4,217 research outputs found
Coercivity and stability results for an extended Navier-Stokes system
In this article we study a system of equations that is known to {\em extend}
Navier-Stokes dynamics in a well-posed manner to velocity fields that are not
necessarily divergence-free. Our aim is to contribute to an understanding of
the role of divergence and pressure in developing energy estimates capable of
controlling the nonlinear terms. We address questions of global existence and
stability in bounded domains with no-slip boundary conditions. Even in two
space dimensions, global existence is open in general, and remains so,
primarily due to the lack of a self-contained energy estimate. However,
through use of new coercivity estimates for the linear equations, we
establish a number of global existence and stability results, including results
for small divergence and a time-discrete scheme. We also prove global existence
in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure
Energy Efficient Service Delivery in Clouds in Compliance with the Kyoto Protocol
Cloud computing is revolutionizing the ICT landscape by providing scalable
and efficient computing resources on demand. The ICT industry - especially data
centers, are responsible for considerable amounts of CO2 emissions and will
very soon be faced with legislative restrictions, such as the Kyoto protocol,
defining caps at different organizational levels (country, industry branch
etc.) A lot has been done around energy efficient data centers, yet there is
very little work done in defining flexible models considering CO2. In this
paper we present a first attempt of modeling data centers in compliance with
the Kyoto protocol. We discuss a novel approach for trading credits for
emission reductions across data centers to comply with their constraints. CO2
caps can be integrated with Service Level Agreements and juxtaposed to other
computing commodities (e.g. computational power, storage), setting a foundation
for implementing next-generation schedulers and pricing models that support
Kyoto-compliant CO2 trading schemes
Realizations of Differential Operators on Conic Manifolds with Boundary
We study the closed extensions (realizations) of differential operators
subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over
a manifold with boundary and conical singularities. Under natural ellipticity
conditions we determine the domains of the minimal and the maximal extension.
We show that both are Fredholm operators and give a formula for the relative
index.Comment: 41 pages, 1 figur
Assessing the role of accuracy-based feedback in value-driven attentional capture
© 2018, The Psychonomic Society, Inc. Despite being physically nonsalient and task-irrelevant, objects rendered in a color that once signaled monetary reward reflexively capture attention during visual search, a phenomenon known as value-driven attentional capture (VDAC). However, it remains a subject of empirical controversy whether learned reward associations are necessary to driving subsequent attentional capture: VDAC-like effects have been observed when accuracy-based feedback alone was used during the VDAC training phase, resulting in attentional capture by objects that were never associated with monetary reward; perplexingly, the presence of these VDAC-like effects in the literature conflicts with those of a number of control studies in which no such capture has been observed, leaving the issue currently unresolved. In this Registered Report, we present new empirical evidence of attentional capture by unrewarded former targets following limited accuracy-based training. We proposed to replicate these results in an independent sample and to test an empirically derived hypothesis concerning a methodological difference between the studies that have shown VDAC-like effects with accuracy-based feedback and those that have not. In short, we found no evidence that this methodological difference accounts for the inconsistencies in the literature, but our replication efforts were overwhelmingly successful, thus reinvigorating debate about the role that selection history may play in value-driven attentional capture
Global Theory of Quantum Boundary Conditions and Topology Change
We analyze the global theory of boundary conditions for a constrained quantum
system with classical configuration space a compact Riemannian manifold
with regular boundary . The space \CM of self-adjoint
extensions of the covariant Laplacian on is shown to have interesting
geometrical and topological properties which are related to the different
topological closures of . In this sense, the change of topology of is
connected with the non-trivial structure of \CM. The space \CM itself can
be identified with the unitary group \CU(L^2(\Gamma,\C^N)) of the Hilbert
space of boundary data L^2(\Gamma,\C^N). A particularly interesting family of
boundary conditions, identified as the set of unitary operators which are
singular under the Cayley transform, \CC_-\cap \CC_+ (the Cayley manifold),
turns out to play a relevant role in topology change phenomena. The singularity
of the Cayley transform implies that some energy levels, usually associated
with edge states, acquire an infinity energy when by an adiabatic change the
boundary condition reaches the Cayley submanifold \CC_-. In this sense
topological transitions require an infinite amount of quantum energy to occur,
although the description of the topological transition in the space \CM is
smooth. This fact has relevant implications in string theory for possible
scenarios with joint descriptions of open and closed strings. In the particular
case of elliptic self--adjoint boundary conditions, the space \CC_- can be
identified with a Lagrangian submanifold of the infinite dimensional
Grassmannian. The corresponding Cayley manifold \CC_- is dual of the Maslov
class of \CM.Comment: 29 pages, 2 figures, harvma
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