1,126 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
Exact Quantum Solutions of Extraordinary N-body Problems
The wave functions of Boson and Fermion gases are known even when the
particles have harmonic interactions. Here we generalise these results by
solving exactly the N-body Schrodinger equation for potentials V that can be
any function of the sum of the squares of the distances of the particles from
one another in 3 dimensions. For the harmonic case that function is linear in
r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) =
\zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2
M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the
solution is given in terms of the one or two body problem with potential U(r)
in 3 dimensions. The degeneracies of the levels are derived for distinguishable
particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter
involve significant combinatorial analysis which may have application to the
shell model of atomic nuclei. For large N the Fermionic ground state gives the
binding energy of a degenerate white dwarf star treated as a giant atom with an
N-body wave function. The N-body forces involved in these extraordinary N-body
problems are not the usual sums of two body interactions, but nor are forces
between quarks or molecules. Bose-Einstein condensation of particles in 3
dimensions interacting via these strange potentials can be treated by this
method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal
Societ
Coupling/decoupling between translational and rotational dynamics in a supercooled molecular liquid
We use molecular dynamics computer simulations to investigate the
coupling/decoupling between translational and rotational dynamics in a
glass-forming liquid of dumbbells. This is done via a careful analysis of the
-relaxation time of the incoherent
center-of-mass density correlator at the structure factor peak, the
-relaxation time of the reorientational correlator, and the
translational () and rotational () diffusion constants. We find
that the coupling between the relaxation times and
increases with decreasing temperature , whereas the coupling
decreases between the diffusivities and . In addition, the
-dependence of decouples from that of , which is
consistent with previous experiments and has been interpreted as a signature of
the "translation-rotation decoupling." We trace back these apparently
contradicting observations to the dynamical heterogeneities in the system. We
show that the decreasing coupling in the diffusivities and is
only apparent due to the inadequacy of the concept of the rotational diffusion
constant for describing the reorientational dynamics in the supercooled state.
We also argue that the coupling between and
and the decoupling between and , both of which strengthen
upon cooling, can be consistently understood in terms of the growing dynamic
length scale.Comment: revised manuscript, to appear in Phys. Rev. Let
17O Nuclear Magnetic Resonance Chemical Shift in Oxyhaemoglobin
The 170 chemical shift of oxygen in oxyhaemoglobin is calculated
for two models, one corresponding to the Griffith structure
and the other to the Pauling structure. In both cases the oxygen
resonance is predicted to be several thousand ppm to low field of
the oxygen resonance in water. The shift between the oxygen
nuclei in the Pauling structure is predicted to be at least one
thousand ppm. This large deshielding arises from the local environment
of the oxygen molecule and depends critically on the
splitting of the degenerate it orbitals on complexing
17O Nuclear Magnetic Resonance Chemical Shift in Oxyhaemoglobin
The 170 chemical shift of oxygen in oxyhaemoglobin is calculated
for two models, one corresponding to the Griffith structure
and the other to the Pauling structure. In both cases the oxygen
resonance is predicted to be several thousand ppm to low field of
the oxygen resonance in water. The shift between the oxygen
nuclei in the Pauling structure is predicted to be at least one
thousand ppm. This large deshielding arises from the local environment
of the oxygen molecule and depends critically on the
splitting of the degenerate it orbitals on complexing
Do Rotations Beyond the Cosmological Horizon Affect the Local Inertial Frame?
If perturbations beyond the horizon have the velocities prescribed everywhere
then the dragging of inertial frames near the origin is suppressed by an
exponential factor. However if perturbations are prescribed in terms of their
angular momenta there is no such suppression.
We resolve this paradox and in doing so give new explicit results on the
dragging of inertial frames in closed, flat and open universe with and without
a cosmological constant.Comment: 12 page
Relativistic Poynting Jets from Accretion Disks
A model is developed for relativistic Poynting jets from the inner region of
a disk around a rotating black hole. The disk is initially threaded by a
dipole-like magnetic field. The model is derived from the special relativistic
equation for a force-free electromagnetic field. The ``head'' of the Poynting
jet is found to propagate outward with a velocity which may be relativistic.
The Lorentz factor of the head (Gamma) is found to be dependent on the magnetic
field strength close to the black hole, B_0, the density of the external medium
n_ext, and on the ratio R=r_0/r_g >1, where r_g is the gravitational radius of
the black hole, and r_0 is the radius of the O-point of the initial dipole
field threading the disk. For conditions pertinent to an active galactic
nuclei, Gamma is approximately equal to 8 (10/R)^(1/3) (B_0/10^3 Gauss)^(1/3)
(1/cm^3/n_ext)^(1/6). This model offers an explanation for the observed Lorentz
factors which are of the order of 10 for the parsec-scale radio jets measured
with very long baseline interferometry.Comment: 4 pages, 1 figur
From infall to rotation around young stellar objects: A transitional phase with a 2000 AU radius contracting disk?
Evidence for a transitional stage in the formation of a low-mass star is
reported, intermediate between the fully embedded and the T Tauri phases.
Millimeter aperture synthesis observations in the HCO+ J=1-0 and 3-2, HCN 1-0,
13CO 1-0, and C18O 1-0 transitions reveal distinctly different velocity fields
around two embedded, low-mass young stellar objects. The 0.6 M(sun) of material
around TMC 1 (IRAS 04381+2517) closely follows inside-out collapse in the
presence of a small amount of rotation (~3 km/s/pc), while L1489 IRS (IRAS
04016+2610) is surrounded by a 2000 AU radius, flared disk containing 0.02
M(sun). This disk shows Keplerian rotation around a ~0.65 M(sun) star and
infall at 1.3 (r/100 AU)^-0.5 km/s, or, equivalently, sub-Keplerian motions
around a central object between 0.65 and 1.4 M(sun). Its density is
characterized by a radial power law and an exponential vertical scale height.
The different relative importance of infall and rotation around these two
objects suggests that rotationally supported structures grow from collapsing
envelopes over a few times 10^5 yr to sizes of a few thousand AU, and then
decrease over a few times 10^4 yr to several hundred AU typical for T Tauri
disks. In this scenario, L1489 IRS represents a transitional phase between
embedded YSOs and T Tauri stars with disks. The expected duration of this phase
of ~5% of the embedded stage is consistent with the current lack of other known
objects like L1489 IRS. Alternative explanations cannot explain L1489 IRS's
large disk, such as formation from a cloud core with an unusually large
velocity gradient or a binary companion that prevents mass accretion onto small
scales. It follows that the transfer and dissipation of angular momentum is key
to understanding the formation of disks from infalling envelopes.Comment: Accepted ApJ. 33 pages, including 10 B/W figures and 1 color figure.
Uses AASTe
Absolute Proper Motion of the Fornax Dwarf Spheroidal Galaxy from Photographic and HST WFPC2 Data
We have measured the absolute proper motion of the Fornax dwarf spheroidal
galaxy from a combination of photographic plate material and HST WFPC2 data
that provide a time baseline of up to 50 years. The extragalactic reference
frame consists of 8 QSO images and 48 galaxies. The absolute proper motion is
mu_alpha cos(delta) = 0.59 +-0.16 mas/yr and mu_delta = -0.15 +- 0.16 mas/yr.
The corresponding orbit of Fornax is polar, with an eccentricity of 0.27, and a
radial period of 4.5 Gyr. Fornax's current location is near pericenter. The
direction of the motion of Fornax supports the notion that Fornax belongs to
the Fornax-LeoI-LeoII-Sculptor-Sextans stream as hypothesized by Lynden-Bell
(1976, 1982) and Majewski (1994).
According to our orbit determination, Fornax crossed the Magellanic plane
\~190 Myr ago, a time that coincides with the termination of the star-formation
process in Fornax. We propose that ram-pressure stripping due to the passage of
Fornax through a gaseous medium denser than the typical intragalactic medium
left behind from the LMC may have caused the end of star formation in Fornax.
The excess, anomalous clouds within the South Galactic pole region of the
Magellanic Stream whose origin has long been debated in the literature as
constituents of either the Magellanic Stream or of the extragalactic Sculptor
group, are found to lie along the orbit of Fornax. We speculate that these
clouds are stripped material from Fornax as the dwarf crossed the Magellanic
Clouds' orbit.Comment: Accepted for publication in Astronomical Journal. The version with
high resolution figures can be found at
ftp://pegasus.astro.yale.edu/pub/dana/paper
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