Related papers: Statistical properties of the gravitational force …
The dynamics of a tagged particle immersed in a fluid of particles of the same size but different mass is studied when the system is confined between two hard parallel plates separated a distance smaller than twice the diameter of the…
We define the notion of mutual quantum measurements of two macroscopic objects and investigate the effect of these measurements on the velocities of the objects. We show that multiple mutual quantum measurements can lead to an effective…
We give the first determination of the observed peculiar velocity distribution function for a representative sample of galaxies (within 50 Mpc (H=100) of the Local Group), which includes a wide range of clustering properties. We explore in…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
In dense, static, polydisperse granular media under isotropic pressure, the probability density and the correlations of particle-wall contact forces are studied. Furthermore, the probability density functions of the populations of pressures…
We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite $N$ fluctuations and perturbations induced by the…
We use IGETS absolute gravitational acceleration measurement data to study the gravitational acceleration variance. The relative variance of $\delta g /g$ in 22 years is less than $4\times 10^{-8}$. Since $\delta G /G\lessapprox\delta g /g…
We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for…
Static observers remain on Killing-vector world lines and measure the rest-mass+kinetic energies of particles moving past them, and the flux of that mechanical energy through space and time. The total mechanical energy is the total flux…
A linear density of mass is assumed uniformly distributed along an infinitely long straight line. All possible motions of a test particle are described, under the newtonian logarithmic gravitational potential alone. Those most interesting…
We describe a complete method for a precise study of gravitational interaction between two nearby quantum masses. Since the displacements of these masses are much smaller than the initial separation between their centers, the…
Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
We examine the notion of Haldane's dimension and the corresponding statistics in a probabilistic spirit. Motivated by the example of dimensional-regularization we define the dimension of a space as the trace of a diagonal `unit operator',…
Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…
We consider a further extension of our previous works in the treatment of the three-dimensional general relativistic Poynting-Robertson effect, which describes the motion of a test particle around a compact object as affected by the…
The Nelson stochastic mechanics of inhomogeneous quantum diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold where this tensor of diffusion plays the role of a metric tensor.…