Related papers: Statistical properties of the gravitational force …
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We solve the problem of spatial distribution of inertial particles that sediment in Navier-Stokes turbulence with small ratio $Fr$ of acceleration of fluid particles to acceleration of gravity $g$. The particles are driven by linear drag…
In this paper I study the probability distribution of the gravitational force in gravitational systems through numerical experiments. I show that Kandrup's (1980) and Antonuccio-Delogu & Atrio-Barandela's (1992) theories describe correctly…
For fixed $t = 2$ or $3$, we investigate the statistical properties of $\{Y_t(n)\}$, the sequence of random variables corresponding to the number of hook lengths divisible by $t$ among the partitions of $n$. We characterize the support of…
The Holtsmark distribution has applications in plasma physics, for the electric-microfield distribution involved in spectral line shapes for instance, as well as in astrophysics for the distribution of gravitating bodies. It is one of the…
We study the diffusion of $N$ particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb Liniger quantum model allows to obtain stationary time…
We numerically study a two-dimensional granular gas of rigid disks where an external driving force is applied to each particle in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due…
The Newtonian constant of gravitation $G$ historically has the largest relative uncertainty over all other fundamental constants with some discrepancies in values between different measurements. We propose a new scheme to measure $G$ by…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
We examine the peculiar velocity distribution function of galaxies in cosmological many-body gravitational clustering. Our statistical mechanical approach derives a previous basic assumption and generalizes earlier results to galaxies with…
We probe the diffusive motion of particles in slowly sheared three dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the…
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…
In 1687, Isaac Newton published the universal law of gravitation stating that two bodies attract each other with a force proportional to the product of their masses and the inverse square of the distance. The constant of proportionality, G,…
Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these…
It is widely believed that quantum gravity effects are negligible in a conventional laboratory experiment because quantum gravity should play its role only at a distance of about Planck's length ($\sim10^{-33}$ cm). Sometimes that is not…
Atomic interferometry methods used to measure the Newtonian gravitational constant. To improve the accuracy, one should measure the phase of an atomic interferometer at extreme values of atomic vertical velocities and coordinates. Owing to…
We construct and study the stochastic force field generated by a Poisson distribution of sources at finite density, $x_1,x_2,\cdots$ in $\mathbb{R}^3$ each of them yielding a long range potential $Q_i\Phi(x-x_i)$ with possibly different…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
In dimension 2 and above, the Burgers dynamics, the so-called "adhesion model" in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is…
We report experimental results on the behavior of an ensemble of inelastically colliding particles, excited by a vibrated piston in a vertical cylinder. When the particle number is increased, we observe a transition from a regime where the…