10,805 research outputs found
From solar-like to anti-solar differential rotation in cool stars
Stellar differential rotation can be separated into two main regimes:
solar-like when the equator rotates faster than the poles and anti-solar when
the polar regions rotate faster than the equator. We investigate the transition
between these two regimes with 3-D numerical simulations of rotating spherical
shells. We conduct a systematic parameter study which also includes models from
different research groups. We find that the direction of the differential
rotation is governed by the contribution of the Coriolis force in the force
balance, independently of the model setup (presence of a magnetic field,
thickness of the convective layer, density stratification). Rapidly-rotating
cases with a small Rossby number yield solar-like differential rotation, while
weakly-rotating models sustain anti-solar differential rotation. Close to the
transition, the two kinds of differential rotation are two possible bistable
states. This study provides theoretical support for the existence of anti-solar
differential rotation in cool stars with large Rossby numbers.Comment: 5 pages, 6 figures, accepted for publication in MNRA
A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra
We study finite loop models on a lattice wrapped around a cylinder. A section
of the cylinder has N sites. We use a family of link modules over the periodic
Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur,
and Graham and Lehrer. These are labeled by the numbers of sites N and of
defects d, and extend the standard modules of the original Temperley-Lieb
algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2}
(weight of contractible loops) and \alpha (weight of non-contractible loops),
this family also depends on a twist parameter v that keeps track of how the
defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends
on the anisotropy \nu and the spectral parameter \lambda that fixes the model.
(The thermodynamic limit of T_N is believed to describe a conformal field
theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).)
The family of periodic XXZ Hamiltonians is extended to depend on this new
parameter v and the relationship between this family and the loop models is
established. The Gram determinant for the natural bilinear form on these link
modules is shown to factorize in terms of an intertwiner i_N^d between these
link representations and the eigenspaces of S^z of the XXZ models. This map is
shown to be an isomorphism for generic values of u and v and the critical
curves in the plane of these parameters for which i_N^d fails to be an
isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop
models and XXZ Hamiltonians", 31 page
Validity of the Adiabatic Approximation
We analyze the validity of the adiabatic approximation, and in particular the
reliability of what has been called the "standard criterion" for validity of
this approximation. Recently, this criterion has been found to be insufficient.
We will argue that the criterion is sufficient only when it agrees with the
intuitive notion of slowness of evolution of the Hamiltonian. However, it can
be insufficient in cases where the Hamiltonian varies rapidly but only by a
small amount. We also emphasize the distinction between the adiabatic {\em
theorem} and the adiabatic {\em approximation}, two quite different although
closely related ideas.Comment: 4 pages, 1 figur
Ma petite histoire d'intégration des TIC en pédagogie
Comprend des références bibliographiques et webographique
Alien Registration- Morin, Ozilda R. (Van Buren, Aroostook County)
https://digitalmaine.com/alien_docs/32255/thumbnail.jp
Alien Registration- Morin, Marie R. (Lewiston, Androscoggin County)
https://digitalmaine.com/alien_docs/27613/thumbnail.jp
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