225,010 research outputs found
Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy
We determine positive-dimensional G-periodic proper subvarieties of an
n-dimensional normal projective variety X under the action of an abelian group
G of maximal rank n-1 and of positive entropy. The motivation of the paper is
to understand the obstruction for X to be G-equivariant birational to the
quotient variety of an abelian variety modulo the action of a finite group.Comment: Asian Journal of Mathematics (to appear), Special issue on the
occasion of Prof N. Mok's 60th birthda
Inverse Statistical Mechanics: Probing the Limitations of Isotropic Pair Potentials to Produce Ground-State Structural Extremes
Inverse statistical-mechanical methods have recently been employed to design
optimized short-ranged radial (isotropic) pair potentials that robustly produce
novel targeted classical ground-state many-particle configurations. The target
structures considered in those studies were low-coordinated crystals with a
high degree of symmetry. In this paper, we further test the fundamental
limitations of radial pair potentials by targeting crystal structures with
appreciably less symmetry, including those in which the particles have
different local structural environments. These challenging target
configurations demanded that we modify previous inverse optimization
techniques. Using this modified optimization technique, we have designed
short-ranged radial pair potentials that stabilize the two-dimensional kagome
crystal, the rectangular kagome crystal, and rectangular lattices, as well as
the three-dimensional structure of CaF crystal inhabited by a single
particle species. We verify our results by cooling liquid configurations to
absolute zero temperature via simulated annealing and ensuring that such states
have stable phonon spectra. Except for the rectangular kagome structure, all of
the target structures can be stabilized with monotonic repulsive potentials.
Our work demonstrates that single-component systems with short-ranged radial
pair potentials can counterintuitively self-assemble into crystal ground states
with low symmetry and different local structural environments. Finally, we
present general principles that offer guidance in determining whether certain
target structures can be achieved as ground states by radial pair potentials
Chiral geometry and rotational structure for Cs in the projected shell model
The projected shell model with configuration mixing for nuclear chirality is
developed and applied to the observed rotational bands in the chiral nucleus
Cs. For the chiral bands, the energy spectra and electromagnetic
transition probabilities are well reproduced. The chiral geometry illustrated
in the and the is confirmed to be stable against the
configuration mixing. The other rotational bands are also described in the same
framework
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