479,276 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
Incubators vs Zombies: Fault-Tolerant, Short, Thin and Lanky Spanners for Doubling Metrics
Recently Elkin and Solomon gave a construction of spanners for doubling
metrics that has constant maximum degree, hop-diameter O(log n) and lightness
O(log n) (i.e., weight O(log n)w(MST). This resolves a long standing conjecture
proposed by Arya et al. in a seminal STOC 1995 paper.
However, Elkin and Solomon's spanner construction is extremely complicated;
we offer a simple alternative construction that is very intuitive and is based
on the standard technique of net tree with cross edges. Indeed, our approach
can be readily applied to our previous construction of k-fault tolerant
spanners (ICALP 2012) to achieve k-fault tolerance, maximum degree O(k^2),
hop-diameter O(log n) and lightness O(k^3 log n)
Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model
Owing to its conceptual simplicity and computational efficiency, the
pseudopotential multiphase lattice Boltzmann (LB) model has attracted
significant attention since its emergence. In this work, we aim to extend the
pseudopotential LB model to simulate multiphase flows at large density ratio
and relatively high Reynolds number. First, based on our recent work [Li et
al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed
for the multiple-relaxation-time pseudopotential LB model in order to achieve
thermodynamic consistency and large density ratio in the model. Next, through
investigating the effects of the parameter a in the Carnahan-Starling equation
of state, we find that the interface thickness is approximately proportional to
1/sqrt(a). Using a smaller a will lead to a wider interface thickness, which
can reduce the spurious currents and enhance the numerical stability of the
pseudopotential model at large density ratio. Furthermore, it is found that a
lower liquid viscosity can be gained in the pseudopotential model by increasing
the kinematic viscosity ratio between the vapor and liquid phases. The improved
pseudopotential LB model is numerically validated via the simulations of
stationary droplet and droplet oscillation. Using the improved model as well as
the above treatments, numerical simulations of droplet splashing on a thin
liquid film are conducted at a density ratio in excess of 500 with Reynolds
numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly
reproduced and the predicted spread radius is found to obey the power law
reported in the literature.Comment: 9 figures, 2 tables, accepted by Physical Review E (in press
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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