Related papers: Galileo's Discovery of Scaling Laws

We present nonsingular, homogeneous and isotropic bouncing solutions of the conformal Galileon model. We show that such solutions necessarily begin with a radiation-dominated contracting phase. This is followed by a quintom scenario in…

Aristotle has split physics at the sphere of the moon; above this sphere there is no change except eternal spherical motion, below are two different kinds of motion: Natural motion (without specific cause) and enforced motion. In modern…

Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…

Gravity plays an important part in the experiments and discoveries of the modern world. But how was it discovered? Surely Newton and Einstein were not the only people to observe it and account for it. It had been a long path before the full…

We propose a notion of hyperbolic system of conservation laws invariant for the Galileo group of transformations. We show that with natural physical and mathematical hypotheses, such a system conducts to the gas dynamics equations or to…

Using the wave equation in d > or = 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincar\'e and Galileo covariant with respect to different sets of independent variables. This provides a method to…

Galileons are stable null energy condition (NEC) violating perturbations. If these NEC violating modes are coupled to Einstein gravity, they can cause violation of the second law of black hole thermodynamics. We demonstrate that galileons…

In different passages of his dialogues, Plato showed deep mathematically-based physical insights. Regrettably most readers overlooked the respective statements, or they utterly did not understand those hints since they were full of…

An attempt is made here to extend to the microscopic domain the scale invariant character of gravitation - which amounts to consider expansion as applying to any physical scale. Surprisingly, this hypothesis does not prevent the redshift…

We consider the impact of a power-law correction to the Newtonian potential, inspired by ungravity or $f(R)$ extensions of the Standard Model, and draw conclusions on the possibility of measuring the relevant parameters through observables…

When identifying instruments that have had great influence on the history of physics, none comes to mind more quickly than the pendulum. Though 'birthed' by Galileo in the 16th century, and in some respects nearly 'dead' by the middle of…

The Jesuit scientist Christopher Clavius (1538-1612) has been the most influential teacher of the renaissance. His contributions to algebra, geometry, astronomy and cartography are enormous. He paved the way, with his texts and his teaching…

The correlation length $\xi$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields…

The main purpose of this paper is to study two scaling methods developed respectively by Pinchuk and Frankel. We introduce first a continuously-varying global coordinate system, and give an alternative proof to the convergence of Pinchuk's…

The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…

The possibility of an increasing gravitational constant $G$ and its implication on the Earth's history are discussed. The model is consistent with geophysical and astronomical data. The number of days in early epochs predicted by the model…

This work examines the coalescence of two unequal-size spherical liquid droplets in the inviscid regime, with an emphasis on exploring the scaling of the liquid bridge evolution. Our experiment suggests that the classical 1/2 power-law…

A set of scaling laws, based on the stochastic motions of the granular components of astronomical systems, is applied to a cosmological model with a positive cosmological constant. It follows that the mass of the dominant particle in the…

We study a Lagrangian with a cubic Galileon term and a standard scalar-field kinetic contribution with two exponential potentials. In this model the Galileon field generates scaling solutions in which the density of the scalar field $\phi$…

Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical…