57,005 research outputs found
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
Gravothermal Catastrophe, an Example
This work discusses gravothermal catastrophe in astrophysical systems and
provides an analytic collapse solution which exhibits many of the catastrophe
properties. The system collapses into a trapped surface with outgoing energy
radiated to a future boundary, and provides an example of catastrophic
collapse.Comment: To appear in Phys. Rev.
- …