667 research outputs found
A near-wall two-equation model for compressible turbulent flows
A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper
Spherically symmetric black holes in minimally modified self-dual gravity
We discuss spherically symmetric black holes in the modified self-dual theory
of gravity recently studied by Krasnov, obtained adding a Weyl-curvature
dependent `cosmological term' to the Plebanski lagrangian for general
relativity. This type of modified gravity admits two different types of
singularities: one is a true singularity for the theory where the fundamental
fields of the theory, as well as the (auxiliary) spacetime metric, become
singular, and the other one is a milder "non-metric singularity" where the
metric description of the spacetime breaks down but the fundamental fields
themselves are regular. We first generalise this modified self-dual gravity to
include Maxwell's field and then study basic features of spherically symmetric,
charged black holes, with particular focus on whether these two types of
singularities are hidden or naked. We restrict our attention to minimal forms
of the modification, and find that the theory exhibits `screening' effects of
the electric charge (or `anti-screening', depending upon the sign of the
modification term), in the sense that it leads to the possibility of charging
the black hole more (or less) than it would be possible in general relativity
without exposing a naked singularity. We also find that for any (even
arbitrarily large) value of charge, true singularities of the theory appear to
be either achronal (non-timelike) covered by the hypersurface of a harmless
non-metric singularity, or simply hidden inside at least one Killing horizon.Comment: 42 pages, many colour figures. v2: discussion of the conformal
ambiguity improved, references added. v3: amended to match published versio
Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum
gravity, using the spinfoam formalism, up to some second order terms in the
expansion parameter.Comment: 41 pages, 6 figure
A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
We study the insertion and value of metric observables in the (discrete) path
integral formulation of the Ponzano-Regge spinfoam model for 3d quantum
gravity. In particular, we discuss the length spectrum and the relation between
insertion of such B-observables and gauge fixing in the path integral.Comment: 17 page
Polyhedra in loop quantum gravity
Interwiners are the building blocks of spin-network states. The space of
intertwiners is the quantization of a classical symplectic manifold introduced
by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to
interpret generic configurations in this space as bounded convex polyhedra in
Euclidean space: a polyhedron is uniquely described by the areas and normals to
its faces. We provide a reconstruction of the geometry of the polyhedron: we
give formulas for the edge lengths, the volume and the adjacency of its faces.
At the quantum level, this correspondence allows us to identify an intertwiner
with the state of a quantum polyhedron, thus generalizing the notion of quantum
tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent
intertwiners result to be peaked on the classical geometry of polyhedra. We
discuss the relevance of this result for loop quantum gravity. In particular,
coherent spin-network states with nodes of arbitrary valence represent a
collection of semiclassical polyhedra. Furthermore, we introduce an operator
that measures the volume of a quantum polyhedron and examine its relation with
the standard volume operator of loop quantum gravity. We also comment on the
semiclassical limit of spinfoams with non-simplicial graphs.Comment: 32 pages, many figures. v2 minor correction
Area-angle variables for general relativity
We introduce a modified Regge calculus for general relativity on a
triangulated four dimensional Riemannian manifold where the fundamental
variables are areas and a certain class of angles. These variables satisfy
constraints which are local in the triangulation. We expect the formulation to
have applications to classical discrete gravity and non-perturbative approaches
to quantum gravity.Comment: 7 pages, 1 figure. v2 small changes to match published versio
Second-order amplitudes in loop quantum gravity
We explore some second-order amplitudes in loop quantum gravity. In
particular, we compute some second-order contributions to diagonal components
of the graviton propagator in the large distance limit, using the old version
of the Barrett-Crane vertex amplitude. We illustrate the geometry associated to
these terms. We find some peculiar phenomena in the large distance behavior of
these amplitudes, related with the geometry of the generalized triangulations
dual to the Feynman graphs of the corresponding group field theory. In
particular, we point out a possible further difficulty with the old
Barrett-Crane vertex: it appears to lead to flatness instead of Ricci-flatness,
at least in some situations. The observation raises the question whether this
difficulty remains with the new version of the vertex.Comment: 22 pages, 18 figure
Euclidean three-point function in loop and perturbative gravity
We compute the leading order of the three-point function in loop quantum
gravity, using the vertex expansion of the Euclidean version of the new spin
foam dynamics, in the region of gamma<1. We find results consistent with Regge
calculus in the limit gamma->0 and j->infinity. We also compute the tree-level
three-point function of perturbative quantum general relativity in position
space, and discuss the possibility of directly comparing the two results.Comment: 16 page
On knottings in the physical Hilbert space of LQG as given by the EPRL model
We consider the EPRL spin foam amplitude for arbitrary embedded
two-complexes. Choosing a definition of the face- and edge amplitudes which
lead to spin foam amplitudes invariant under trivial subdivisions, we
investigate invariance properties of the amplitude under consistent
deformations, which are deformations of the embedded two-complex where faces
are allowed to pass through each other in a controlled way. Using this
surprising invariance, we are able to show that in the physical Hilbert space
as defined by the sum over all spin foams contains no knotting classes of
graphs anymore.Comment: 22 pages, 14 figure
Joint PDF modelling of turbulent flow and dispersion in an urban street canyon
The joint probability density function (PDF) of turbulent velocity and
concentration of a passive scalar in an urban street canyon is computed using a
newly developed particle-in-cell Monte Carlo method. Compared to moment
closures, the PDF methodology provides the full one-point one-time PDF of the
underlying fields containing all higher moments and correlations. The
small-scale mixing of the scalar released from a concentrated source at the
street level is modelled by the interaction by exchange with the conditional
mean (IECM) model, with a micro-mixing time scale designed for geometrically
complex settings. The boundary layer along no-slip walls (building sides and
tops) is fully resolved using an elliptic relaxation technique, which captures
the high anisotropy and inhomogeneity of the Reynolds stress tensor in these
regions. A less computationally intensive technique based on wall functions to
represent boundary layers and its effect on the solution are also explored. The
calculated statistics are compared to experimental data and large-eddy
simulation. The present work can be considered as the first example of
computation of the full joint PDF of velocity and a transported passive scalar
in an urban setting. The methodology proves successful in providing high level
statistical information on the turbulence and pollutant concentration fields in
complex urban scenarios.Comment: Accepted in Boundary-Layer Meteorology, Feb. 19, 200
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