338,707 research outputs found
Equivariant localization and completion in cyclic homology and derived loop spaces
We prove an equivariant localization theorem over an algebraically closed
field of characteristic zero for smooth quotient stacks by reductive groups
in the setting of derived loop spaces as well as Hochschild homology and
its cyclic variants. We show that the derived loop spaces of the stack
and its classical -fixed point stack become equivalent
after completion along a semisimple parameter , implying the
analogous statement for Hochschild and cyclic homology of the dg category of
perfect complexes . We then prove an analogue of the
Atiyah-Segal completion theorem in the setting of periodic cyclic homology,
where the completion of the periodic cyclic homology of at
the identity is identified with a 2-periodic version of the
derived de Rham cohomology of . Together, these results identify the
completed periodic cyclic homology of a stack over a parameter with the 2-periodic derived de Rham cohomology of its -fixed points.Comment: Pre-publication version. 42 pages. Comments welcom
ac Losses in a Finite Z Stack Using an Anisotropic Homogeneous-Medium Approximation
A finite stack of thin superconducting tapes, all carrying a fixed current I,
can be approximated by an anisotropic superconducting bar with critical current
density Jc=Ic/2aD, where Ic is the critical current of each tape, 2a is the
tape width, and D is the tape-to-tape periodicity. The current density J must
obey the constraint \int J dx = I/D, where the tapes lie parallel to the x axis
and are stacked along the z axis. We suppose that Jc is independent of field
(Bean approximation) and look for a solution to the critical state for
arbitrary height 2b of the stack. For c<|x|<a we have J=Jc, and for |x|<c the
critical state requires that Bz=0. We show that this implies \partial
J/\partial x=0 in the central region. Setting c as a constant (independent of
z) results in field profiles remarkably close to the desired one (Bz=0 for
|x|<c) as long as the aspect ratio b/a is not too small. We evaluate various
criteria for choosing c, and we show that the calculated hysteretic losses
depend only weakly on how c is chosen. We argue that for small D/a the
anisotropic homogeneous-medium approximation gives a reasonably accurate
estimate of the ac losses in a finite Z stack. The results for a Z stack can be
used to calculate the transport losses in a pancake coil wound with
superconducting tape.Comment: 21 pages, 17 figures, accepted by Supercond. Sci. Techno
Brokering Community–campus Partnerships: An Analytical Framework
Academic institutions and community-based organizations have increasingly recognized the value of working together to meet their different objectives and address common societal needs. In an effort to support the development and maintenance of these partnerships, a diversity of brokering initiatives has emerged. We describe these brokering initiatives broadly as coordinating mechanisms that act as an intermediary with an aim to develop collaborative and sustainable partnerships that provide mutual benefit. A broker can be an individual or an organization that helps connect and support relationships and share knowledge. To date, there has been little scholarly discussion or analysis of the various elements of these initiatives that contribute to successful community–campus partnerships. In an effort to better understand where these features may align and diverge, we reviewed a sample of community–campus brokering initiatives across North America and the United Kingdom to consider their different roles and activities. From this review, we developed a framework to delineate characteristics of different brokering initiatives to better understand their contributions to successful partnerships. The framework is divided into two parts. The first examines the different structural allegiances of the brokering initiatives by identifying their affiliation, principle purpose, and who received primary benefits. The second considers the dimensions of brokering activities in respect to their level of engagement, platforms used, scale of activity, and area of focus. The intention of the community campus engagement brokering framework is to provide an analytical tool for academics and community-based practitioners engaged in teaching and research partnerships. When developing a brokering initiative, these categories describing the different structures and dimensions encourage participants to think through the overall goals and objectives of the partnership and adapt the initiative accordingly
Deformation-Quantization of Complex Involutive Submanifolds
The sheaf of rings of WKB operators provides a deformation-quantization of
the cotangent bundle to a complex manifold. On a complex symplectic manifold
there may not exist a sheaf of rings locally isomorphic to a ring of WKB
operators. The idea is then to consider the whole family of locally defined
sheaves of WKB operators as the deformation-quantization of . To state it
precisely, one needs the notion of algebroid stack, introduced by Kontsevich.
In particular, the stack of WKB modules over defined in Polesello-Schapira
(see also Kashiwara for the contact case) is better understood as the stack of
modules over the algebroid stack of deformation-quantization of .
Let be an involutive submanifold of , and assume for simplicity that
the quotient of by its bicharacteristic leaves is isomorphic to a complex
symplectic manifold . The algebra of endomorphisms of a simple WKB module
along is locally (anti-)isomorphic to the pull-back of WKB operators on
. Hence we may say that a simple module provides a deformation-quantization
of . Again, since in general there do not exist globally defined simple WKB
modules, the idea is to consider the algebroid stack of locally defined simple
WKB modules as the deformation-quantization of .
In this paper we start by defining what an algebroid stack is, and how it is
locally described. We then discuss the algebroid stack of WKB operators on a
complex symplectic manifold , and define the deformation-quantization of an
involutive submanifold by means of simple WKB modules along . Finally,
we relate this deformation-quantization to that given by WKB operators on the
quotient of by its bicharacteristic leaves.Comment: 11 page
Characteristic classes for curves of genus one
We compute the cohomology of the stack M_1 with coefficients in Z[1/2], and
in low degrees with coefficients in Z. Cohomology classes on M_1 give rise to
characteristic classes, cohomological invariants of families of curves of genus
one. We prove a number of vanishing results for those characteristic classes,
and give explicit examples of families with non-vanishing characteristic
classes
The dynamics of z~1 clusters of galaxies from the GCLASS survey
We constrain the internal dynamics of a stack of 10 clusters from the GCLASS
survey at 0.87<z<1.34. We determine the stack cluster mass profile M(r) using
the MAMPOSSt algorithm of Mamon et al., the velocity anisotropy profile beta(r)
from the inversion of the Jeans equation, and the pseudo-phase-space density
profiles Q(r) and Qr(r), obtained from the ratio between the mass density
profile and the third power of the (total and, respectively, radial) velocity
dispersion profiles of cluster galaxies. Several M(r) models are statistically
acceptable for the stack cluster (Burkert, Einasto, Hernquist, NFW). The total
mass distribution has a concentration c=r200/r-2=4.0-0.6+1.0, in agreement with
theoretical expectations, and is less concentrated than the cluster
stellar-mass distribution. The stack cluster beta(r) is similar for passive and
star-forming galaxies and indicates isotropic galaxy orbits near the cluster
center and increasingly radially elongated with increasing cluster-centric
distance. Q(r) and Qr(r) are almost power-law relations with slopes similar to
those predicted from numerical simulations of dark matter halos. Combined with
results obtained for lower-z clusters we determine the dynamical evolution of
galaxy clusters, and compare it with theoretical predictions. We discuss
possible physical mechanisms responsible for the differential evolution of
total and stellar mass concentrations, and of passive and star-forming galaxy
orbits [abridged].Comment: 12 pages, 7 figures. Version accepted for publication in A&A after
minor modification
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