18,819 research outputs found
Intermittency in passive scalar advection
A Lagrangian method for the numerical simulation of the Kraichnan passive
scalar model is introduced. The method is based on Monte--Carlo simulations of
tracer trajectories, supplemented by a point-splitting procedure for coinciding
points. Clean scaling behavior for scalar structure functions is observed. The
scheme is exploited to investigate the dependence of scalar anomalies on the
scaling exponent of the advecting velocity field. The three-dimensional
fourth-order structure function is specifically considered.Comment: 4 pages, 5 figure
Electromagnetic Vacuum of Complex Media: Dipole Emission vs. Light Propagation, Vacuum Energy, and Local Field Factors
We offer a unified approach to several phenomena related to the
electromagnetic vacuum of a complex medium made of point electric dipoles. To
this aim, we apply the linear response theory to the computation of the
polarization field propagator and study the spectrum of vacuum fluctuations.
The physical distinction among the local density of states which enter the
spectra of light propagation, total dipole emission, coherent emission, total
vacuum energy and Schwinger-bulk energy is made clear. Analytical expressions
for the spectrum of dipole emission and for the vacuum energy are derived.
Their respective relations with the spectrum of external light and with the
Schwinger-bulk energy are found. The light spectrum and the Schwinger-bulk
energy are determined by the Dyson propagator. The emission spectrum and the
total vacuum energy are determined by the polarization propagator. An exact
relationship of proportionality between both propagators is found in terms of
local field factors. A study of the nature of stimulated emission from a single
dipole is carried out. Regarding coherent emission, it contains two components.
A direct one which is transferred radiatively and directly from the emitter
into the medium and whose spectrum is that of external light. And an indirect
one which is radiated by induced dipoles. The induction is mediated by one (and
only one) local field factor. Regarding the vacuum energy, we find that in
addition to the Schwinger-bulk energy the vacuum energy of an effective medium
contains local field contributions proportional to the resonant frequency and
to the spectral line-width.Comment: Typos fixed, journal ref. adde
Passive Scalar Structures in Supersonic Turbulence
We conduct a systematic numerical study of passive scalar structures in
supersonic turbulent flows. We find that the degree of intermittency in the
scalar structures increases only slightly as the flow changes from transonic to
highly supersonic, while the velocity structures become significantly more
intermittent. This difference is due to the absence of shock-like
discontinuities in the scalar field. The structure functions of the scalar
field are well described by the intermittency model of She and L\'{e}v\^{e}que
[Phys. Rev. Lett. 72, 336 (1994)], and the most intense scalar structures are
found to be sheet-like at all Mach numbers.Comment: 4 pages, 3 figures, to appear in PR
Nonlocal pseudopotentials and magnetic fields
We show how to describe the coupling of electrons to non-uniform magnetic
fields in the framework of the widely used norm-conserving pseudopotential
appro ximation for electronic structure calculations. Our derivation applies to
magnetic fields that are smooth on the scale of the core region. The method is
validated by application to the calculation of the magnetic susceptibility of
molecules. Our results are compared with high quality all electron quantum
chemical results, and another recently proposed formalism.Comment: 4 pages, submitted to Physical Review Letter
"Locally homogeneous turbulence" Is it an inconsistent framework?
In his first 1941 paper Kolmogorov assumed that the velocity has increments
which are homogeneous and independent of the velocity at a suitable reference
point. This assumption of local homogeneity is consistent with the nonlinear
dynamics only in an asymptotic sense when the reference point is far away. The
inconsistency is illustrated numerically using the Burgers equation.
Kolmogorov's derivation of the four-fifths law for the third-order structure
function and its anisotropic generalization are actually valid only for
homogeneous turbulence, but a local version due to Duchon and Robert still
holds. A Kolomogorov--Landau approach is proposed to handle the effect of
fluctuations in the large-scale velocity on small-scale statistical properties;
it is is only a mild extension of the 1941 theory and does not incorporate
intermittency effects.Comment: 4 pages, 2 figure
Statistics of mixing in three-dimensional Rayleigh--Taylor turbulence at low Atwood number and Prandtl number one
Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood
number and at Prandtl number one is investigated by means of high resolution
direct numerical simulations of the Boussinesq equations. RT turbulence is a
paradigmatic time-dependent turbulent system in which the integral scale grows
in time following the evolution of the mixing region. In order to fully
characterize the statistical properties of the flow, both temporal and spatial
behavior of relevant statistical indicators have been analyzed.
Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynolds
numbers) and scale dependent observables built in terms of velocity and
temperature fluctuations are considered. We extend the mean-field analysis for
velocity and temperature fluctuations to take into account intermittency, both
in time and space domains. We show that the resulting scaling exponents are
compatible with those of classical Navier--Stokes turbulence advecting a
passive scalar at comparable Reynolds number. Our results support the scenario
of universality of turbulence with respect to both the injection mechanism and
the geometry of the flow
On the von Karman-Howarth equations for Hall MHD flows
The von Karman-Howarth equations are derived for three-dimensional (3D) Hall
magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic
turbulence. From these equations, we derive exact scaling laws for the
third-order correlation tensors. We show how these relations are compatible
with previous heuristic and numerical results. These multi-scale laws provide a
relevant tool to investigate the non-linear nature of the high frequency
magnetic field fluctuations in the solar wind or, more generally, in any plasma
where the Hall effect is important.Comment: 11 page
Phase ordering of two-dimensional symmetric binary fluids: a droplet scaling state
The late-stage phase ordering, in dimensions, of symmetric fluid
mixtures violates dynamical scaling. We show however that, even at 50/50 volume
fractions, if an asymmetric droplet morphology is initially present then this
sustains itself, throughout the viscous hydrodynamic regime, by a
`coalescence-induced coalescence' mechanism. Scaling is recovered (with length
scale , as in ). The crossover to the inertial hydrodynamic
regime is delayed even longer than in ; on entering it, full symmetry is
finally restored and we find , regardless of the initial state.Comment: 4 pages, three figures include
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