18,375 research outputs found
Nonlinear r-modes in a spherical shell: issues of principle
We use a simple physical model to study the nonlinear behaviour of the r-mode
instability. We assume that r-modes (Rossby waves) are excited in a thin
spherical shell of rotating incompressible fluid. For this case, exact Rossby
wave solutions of arbitrary amplitude are known. We find that:
(a) These nonlinear Rossby waves carry ZERO physical angular momentum and
positive physical energy, which is contrary to the folklore belief that the
r-mode angular momentum and energy are negative.
(b) Within our model, we confirm the differential drift reported by Rezzolla,
Lamb and Shapiro (1999).
Radiation reaction is introduced into the model by assuming that the fluid is
electrically charged; r-modes are coupled to electromagnetic radiation through
current (magnetic) multipole moments. We find that:
(c) To linear order in the mode amplitude, r-modes are subject to the CFS
instability, as expected.
(d) Radiation reaction decreases the angular velocity of the shell and causes
differential rotation (which is distinct from but similar in magnitude to the
differential drift reported by Rezzolla et al.) prior to saturation of the
r-mode growth. This is contrary to the phenomenological treatments to date,
which assume that the loss of stellar angular momentum is accounted for by the
r-mode growth. We demonstrate, for the first time, that r-mode radiation
reaction leads to differential rotation.
(e) We show that for l=2 r-mode electromagnetic radiation reaction is
equivalent to gravitational radiation reaction in the lowest post-Newtonian
order.Comment: 8 pages, no figures, uses MNRAS style, abstract abridged to fit into
24 line
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
The problem of counting plane trees with edges and an even or an odd
number of leaves was studied by Eu, Liu and Yeh, in connection with an identity
on coloring nets due to Stanley. This identity was also obtained by Bonin,
Shapiro and Simion in their study of Schr\"oder paths, and it was recently
derived by Coker using the Lagrange inversion formula. An equivalent problem
for partitions was independently studied by Klazar. We present three parity
reversing involutions, one for unlabelled plane trees, the other for labelled
plane trees and one for 2-Motzkin paths which are in one-to-one correspondence
with Dyck paths.Comment: 8 pages, 4 figure
Mode-Locked Two-Photon States
The concept of mode locking in laser is applied to a two-photon state with
frequency entanglement. Cavity enhanced parametric down-conversion is found to
produce exactly such a state. The mode-locked two-photon state exhibits a
comb-like correlation function. An unbalanced Hong-Ou-Mandel type
interferometer is used to measure the correlation function. A revival of the
typical interference dip is observed. We will discuss schemes for engineering
of quantum states in time domain.Comment: 4 pages, 5 figure
Medium effects of magnetic moments of baryons on neutron stars under strong magnetic fields
We investigate medium effects due to density-dependent magnetic moments of
baryons on neutron stars under strong magnetic fields. If we allow the
variation of anomalous magnetic moments (AMMs) of baryons in dense matter under
strong magnetic fields, AMMs of nucleons are enhanced to be larger than those
of hyperons. The enhancement naturally affects the chemical potentials of
baryons to be large and leads to the increase of a proton fraction.
Consequently, it causes the suppression of hyperons, resulting in the stiffness
of the equation of state. Under the presumed strong magnetic fields, we
evaluate relevant particles' population, the equation of state and the maximum
masses of neutron stars by including density-dependent AMMs and compare them
with those obtained from AMMs in free space
- …