Related papers: Galileo's Discovery of Scaling Laws
Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
Degenerate scalar-tensor theories are recently proposed covariant theories of gravity coupled with a scalar field. Despite being characterised by higher order equations of motion, they do not propagate more than three degrees of freedom,…
Galileon interactions represent a class of effective field theories that have received much attention since their inception. They can be treated in their own right as scalar field theories with a specific global shift and Galilean symmetry…
Galileons are higher-derivative theories of a real scalar which nevertheless admit second order equations of motion. They have interesting applications as dark energy models and in early universe cosmology, and have been conjectured to…
Astronomers in the early 17th century misunderstood the images of stars that they saw in their telescopes. For this reason, the data a skilled observer of that time acquired via telescopic observation of the heavens appeared to support a…
More than five hundred years ago Leonardo Da Vinci found a pattern in the growth of trees nowadays known as the Leonardo's rule. This rule relates the thickness of the stem with the thickness of the branches at different bifurcation stages…
We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon…
In the last few years, the so-called flyby anomaly has been widely discussed, but remains still an illusive topic. This is due to the harsh conditions experienced during an Earth flyby as well as due to the limited data available. In this…
We provide a complete classification of all abelian gauge invariant $p$-form theories with equations of motion depending only on the second derivative of the field---the $p$-form analogues of the Galileon scalar field theory. We construct…
The laws of gravitation devised by Newton, and by Hilbert and Einstein, have failed many experimental and observational tests, namely the bore hole g anomaly, flat rotation curves for spiral galaxies, supermassive black hole mass spectrum,…
The LIGO results are among the greatest experimental achievements of all times. Time and again scientists have compared this feat to Galileo pointing his telescope to the sky, offering instead an 'ear' to the cosmos. After the remarkable…
We use Lie-algebraic arguments to classify Lorentz-invariant theories of massless interacting scalars that feature coordinate-dependent redundant symmetries of the Galileon type. We show that such theories are determined, up to a set of…
We discuss a formulation of Galileon actions in terms of matrix determinants in four dimensions. This approach allows one to straightforwardly determine derivative couplings between Galileons and scalar or vector degrees of freedom that…
I recently demonstrated that the Earth is a mechanical oscillator in which springtide induced magnification of all-masses resonance forces tectonics. I here generalize this georesonator concept so to make it apply to any body, anywhere in…
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
The event GW150914 was the first historical detection of gravitational waves (GWs). The emergence of this ground-breaking discovery came not only from incredibly innovative experimental work, but also from a centennial of theoretical…
The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only…
The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only…
With the manuscript of the Sidereus Nuncius preserved at the Biblioteca Nazionale of Florence are included 7 watercolors of the Moon painted by Galileo himself. We suggest that some of them, and in particular the drawing of the 30 Nov 1609…