71,711 research outputs found
Exact General Solutions to Extraordinary N-body Problems
We solve the N-body problems in which the total potential energy is any
function of the mass-weighted root-mean-square radius of the system of N point
masses. The fundamental breathing mode of such systems vibrates non-linearly
for ever. If the potential is supplemented by any function that scales as the
inverse square of the radius there is still no damping of the fundamental
breathing mode. For such systems a remarkable new statistical equilibrium is
found for the other coordinates and momenta, which persists even as the radius
changes continually.Comment: 15 pages, LaTeX. Accepted for publication in Proc. Roy. Soc.
Relaxation to a Perpetually Pulsating Equilibrium
Paper in honour of Freeman Dyson on the occasion of his 80th birthday.
Normal N-body systems relax to equilibrium distributions in which classical
kinetic energy components are 1/2 kT, but, when inter-particle forces are an
inverse cubic repulsion together with a linear (simple harmonic) attraction,
the system pulsates for ever. In spite of this pulsation in scale, r(t), other
degrees of freedom relax to an ever-changing Maxwellian distribution. With a
new time, tau, defined so that r^2d/dt =d/d tau it is shown that the remaining
degrees of freedom evolve with an unchanging reduced Hamiltonian. The
distribution predicted by equilibrium statistical mechanics applied to the
reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature
pulsates like r^-2. Numerical simulation with 1000 particles demonstrate a
rapid relaxation to this pulsating equilibrium.Comment: 9 pages including 4 figure
From Quasars to Extraordinary N-body Problems
We outline reasoning that led to the current theory of quasars and look at
George Contopoulos's place in the long history of the N-body problem. Following
Newton we find new exactly soluble N-body problems with multibody forces and
give a strange eternally pulsating system that in its other degrees of freedom
reaches statistical equilibrium.Comment: 13 pages, LaTeX with 1 postscript figure included. To appear in
Proceedings of New York Academy of Sciences, 13th Florida Workshop in
Nonlinear Astronomy and Physic
Heated element fluid flow sensor Patent
Heated element sensor for fluid flow detection in thermal conductive conduit with adaptive means to determine flow rate and directio
The Structure of the Outer Halo of the Galaxy and its Relationship to Nearby Large-Scale Structure
We present evidence to support an earlier indication that the Galaxy is
embedded in an extended, highly inclined, triaxial halo outlined by the spatial
distribution of companion galaxies to the Milky Way. Signatures of this spatial
distribution are seen in 1) the angular variation of the radial-velocity
dispersion of the companion galaxies, 2) the spatial distribution of the M~31
sub-group of galaxies, 3) the spatial distribution of the isolated, mainly
dwarf irregular, galaxies of the Local Group, 4) the velocity anisotropy
quadrupole of a sub-group of high-velocity clouds, and 5) the spatial
distribution of galaxies in the Coma-Sculptor cloud. Tidal effects of M~31 and
surrounding galaxies on the Galaxy are not strong enough to have affected the
observed structure. We conclude that this distribution is a reflection of
initial conditions. A simple galaxy formation scenario is proposed which ties
together the results found here with those of Holmberg (1969) and Zaritsky et
al. (1997) on the peculiar distribution of satellites around a large sample of
spiral galaxies.Comment: Accepted for publication in the Astron J., March 2000, 12 pages with
1 figur
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