365,707 research outputs found
On quantum vertex algebras and their modules
We give a survey on the developments in a certain theory of quantum vertex
algebras, including a conceptual construction of quantum vertex algebras and
their modules and a connection of double Yangians and Zamolodchikov-Faddeev
algebras with quantum vertex algebras.Comment: 18 pages; contribution to the proceedings of the conference in honor
of Professor Geoffrey Maso
Modules-at-infinity for quantum vertex algebras
This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study
vertex algebra-like structures arising from various algebras such as quantum
affine algebras and Yangians. In this paper, we study two versions of the
double Yangian , denoted by and
with a nonzero complex number. For each nonzero
complex number , we construct a quantum vertex algebra and prove
that every -module is naturally a -module. We also show
that -modules are what we call
-modules-at-infinity. To achieve this goal, we study what we call
-local subsets and quasi-local subsets of \Hom (W,W((x^{-1}))) for any
vector space , and we prove that any -local subset generates a (weak)
quantum vertex algebra and that any quasi-local subset generates a vertex
algebra with as a (left) quasi module-at-infinity. Using this result we
associate the Lie algebra of pseudo-differential operators on the circle with
vertex algebras in terms of quasi modules-at-infinity.Comment: Latex, 48 page
A generalized approach to construct benchmark problems for dynamic optimization
Copyright @ Springer-Verlag Berlin Heidelberg 2008.There has been a growing interest in studying evolutionary algorithms in dynamic environments in recent years due to its importance in real applications. However, different dynamic test problems have been used to test and compare the performance of algorithms. This paper proposes a generalized dynamic benchmark generator (GDBG) that can be instantiated into the binary space, real space and combinatorial space. This generator can present a set of different properties to test algorithms by tuning some control parameters. Some experiments are carried out on the real space to study the performance of the generator.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1
Eruption of a multi-flux-rope system in solar active region 12673 leading to the two largest flares in Solar Cycle 24
Solar active region (AR) 12673 in 2017 September produced two largest flares
in Solar Cycle 24: the X9.3 flare on September 06 and the X8.2 flare on
September 10. We attempt to investigate the evolutions of the two great flares
and their associated complex magnetic system in detail. Aided by the NLFFF
modeling, we identify a double-decker flux rope configuration above the
polarity inversion line (PIL) in the AR core region. The north ends of these
two flux ropes were rooted in a negative- polarity magnetic patch, which began
to move along the PIL and rotate anticlockwise before the X9.3 flare on
September 06. The strong shearing motion and rotation contributed to the
destabilization of the two magnetic flux ropes, of which the upper one
subsequently erupted upward due to the kink-instability. Then another two sets
of twisted loop bundles beside these ropes were disturbed and successively
erupted within 5 minutes like a chain reaction. Similarly, multiple ejecta
components were detected to consecutively erupt during the X8.2 flare occurring
in the same AR on September 10. We examine the evolution of the AR magnetic
fields from September 03 to 06 and find that five dipoles emerged successively
at the east of the main sunspot. The interactions between these dipoles took
place continuously, accompanied by magnetic flux cancellations and strong
shearing motions. In AR 12673, significant flux emergence and successive
interactions between the different emerging dipoles resulted in a complex
magnetic system, accompanied by the formations of multiple flux ropes and
twisted loop bundles. We propose that the eruptions of a multi-flux-rope system
resulted in the two largest flares in Solar Cycle 24.Comment: 10 pages, 8 figures. To be published in A&
Type I Planet Migration in Nearly Laminar Disks
We describe 2D hydrodynamic simulations of the migration of low-mass planets
() in nearly laminar disks (viscosity parameter ) over timescales of several thousand orbit periods. We consider disk
masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness
parameters of and 0.05, and a variety of values and
planet masses. Disk self-gravity is fully included. Previous analytic work has
suggested that Type I planet migration can be halted in disks of sufficiently
low turbulent viscosity, for . The halting is due to a
feedback effect of breaking density waves that results in a slight mass
redistribution and consequently an increased outward torque contribution. The
simulations confirm the existence of a critical mass () beyond which migration halts in nearly laminar disks. For \alpha
\ga 10^{-3}, density feedback effects are washed out and Type I migration
persists. The critical masses are in good agreement with the analytic model of
Rafikov (2002). In addition, for \alpha \la 10^{-4} steep density gradients
produce a vortex instability, resulting in a small time-varying eccentricity in
the planet's orbit and a slight outward migration. Migration in nearly laminar
disks may be sufficiently slow to reconcile the timescales of migration theory
with those of giant planet formation in the core accretion model.Comment: 3 figures, accepted to ApJ
Type I planet migration in nearly laminar disks - long term behavior
We carry out 2-D high resolution numerical simulations of type I planet
migration with different disk viscosities. We find that the planet migration is
strongly dependent on disk viscosities. Two kinds of density wave damping
mechanisms are discussed. Accordingly, the angular momentum transport can be
either viscosity dominated or shock dominated, depending on the disk
viscosities. The long term migration behavior is different as well. Influences
of the Rossby vortex instability on planet migration are also discussed. In
addition, we investigate very weak shock generation in inviscid disks by small
mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap
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