arXiv subjects

Shu-Ju Tu

Publications and source records attributed to Shu-Ju Tu.

4 recordsLinked to original sources

arXiv2002

Geometric Random Inner Products: A New Family of Tests for Random Number Generators

We present a new computational scheme, GRIP (Geometric Random Inner Products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors generated in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants which can be used to evaluate the quality of random number generators. We explicitly apply the GRIP tests to several random number generators frequently used in Monte Carlo simulations, and demonstrate a new statistical property for good random number generators.

physics.comp-ph↗

arXiv2002

Random Distance Distribution for Spherical Objects: General Theory and Applications to n-Dimensional Physics

A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to be calculated for a spherical (n)-ball having an arbitrary volume density, and reproduces the well-known results for the case of uniform density. The results find applications in stochastic geometry, computational science, molecular biological systems, statistical physics, astrophysics, condensed matter physics, nuclear physics, and elementary particle physics. As one application of these results, we propose a new statistical method obtained from our formalism to study random number generators in (n)-dimensions used in Monte Carlo simulations.

math-ph↗

arXiv2001

A New Geometric Probability Technique for an N-dimensional Sphere and Its Applications to Physics

A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to be calculated for a sphere having an arbitrary density distribution, and reproduces the well-known results for the case of a sphere with uniform density. The results find applications in stochastic geometry, probability distribution theory, astrophysics, nuclear physics, and elementary particle physics.

math-ph↗

arXiv1997

Neutrino Trapping and Neutrino Mass Bounds

It has been shown recently that the exchange of virtual neutrino pairs leads to an unphysically large energy-density in neutron stars and white dwarfs, unless neutrinos have a minimum mass, m > 0.4 eV. Here we consider the possibility that the presence of trapped low-energy neutrinos can suppress the exchange of virtual neutrino pairs, thereby avoiding a large energy-density even for massless neutrinos. We show that a) there can be subvolumes in a neutron star or white dwarf where neutrino-trapping does not take place, and which can thus have an unphysically large energy density, and b) even in those volumes where trapping does occur, the resulting suppression can be too small to alter the conclusion that neutrinos must have a minimum mass.

hep-ph↗