451 research outputs found
Tilings of quadriculated annuli
Tilings of a quadriculated annulus A are counted according to volume (in the
formal variable q) and flux (in p). We consider algebraic properties of the
resulting generating function Phi_A(p,q). For q = -1, the non-zero roots in p
must be roots of unity and for q > 0, real negative.Comment: 33 pages, 12 figures; Minor changes were made to make some passages
cleare
Stability and Motion around Equilibrium Points in the Rotating Plane-Symmetric Potential Field
This study presents a study of equilibrium points, periodic orbits,
stabilities, and manifolds in a rotating plane symmetric potential field. It
has been found that the dynamical behaviour near equilibrium points is
completely determined by the structure of the submanifolds and subspaces. The
non-degenerate equilibrium points are classified into twelve cases. The
necessary and sufficient conditions for linearly stable, non resonant unstable
and resonant equilibrium points are established. Furthermore, the results show
that a resonant equilibrium point is a Hopf bifurcation point. In addition, if
the rotating speed changes, two non degenerate equilibria may collide and
annihilate each other. The theory developed here is lastly applied to two
particular cases, motions around a rotating, homogeneous cube and the asteroid
1620 Geographos. We found that the mutual annihilation of equilibrium points
occurs as the rotating speed increases, and then the first surface shedding
begins near the intersection point of the x axis and the surface. The results
can be applied to planetary science, including the birth and evolution of the
minor bodies in the Solar system, the rotational breakup and surface mass
shedding of asteroids, etc.Comment: 38 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1403.040
A Simple Model for Lensing by Black Holes in Galactic Nuclei
The lensing properties of the Plummer model with a central point mass and
external shear are derived, including the image multiplicities, critical curves
and caustics. This provides a simple model for a flattened galaxy with a
central supermassive black hole. For the Plummer model with black hole, the
maximum number of images is 4, provided the black hole mass is less than an
upper bound which is calculated analytically. This introduces a method to
constrain black hole masses by counting images, thus applicable at cosmological
distance. With shear, the maximum number of images is 6 and we illustrate the
occurrence of an astroid caustic and two metamorphoses.Comment: 7 pages, 4 figures, MNRAS, in press, small changes mad
On the Moduli Space of SU(3) Seiberg-Witten Theory with Matter
We present a qualitative model of the Coulomb branch of the moduli space of
low-energy effective N=2 SQCD with gauge group SU(3) and up to five flavours of
massive matter. Overall, away from double cores, we find a situation broadly
similar to the case with no matter, but with additional complexity due to the
proliferation of extra BPS states. We also include a revised version of the
pure SU(3) model which can accommodate just the orthodox weak coupling
spectrum.Comment: 32 pages, 25 figures, uses JHEP.cls, added references, deleted joke
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