1,250 research outputs found
A Class of Distal Functions on Semitopological Semigroups
The norm closure of the algebra generated by the set and of
functions on was studied in \cite{S} (and was named as the
Weyl algebra). In this paper, by a fruitful result of Namioka, this algebra is
generalized for a general semitopological semigroup and, among other things, it
is shown that the elements of the involved algebra are distal. In particular,
we examine this algebra for and (more generally) for the
discrete (additive) group of any countable ring. Finally, our results are
treated for a bicyclic semigroup.Comment: To appear in Methods Funct. Anal. Topolog
Near-Horizon Extremal Geometries: Coadjoint Orbits and Quantization
The NHEG algebra is an extension of Virasoro introduced in
[arXiv:1503.07861]; it describes the symplectic symmetries of
-dimensional Near Horizon Extremal Geometries with isometry. In this work we construct the NHEG group and classify the
(coadjoint) orbits of its action on phase space. As we show, the group consists
of maps from an -torus to the Virasoro group, so its orbits are bundles of
standard Virasoro coadjoint orbits over . We also describe the unitary
representations that are expected to follow from the quantization of these
orbits, and display their characters. Along the way we show that the NHEG
algebra can be built from u(1) currents using a twisted Sugawara construction.Comment: 22 pages, one figure. v2: Title expanded, various minor
clarifications added. Published in JHE
On Rigidity of 3d Asymptotic Symmetry Algebras
We study rigidity and stability of infinite dimensional algebras which are
not subject to the Hochschild-Serre factorization theorem. In particular, we
consider algebras appearing as asymptotic symmetries of three dimensional
spacetimes, the BMS3, u(1) Kac-Moody and Virasoro algebras. We construct and
classify the family of algebras which appear as deformations of BMS3, u(1)
Kac-Moody and their central extensions by direct computations and also by
cohomological analysis. The Virasoro algebra appears as a specific member in
this family of rigid algebras; for this case stabilization procedure is inverse
of the In\"on\"u-Wigner contraction relating Virasoro to BMS3 algebra. We
comment on the physical meaning of deformation and stabilization of these
algebras and relevance of the family of rigid algebras we obtainComment: 50 pages, one figure and two tables; v2: minor improvements,
references adde
Magnetic flux concentrations from dynamo-generated fields
The mean-field theory of magnetized stellar convection gives rise to the two
possibility of distinct instabilities: the large-scale dynamo instability,
operating in the bulk of the convection zone, and a negative effective magnetic
pressure instability (NEMPI) operating in the strongly stratified surface
layers. The latter might be important in connection with magnetic spot
formation, but the growth rate of NEMPI is suppressed with increasing rotation
rates, although recent direct numerical simulations (DNS) have shown a
subsequent increase in the growth rate. We examine quantitatively whether this
increase in the growth rate of NEMPI can be explained by an alpha squared
mean-field dynamo, and whether both NEMPI and the dynamo instability can
operate at the same time. We use both DNS and mean-field simulations (MFS) to
solve the underlying equations numerically either with or without an imposed
horizontal field. We use the test-field method to compute relevant dynamo
coefficients. DNS show that magnetic flux concentrations are still possible up
to rotation rates above which the large-scale dynamo effect produces mean
magnetic fields. The resulting DNS growth rates are quantitatively well
reproduced with MFS. As expected, for weak or vanishing rotation, the growth
rate of NEMPI increases with increasing gravity, but there is a correction term
for strong gravity and large turbulent magnetic diffusivity. Magnetic flux
concentrations are still possible for rotation rates above which dynamo action
takes over. For the solar rotation rate, the corresponding turbulent turnover
time is about 5 hours, with dynamo action commencing in the layers beneath.Comment: 10 pages, 10 figures, submitted to A&
Dynamical heterogeneity in aging colloidal glasses of Laponite
Glasses behave as solids due to their long relaxation time; however the
origin of this slow response remains a puzzle. Growing dynamic length scales
due to cooperative motion of particles are believed to be central to the
understanding of both the slow dynamics and the emergence of rigidity. Here, we
provide experimental evidence of a growing dynamical heterogeneity length scale
that increases with increasing waiting time in an aging colloidal glass of
Laponite. The signature of heterogeneity in the dynamics follows from dynamic
light scattering measurements in which we study both the rotational and
translational diffusion of the disk-shaped particles of Laponite in suspension.
These measurements are accompanied by simultaneous microrheology and
macroscopic rheology experiments. We find that rotational diffusion of
particles slows down at a faster rate than their translational motion. Such
decoupling of translational and orientational degrees of freedom finds its
origin in the dynamic heterogeneity since rotation and translation probe
different length scales in the sample. The macroscopic rheology experiments
show that the low frequency shear viscosity increases at a much faster rate
than both rotational and translational diffusive relaxation times.Comment: 12 pages, 5 figures, Accepted in Soft Matter 201
Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM
We study near-horizon limits of near-extremal charged black hole solutions to
five-dimensional gauged supergravity carrying two charges, extending
the recent work of Balasubramanian et.al. We show that there are two
near-horizon decoupling limits for the near-extremal black holes, one
corresponding to the near-BPS case and the other for the far from BPS case.
Both of these limits are only defined on the 10d IIB uplift of the 5d black
holes, resulting in a decoupled geometry with a six-dimensional part (conformal
to) a rotating BTZ X . We study various aspects of these decoupling limits
both from the gravity side and the dual field theory side. For the latter we
argue that there should be two different, but equivalent, dual gauge theory
descriptions, one in terms of the 2d CFT's dual to the rotating BTZ and the
other as certain large R-charge sectors of d=4,N =4 U(N) SYM theory. We discuss
new BMN-type sectors of the N=4 SYM in the limit in which the
engineering dimensions scale as (for the near-BPS case) and as
(for the far from BPS case).Comment: 44 pages, references added, minor change
Negotiations for meaning in the context of a massively multiplayer online role-playing game
This study investigated negotiations for meaning as conditions for second language (L2) learning in the context of a massively multiplayer online role-playing game, World of Warcraft (WoW) (Blizzard Entertainment, 2004). Varonis and Gass’s (1985) and Smith’s (2003a) models were used to identify negotiation episodes during on-task and off-task talks among the participants while playing WoW. The participants were six non-native (NNS) and one native English speaker (NS). The NNSs were divided into two teams of three: Team 1 (T1) pre-intermediate and Team 2 (T2) upper-intermediate. The NS played the game with both teams. The study lasted for six months and resulted in 59.96 hours of recorded audio and nine hours of screen-recorded gaming sessions. Negotiation patterns were compared across the L2 proficiency levels and three different types of dyads. The results revealed that (a) T1 encountered more communication breakdowns, but T2 engaged in more negotiations, (b) T1 engaged in more complex negotiations, (c) breakdowns and negotiations occurred more during off-task talk, and (d) breakdowns were triggered more by the NS’s utterances in T1 and by NNSs’ utterances in T2. The results also showed the participants’ abundant L2 use to undertake authentically contextualized game-driven tasks, meticulous involvement in bi- and multi-lateral negotiations, and creative strategies to resolve incomprehension
Controlling stability and transport of magnetic microswimmers by an external field
We investigate the hydrodynamic stability and transport of magnetic
microswimmers in an external field using a kinetic theory framework. Combining
linear stability analysis and nonlinear 3D continuum simulations, we show that
for sufficiently large activity and magnetic field strengths, a homogeneous
polar steady state is unstable for both puller and pusher swimmers. This
instability is caused by the amplification of anisotropic hydrodynamic
interactions due to the external alignment and leads to a partial
depolarization and a reduction of the average transport speed of the swimmers
in the field direction. Notably, at higher field strengths a reentrant
hydrodynamic stability emerges where the homogeneous polar state becomes stable
and a transport efficiency identical to that of active particles without
hydrodynamic interactions is restored
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