20 research outputs found
Lane-Emden Equation: perturbation method
The perturbation method is applied to numerical solution of the Lane-Emden
Equation of arbitrary index n, and the global parameters of polytropes are
found as function of polytropic index n.Comment: 32 pp, LATE
Gravitational potential energy of simple bodies: the method of negative density
The method of negative density is presented which allows to obtain the
analytical solutions for potential energy of new kinds of homogeneous and
ihhomogeneous self-gravitating bodies. The homogeneous bispherical
concavo-convex lens is considered in particular.Comment: 4 pages, 3 figure
On the angular momentum of the neutron star
It is shown that the mass loss due to rotation-driven hydrodynamical
instability during the catastrophic collapse of the star is small. Neutron star
is formed with a large rotational kinetic energy and the spin-down takes place
in the following life of neutron star as a pulsar.Comment: 3 page
Rotation, mass loss and pulsations of the star: an analytical model
The characteristics of the star with the "prescribed" density distribution
are analytically studied.Comment: 8 pages, 6 figure
Isotope Separation and Solar Neutrino Experiments
The isotope composition of target chemical elements in the Solar Neutrino
Experiments is discussed and the possibility of improving this isotope
composition is speculated.Comment: 2 pages, no figures; replaced by revtex file with 1 reference added
and minor text changes mad
Permutations and primes
The problem of N-digit sets all permutations of which give primes is
discussed. Such sets may include only digits 1, 3, 7 and 9, and none of 0, 2,
5, 4, 6, 8. Direct calculations show that such full-permutation digit sets
occur at N = 1, 2, 3 and are absent in the 4 - 10 interval of N. On the other
hand the formal full permutation at N = 19, 23, 317 and 1031 (as well at N = 2)
cases is provided by repunits (integers all digits of which are 1). The
existence/nonexistence of other (not repunits) full-permutation digit sets for
arbitrary large N is an open question with probable negative answer. The
maximal-permutation digit sets with maximal number of primes are given for N =
4 - 10.Comment: 25 pages, 5 figure
Gravitational potential energy of simple bodies: the homogeneous bispherical concavo-convex lens
Gravitational potential energy of the homogeneous bispherical concavo-convex
lens, with the equal absolute values of radii of curvature of both surfaces is
studied.Comment: 3 pages, 3 figure
Surprises of phase transition astrophysics
Highly personalysed and subjective review of studies of the equilibrium,
pulsations and stability of stars with the first-order phase transition.Comment: 4 pages, 1 fig, revtex. Essays on Gravitation-99, Gravity Research
Foundation, US
Planck Scale Mixing and Neutrino Puzzles
It is hypotesized that neutrinos are massles and mixed among three (muon,
electron and tau) flavors with a mixing length proportional to
(E_nu/E_Planck)^-2. It is suggested that this hypothesis mostly reconciles the
standard solar models with the observations of the solar Boron and pp
neutrinos, and the atmospheric muon-to-electron neutrinos ratio.Comment: 5 pp, revtex, 2 figures; Table II replaced, 1 reference added, minor
text changed in sec. V, and other minor typos correcte
Lane-Emden Equation: Picard vs Pade
The very accurate analytical solutions are found to Lane-Emden equation of
arbitrary index, n, using Picard type iteration scheme and rational Pade
approximants. For n=2 the dimensionless polytropic "radius" and "mass" are
4.35287459595 and 2.4110450121, with the largest ever accuracy.Comment: 6 pp, Mathematica notebook source include