1,212 research outputs found
Twisted geometries: A geometric parametrisation of SU(2) phase space
A cornerstone of the loop quantum gravity program is the fact that the phase
space of general relativity on a fixed graph can be described by a product of
SU(2) cotangent bundles per edge. In this paper we show how to parametrize this
phase space in terms of quantities describing the intrinsic and extrinsic
geometry of the triangulation dual to the graph. These are defined by the
assignment to each triangle of its area, the two unit normals as seen from the
two polyhedra sharing it, and an additional angle related to the extrinsic
curvature. These quantities do not define a Regge geometry, since they include
extrinsic data, but a looser notion of discrete geometry which is twisted in
the sense that it is locally well-defined, but the local patches lack a
consistent gluing among each other. We give the Poisson brackets among the new
variables, and exhibit a symplectomorphism which maps them into the Poisson
brackets of loop gravity. The new parametrization has the advantage of a simple
description of the gauge-invariant reduced phase space, which is given by a
product of phase spaces associated to edges and vertices, and it also provides
an abelianisation of the SU(2) connection. The results are relevant for the
construction of coherent states, and as a byproduct, contribute to clarify the
connection between loop gravity and its subset corresponding to Regge
geometries.Comment: 28 pages. v2 and v3 minor change
On the geometry of loop quantum gravity on a graph
We discuss the meaning of geometrical constructions associated to loop
quantum gravity states on a graph. In particular, we discuss the "twisted
geometries" and derive a simple relation between these and Regge geometries.Comment: 6 pages, 1 figure. v2: some typos corrected, references update
Discussion of the potential and limitations of direct and large-eddy simulations
The full text of the discussion paper presented at the Whither Turbulence Workshop on the potential and limitations of direct and large-eddy simulations is provided. Particular emphasis is placed on discussing the role of numerics and mathematical theory in direct simulations of both compressible and incompressible flows. A variety of unresolved issues with large-eddy simulations such as their implementation in high-order finite difference codes, problems with defiltering, and modifications to accommodate integrations to solid boundaries are elaborated on. These as well as other points are discussed in detail along with the authors' views concerning the prospects for future research
Sustainability Reporting as a Challenge for Performance Measurement: Literature Review
This paper aims to provide a systematic literature review of scientific works on the integration of performance measurement (PM) and sustainability reporting (SR) applying content analysis. The research question is how performance measurement system (PMS) could help to ensure an effective sustainability reporting. The literature review shows the relationship between PMS and sustainability reporting in terms of integrated purpose, measurements and actors/ownership in supporting the decision-making process at different stages: planning, control, and reporting
On the prediction of turbulent secondary flows
The prediction of turbulent secondary flows, with Reynolds stress models, in circular pipes and non-circular ducts is reviewed. Turbulence-driven secondary flows in straight non-circular ducts are considered along with turbulent secondary flows in pipes and ducts that arise from curvature or a system rotation. The physical mechanisms that generate these different kinds of secondary flows are outlined and the level of turbulence closure required to properly compute each type is discussed in detail. Illustrative computations of a variety of different secondary flows obtained from two-equation turbulence models and second-order closures are provided to amplify these points
From twistors to twisted geometries
In a previous paper we showed that the phase space of loop quantum gravity on
a fixed graph can be parametrized in terms of twisted geometries, quantities
describing the intrinsic and extrinsic discrete geometry of a cellular
decomposition dual to the graph. Here we unravel the origin of the phase space
from a geometric interpretation of twistors.Comment: 9 page
On the large-eddy simulation of transitional wall-bounded flows
The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed
Toward the large-eddy simulation of compressible turbulent flows
New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96(exp 3) grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence (conducted on a coarse 32(exp 3) grid) is shown to yield results that are in excellent agreement with the fine grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly
On the subgrid-scale modeling of compressible turbulence
A subgrid-scale model recently derived for use in the large-eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is applicable only to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre-filtered fields, is suggested which appears to reduce these limitations
Physical boundary state for the quantum tetrahedron
We consider stability under evolution as a criterion to select a physical
boundary state for the spinfoam formalism. As an example, we apply it to the
simplest spinfoam defined by a single quantum tetrahedron and solve the
associated eigenvalue problem at leading order in the large spin limit. We show
that this fixes uniquely the free parameters entering the boundary state.
Remarkably, the state obtained this way gives a correlation between edges which
runs at leading order with the inverse distance between the edges, in agreement
with the linearized continuum theory. Finally, we give an argument why this
correlator represents the propagation of a pure gauge, consistently with the
absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure
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