case where masses of planets and asteroids have no errors. The current value, obtained from ground based experiments and lunar laser ranging measurements, is $\sigma[\eta]\approx 4.4\times 10^{-4}$. Therefore, we conclude that, even in presence of uncertainties on solar system parameters, the measurement of $\eta$ by MORE can improve the current precision of about 1~order of magnitude.

General relativity is supported by great experimental evidence. Yet there is a lot of interest in precisely setting its limits with on going and future experiments. A question to answer is about the validity of the Strong Equivalence Principle. Ground experiments and Lunar Laser Ranging have provided the best upper limit on the Nordtvedt parameter $\sigma[\eta]=4.4\times 10^{-4}$. With the future planetary mission BepiColombo, this parameter will be further improved by at least an order of magnitude. In this paper we envisage yet another possible testing environment with spacecraft ranging towards the nearby Sun-Earth collinear Lagrangian points. Neglecting errors in planetary masses and ephemerides, we forecast $\sigma[\eta]=6.4\,(2.0)\times10^{-4}$ (5 yr integration time) via ranging towards $L_1$ in a realistic (optimistic) scenario depending on current (future) range capabilities and knowledge of the Earth's ephemerides. A combined measurement, $L_1$+$L_2$, gives instead $4.8\,(1.7)\times10^{-4}$. In the optimistic scenario a single measurement of one year would be enough to reach $\approx3\times10^{-4}$. All figures are comparable with Lunar Laser Ranging, but worse than BepiColombo. Performances could be much improved if data were integrated over time and over the number of satellites flying around either of the two Lagrangian points. We point out that some systematics (gravitational perturbations of other planets or figure effects) are much more in control compared to other experiments. We do not advocate a specific mission to constrain the Strong Equivalence Principle, but we do suggest analysing ranging data of present and future spacecrafts flying around $L_1$/$L_2$ (one key mission is, for instance, LISA Pathfinder). This spacecraft ranging would be a new and complementary probe to constrain the Strong Equivalence Principle in space., Comment: 8 pages, 2 figures, 2 tables

We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the modulation of the torsion mode at a higher frequency and the frequency splitting of the swinging motion. Comparison with observed values yields estimates for the misalignment angles and other parameters of the model., Comment: 17 pages, 4 figures

We present a dynamical model for the double torsion pendulum nicknamed PETER, where one torsion pendulum hangs in cascade, but off-axis, from the other. The dynamics of interest in these devices lies around the torsional resonance, that is at very low frequencies (mHz). However, we find that, in order to properly describe the forced motion of the pendulums, also other modes must be considered, namely swinging and bouncing oscillations of the two suspended masses, that resonate at higher frequencies (Hz). Although the system has obviously 6+6 Degrees of Freedom, we find that 8 are sufficient for an accurate description of the observed motion. This model produces reliable estimates of the response to generic external disturbances and actuating forces or torques. In particular, we compute the effect of seismic floor motion (tilt noise) on the low frequency part of the signal spectra and show that it properly accounts for most of the measured low frequency noise., Comment: 15 pages, 6 figures

The analysis of the noise sources perturbing a test mass (TM) geodesic motion is the main scientific objective of the LISA Technology Package experiment (LTP) on board of the LISA Pathfinder space mission. Information on force noise acting on TMs are obtained with a data reduction procedure involving system parameters. Such parameters can be estimated from dedicated experimental runs. Therefore the final estimation of force noise is affected by two sources of uncertainty. One is statistical and connected to the random nature of noisy signals. The other is connected to the uncertainties on the system parameters. The analysis of simulated LTP data is indicating that the major contribution to the force noise power spectral density uncertainties is coming from the statistical properties of the spectrum estimator., Comment: To be published in Journal of Physics: Conference Series, Proceedings of the 8th International LISA Symposium

We present a general survey of heliocentric LISA orbits, hoping it might help in the exercise of rescoping the mission. We try to semi-analytically optimize the orbital parameters in order to minimize the disturbances coming from the Earth-LISA interaction. In a set of numerical simulations we include nonautonomous perturbations and provide an estimate of Doppler shift and breathing as a function of the trailing angle., Comment: 18 pages, 16 figures. Submitted on CQG

The analysis of non-radiative sources of static or time-dependent gravitational fields in the Solar System is crucial to accurately estimate the free-fall orbits of the LISA space mission. In particular, we take into account the gravitational effects of Interplanetary Dust (ID) on the spacecraft trajectories. The perturbing gravitational field has been calculated for some ID density distributions that fit the observed zodiacal light. Then we integrated the Gauss planetary equations to get the deviations from the LISA keplerian orbits around the Sun. This analysis can be eventually extended to Local Dark Matter (LDM), as gravitational fields are expected to be similar for ID and LDM distributions. Under some strong assumptions on the displacement noise at very low frequency, the Doppler data collected during the whole LISA mission could provide upper limits on ID and LDM densities., Comment: 11 pages, 6 figures, to be published on the special issue of "Celestial Mechanics and Dynamical Astronomy" on the CELMEC V conference

This work presents the first high-precision variability survey in the field of the intermediate-age, metal--rich open cluster NGC 6253. Clusters of this type are benchmarks for stellar evolution models. Continuous photometric monitoring of the cluster and its surrounding field was performed over a time span of ten nights using the Wide Field Imager mounted at the ESO-MPI 2.2m telescope. High-quality timeseries, each composed of about 800 datapoints, were obtained for 250,000 stars using ISIS and DAOPHOT packages. Candidate members were selected by using the colour-magnitude diagrams and period-luminosity-colour relations. Membership probabilities based on the proper motions were also used. The membership of all the variables discovered within a radius of 8 arcmin from the centre is discussed by comparing the incidence of the classes in the cluster direction and in the surrounding field. We discovered 595 variables and we also characterized most of them providing their variability classes, periods, and amplitudes. The sample is complete for short periods: we classified 20 pulsating variables, 225 contact systems, 99 eclipsing systems (22 Beta Lyr type, 59 Beta Per type, 18 RS CVn type), and 77 rotational variables. The time-baseline hampered the precise characterization of 173 variables with periods longer than 4-5 days. Moreover, we found a cataclysmic system undergoing an outburst of about 2.5 mag. We propose a list of 35 variable stars (8 contact systems, 2 eclipsing systems, 15 rotational variables, 9 long-period variables and the cataclysmic variable) as probable members of NGC 6253., Comment: Astronomy and Astrophysics, in press. Extended version with tables and light curves