The GALILEO GALILEI small-satellite mission with FEEP thrusters (GG)

The Equivalence Principle, formulated by Einstein generalizing Galileo’s and Newton’s work, is a fundamental principle of modern physics. As such it should be tested as accurately as possible. Its most direct consequence, namely the Universality of Free Fall, can be tested in space, in a low Earth orbit, the crucial advantage being that the driving signal is about three orders of magnitude stronger than on Earth. GALILEO GALILEI (GG) is a small space mission designed for such a high-accuracy test. At the time of print, GG has been selected by ASI (Agenzia Spaziale Italiana) as a candidate for the next small Italian mission. Ground tests of the proposed apparatus now indicate that an accuracy of 1 part in 1017 is within the reach of this small mission

Parabolic oblique derivative problem in generalized Morrey spaces

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space

Setup of a High-Speed Optical System for The Characterization of Cavitation Instabilities in Space Rocket Turbopumps

The present paper illustrates the set-up and the preliminary results of an experimental investigation of cavitation flow instabilities carried out by means of a high-speed camera on a three bladed inducer in the CPRTF (Cavitating Pump Rotordynamic Test Facility) at Alta S.p.A. The brightness thresholding technique adopted for cavitation recognition is described and implemented in a semi-automatic algorithm. In order to test the capabilities of the algorithm, the mean frontal cavitating area has been computed under different operating conditions. The tip cavity length has also been evaluated as a function of time. Inlet pressure signal and video acquisitions have been synchronized in order to analyze possible cavitation fluid-dynamic instabilities both optically and by means of pressure fluctuation analysis. Fourier analysis showed the occurrence of a cavity length oscillation at ..

Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520

Dynamical response of the "GGG" rotor to test the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes

Recent theoretical work suggests that violation of the Equivalence Principle might be revealed in a measurement of the fractional differential acceleration $\eta$ between two test bodies -of different composition, falling in the gravitational field of a source mass- if the measurement is made to the level of $\eta\simeq 10^{-13}$ or better. This being within the reach of ground based experiments, gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the "Galileo Galilei on the Ground" (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following paper (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rotation -in particular its normal modes (Part I) and rejection of common mode effects (Part II)- can be predicted by means of a simple but effective model that embodies all the relevant physics. Analytical solutions are obtained under special limits, which provide the theoretical understanding. A simulation environment is set up, obtaining quantitative agreement with the available experimental data on the frequencies of the normal modes, and on the whirling behavior. This is a needed and reliable tool for controlling and separating perturbative effects from the expected signal, as well as for planning the optimization of the apparatus.Comment: Accepted for publication by "Review of Scientific Instruments" on Jan 16, 2006. 16 2-column pages, 9 figure

COVID-19 and individual genetic susceptibility/receptivity: Role of ACE1/ACE2 genes, immunity, inflammation and coagulation. might the double x-chromosome in females be protective against SARS-COV-2 compared to the single x-chromosome in males?

In December 2019, a novel severe acute respiratory syndrome (SARS) from a new coronavirus (SARS-CoV-2) was recognized in the city of Wuhan, China. Rapidly, it became an epidemic in China and has now spread throughout the world reaching pandemic proportions. High mortality rates characterize SARS-CoV-2 disease (COVID-19), which mainly affects the elderly, causing unrestrained cytokines-storm and subsequent pulmonary shutdown, also suspected micro thromboembolism events. At the present time, no specific and dedicated treatments, nor approved vaccines, are available, though very promising data come from the use of anti-inflammatory, anti-malaria, and anti-coagulant drugs. In addition, it seems that males are more susceptible to SARS-CoV-2 than females, with males 65% more likely to die from the infection than females. Data from the World Health Organization (WHO) and Chinese scientists show that of all cases about 1.7% of women who contract the virus will die compared with 2.8% of men, and data from Hong Kong hospitals state that 32% of male and 15% of female COVID-19 patients required intensive care or died. On the other hand, the long-term fallout of coronavirus may be worse for women than for men due to social and psychosocial reasons. Regardless of sex-or gender-biased data obtained from WHO and those gathered from sometimes controversial scientific journals, some central points should be considered. Firstly, SARS-CoV-2 has a strong interaction with the human ACE2 receptor, which plays an essential role in cell entry together with transmembrane serine protease 2 (TMPRSS2); it is interesting to note that the ACE2 gene lays on the X-chromosome, thus allowing females to be potentially heterozygous and differently assorted compared to men who are definitely hemizygous. Secondly, the higher ACE2 expression rate in females, though controversial, might ascribe them the worst prognosis, in contrast with worldwide epidemiological data. Finally, several genes involved in inflammation are located on the X-chromosome, which also contains high number of immune-related genes responsible for innate and adaptive immune responses to infection. Other genes, out from the RAS-pathway, might directly or indirectly impact on the ACE1/ACE2 balance by influencing its main actors (e.g., ABO locus, SRY, SOX3, ADAM17). Unexpectedly, the higher levels of ACE2 or ACE1/ACE2 rebalancing might improve the outcome of COVID-19 in both sexes by reducing inflammation, thrombosis, and death. Moreover, X-heterozygous females might also activate a mosaic advantage and show more pronounced sex-related differences resulting in a sex dimorphism, further favoring them in counteracting the progression of the SARS-CoV-2 infection

Testing the weak equivalence principle

AbstractThe discovery of Dark Energy and the fact that only about 5% of the mass of the universe can be explained on the basis of the current laws of physics have led to a serious impasse. Based on past history, physics might indeed be on the verge of major discoveries; but the challenge is enormous. The way to tackle it is twofold. On one side, scientists try to perform large scale direct observations and measurements – mostly from space. On the other, they multiply their efforts to put to the most stringent tests ever the physical theories underlying the current view of the physical world, from the very small to the very large. On the extremely small scale very exciting results are expected from one of the most impressive experiments in the history of mankind: the Large Hadron Collider. On the very large scale, the universe is dominated by gravity and the present impasse undoubtedly calls for more powerful tests of General Relativity – the best theory of gravity to date. Experiments testing the Weak Equivalence Principle, on which General Relativity ultimately lies, have the strongest probing power of them all; a breakthrough in sensitivity is possible with the "Galileo Galilei" (GG) satellite experiment to fly in low Earth orbit

EXPERIMENTAL VALIDATION OF A HIGH ACCURACY TEST OF THE EQUIVALENCE PRINCIPLE WITH THE SMALL SATELLITE "GALILEO GALILEI"

The small satellite "Galileo Galilei" (GG) has been designed to test the equivalence principle (EP) to 10-17 with a total mass at launch of 250 kg. The key instrument is a differential accelerometer made up of weakly coupled coaxial, concentric test cylinders rapidly spinning around the symmetry axis and sensitive in the plane perpendicular to it, lying at a small inclination from the orbit plane. The whole spacecraft spins around the same symmetry axis so as to be passively stabilized. The test masses are large (10 kg each, to reduce thermal noise), their coupling is very weak (for high sensitivity to differential effects), and rotation is fast (for high frequency modulation of the signal). A 1 g version of the accelerometer ("Galileo Galilei on the Ground" — GGG) has been built to the full scale — except for coupling, which cannot be as weak as in the absence of weight, and a motor to maintain rotation (not needed in space due to angular momentum conservation). GGG has proved: (i) high Q; (ii) auto-centering and long term stability; (iii) a sensitivity to EP testing which is close to the target sensitivity of the GG experiment provided that the physical properties of the experiment in space are going to be fully exploited

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde