434 research outputs found
Spinors in Weyl Geometry
We consider the wave equation for spinors in -dimensional Weyl
geometry. By appropriately coupling the Weyl vector as well as
the spin connection to the spinor field, conformal
invariance can be maintained. The one loop effective action generated by the
coupling of the spinor field to an external gravitational field is computed in
two dimensions. It is found to be identical to the effective action for the
case of a scalar field propagating in two dimensions.Comment: 13 pages, REVTEX, no figure
Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues
Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of
research in recent years. Many challenges remain in theory, scaling, physical understanding,
experimental techniques, and numerical simulations. In this paper we distill the salient advances of
recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding
questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the
principal model parameters such as the von Kármán “constant,” the parametrization of roughness
effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that
may provide answers to these questions, notably the improvement of measuring techniques and the
construction of new facilities, are identified. We also highlight aspects where differences of opinion
persist, with the expectation that this discussion might mark the beginning of their resolution
Scaling in Wall Turbulence: Scale Separation and Interaction (Invited Paper)
High Reynolds number pipe flow data are used to demonstrate the importance of several conditions related to scale separation that are either assumed in the classical theories
or may be used in light of recent results in wall turbulence to infer a minimum Reynolds number condition above which scaling results may be suitable for extrapolation. Results from the Princeton Superpipe have suggested Re_τ > 5000 as the minimum Reynolds number
for which key properties of pipe flow reach a “fully-developed” condition, based on observations of streamwise mean and turbulent velocity structure. Additional values related to finer constraints on the structural development are also discussed. A “skeleton” of wall turbulence is introduced, based on structural components identified as having a dominant role in the dynamics of near-wall turbulence in recent experiments by a variety of authors.
Possible interaction mechanisms between these components are described alongside some outstanding questions concerning scale separation and interaction
Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes
This article reports on one component of a larger study on measurement of the zero-pressure-gradient turbulent flat plate boundary layer, in which a detailed investigation was conducted of the suite of corrections required for mean velocity measurements performed using Pitot tubes. In particular, the corrections for velocity shear across the tube and for blockage effects which occur when the tube is in close proximity to the wall were investigated using measurements from Pitot tubes of five different diameters, in two different facilities, and at five different Reynolds numbers ranging from Re_θ = 11 100 to 67 000. Only small differences were found amongst commonly used corrections for velocity shear, but improvements were found for existing near-wall proximity corrections. Corrections for the nonlinear averaging of the velocity fluctuations were also investigated, and the results compared to hot-wire data taken as part of the same measurement campaign. The streamwise turbulence-intensity correction was found to be of comparable magnitude to that of the shear correction, and found to bring the hot-wire and Pitot results into closer agreement when applied to the data, along with the other corrections discussed and refined here
Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory
We examine in non-Abelian gauge theory the heavy quark limit in the presence
of the (anti-)self-dual homogeneous background field and see that a confining
potential emerges, consistent with the Wilson criterion, although the potential
is quadratic and not linear in the quark separation. This builds upon the
well-known feature that propagators in such a background field are entire
functions. The way in which deconfinement can occur at finite temperature is
then studied in the static temporal gauge by calculation of the effective
potential at high temperature. Finally we discuss the problems to be surmounted
in setting up the calculation of the effective potential nonperturbatively on
the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2
and
Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
We apply the open systems concept and the influence functional formalism
introduced in Paper I to establish a stochastic theory of relativistic moving
spinless particles in a quantum scalar field. The stochastic regime resting
between the quantum and semi-classical captures the statistical mechanical
attributes of the full theory. Applying the particle-centric world-line
quantization formulation to the quantum field theory of scalar QED we derive a
time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it
is the correct semiclassical limit for nonlinear particle-field systems without
the need of making the dipole or non-relativistic approximations. Progressing
to the stochastic regime, we derive multiparticle ALD-Langevin equations for
nonlinearly coupled particle-field systems. With these equations we show how to
address time-dependent dissipation/noise/renormalization in the semiclassical
and stochastic limits of QED. We clarify the the relation of radiation
reaction, quantum dissipation and vacuum fluctuations and the role that initial
conditions may play in producing non-Lorentz invariant noise. We emphasize the
fundamental role of decoherence in reaching the semiclassical limit, which also
suggests the correct way to think about the issues of runaway solutions and
preacceleration from the presence of third derivative terms in the ALD
equation. We show that the semiclassical self-consistent solutions obtained in
this way are ``paradox'' and pathology free both technically and conceptually.
This self-consistent treatment serves as a new platform for investigations into
problems related to relativistic moving charges.Comment: RevTex; 20 pages, 3 figures, Replaced version has corrected typos,
slightly modified derivation, improved discussion including new section with
comparisons to related work, and expanded reference
Radiative Corrections to the Inflaton Potential as an Explanation of Suppressed Large Scale Power in Density Perturbations and the Cosmic Microwave Background
The Wilkinson Microwave Anisotropy Probe microwave background data suggest
that the primordial spectrum of scalar curvature fluctuations is suppressed at
small wavenumbers. We propose a UV/IR mixing effect in small-field inflationary
models that can explain the observable deviation in WMAP data from the
concordance model. Specifically, in inflationary models where the inflaton
couples to an asymptotically free gauge theory, the radiative corrections to
the effective inflaton potential can be anomalously large. This occurs for
small values of the inflaton field which are of the order of the gauge theory
strong coupling scale. Radiative corrections cause the inflaton potential to
blow up at small values of the inflaton field. As a result, these corrections
can violate the slow-roll condition at the initial stage of the inflation and
suppress the production of scalar density perturbations.Comment: 20 pages, 2 figures, v2: refs added, v3: JCAP versio
Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata
A discretized time evolution of the wave function for a Dirac particle on a
cubic lattice is represented by a very simple quantum cellular automaton. In
each evolution step the updated value of the wave function at a given site
depends only on the values at the nearest sites, the evolution is unitary and
preserves chiral symmetry. Moreover, it is shown that the relationship between
Dirac particles and cellular automata operating on two component objects on a
lattice is indeed very close. Every local and unitary automaton on a cubic
lattice, under some natural assumptions, leads in the continuum limit to the
Weyl equation. The sum over histories is evaluated and its connection with path
integrals and theories of fermions on a lattice is outlined.Comment: 6, RevTe
External and Turbomachinery Flow Control Working Group
Broad Flow Control Issues: a) Understanding flow physics. b) Specific control objective(s). c) Actuation. d) Sensors. e) Integrated active flow control system. f) Development of design tools (CFD, reduced order models, controller design, understanding and utilizing instabilities and other mechanisms, e.g., streamwise vorticity)
Statistical Properties of Turbulence: An Overview
We present an introductory overview of several challenging problems in the
statistical characterisation of turbulence. We provide examples from fluid
turbulence in three and two dimensions, from the turbulent advection of passive
scalars, turbulence in the one-dimensional Burgers equation, and fluid
turbulence in the presence of polymer additives.Comment: 34 pages, 31 figure
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