1,948 research outputs found
The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
For low density gases the validity of the Boltzmann transport equation is
well established. The central object is the one-particle distribution function,
, which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad
and, much refined, Cercignani argue for the existence of this limit on the
basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic
time span, the argument can be made mathematically precise following the
seminal work of Lanford. In this article a corresponding programme is
undertaken for weakly nonlinear, both discrete and continuum, wave equations.
Our working example is the harmonic lattice with a weakly nonquadratic on-site
potential. We argue that the role of the Boltzmann -function is taken over
by the Wigner function, which is a very convenient device to filter the slow
degrees of freedom. The Wigner function, so to speak, labels locally the
covariances of dynamically almost stationary measures. One route to the phonon
Boltzmann equation is a Gaussian decoupling, which is based on the fact that
the purely harmonic dynamics has very good mixing properties. As a further
approach the expansion in terms of Feynman diagrams is outlined. Both methods
are extended to the quantized version of the weakly nonlinear wave equation.
The resulting phonon Boltzmann equation has been hardly studied on a rigorous
level. As one novel contribution we establish that the spatially homogeneous
stationary solutions are precisely the thermal Wigner functions. For three
phonon processes such a result requires extra conditions on the dispersion law.
We also outline the reasoning leading to Fourier's law for heat conduction.Comment: special issue on "Kinetic Theory", Journal of Statistical Physics,
improved versio
A stability condition for turbulence model: From EMMS model to EMMS-based turbulence model
The closure problem of turbulence is still a challenging issue in turbulence
modeling. In this work, a stability condition is used to close turbulence.
Specifically, we regard single-phase flow as a mixture of turbulent and
non-turbulent fluids, separating the structure of turbulence. Subsequently,
according to the picture of the turbulent eddy cascade, the energy contained in
turbulent flow is decomposed into different parts and then quantified. A
turbulence stability condition, similar to the principle of the
energy-minimization multi-scale (EMMS) model for gas-solid systems, is
formulated to close the dynamic constraint equations of turbulence, allowing
the heterogeneous structural parameters of turbulence to be optimized. We call
this model the `EMMS-based turbulence model', and use it to construct the
corresponding turbulent viscosity coefficient. To validate the EMMS-based
turbulence model, it is used to simulate two classical benchmark problems,
lid-driven cavity flow and turbulent flow with forced convection in an empty
room. The numerical results show that the EMMS-based turbulence model improves
the accuracy of turbulence modeling due to it considers the principle of
compromise in competition between viscosity and inertia.Comment: 26 pages, 13 figures, 2 table
Turbulent Cells in Stars: I. Fluctuations in Kinetic Energy and Luminosity
Three-dimensional (3D) hydrodynamic simulations of shell oxygen burning
(Meakin and Arnett, 2007b) exhibit bursty, recurrent fluctuations in turbulent
kinetic energy. These are shown to be due to a general instability of the
convective cell, requiring only a localized source of heating or cooling. Such
fluctuations are shown to be suppressed in simulations of stellar evolution
which use mixing-length theory (MLT).
Quantitatively similar behavior occurs in the model of a convective roll
(cell) of Lorenz (1963), which is known to have a strange attractor that gives
rise to chaotic fluctuations in time of velocity and, as we show, luminosity.
Study of simulations suggests that the behavior of a Lorenz convective roll may
resemble that of a cell in convective flow. We examine some implications of
this simplest approximation, and suggest paths for improvement.
Using the Lorenz model as representative of a convective cell, a
multiple-cell model of a convective layer gives total luminosity fluctuations
which are suggestive of irregular variables (red giants and supergiants
(Schwarzschild 1975)), and of the long secondary period feature in semi-regular
AGB variables (Stothers 2010, Wood, Olivier and Kawaler 2004). This
"tau-mechanism" is a new source for stellar variability, which is inherently
non-linear (unseen in linear stability analysis), and one closely related to
intermittency in turbulence. It was already implicit in the 3D global
simulations of Woodward, Porter and Jacobs (2003). This fluctuating behavior is
seen in extended 2D simulations of CNeOSi burning shells (Arnett and Meakin
2011b), and may cause instability which leads to eruptions in progenitors of
core collapse supernovae PRIOR to collapse.Comment: 30 pages, 13 figure
Resolution Study for Three-dimensional Supernova Simulations with the Prometheus-Vertex Code
We present a carefully designed, systematic study of the angular resolution
dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics
code. Employing a simplified neutrino heating-cooling scheme in the Prometheus
hydrodynamics module allows us to sample the angular resolution between 4
degrees and 0.5 degrees. With a newly-implemented static mesh refinement (SMR)
technique on the Yin-Yang grid, the angular coordinates can be refined in
concentric shells, compensating for the diverging structure of the spherical
grid. In contrast to previous studies with Prometheus and other codes, we find
that higher angular resolution and therefore lower numerical viscosity provides
more favorable explosion conditions and faster shock expansion. We discuss the
possible reasons for the discrepant results. The overall dynamics seem to
converge at a resolution of about 1 degree. Applying the SMR setup to
marginally exploding progenitors is disadvantageous for the shock expansion,
however, because kinetic energy of downflows is dissipated to internal energy
at resolution interfaces, leading to a loss of turbulent pressure support and a
steeper temperature gradient. We also present a way to estimate the numerical
viscosity on grounds of the measured turbulent kinetic-energy spectrum, leading
to smaller values that are better compatible with the flow behavior witnessed
in our simulations than results following calculations in previous literature.
Interestingly, the numerical Reynolds numbers in the turbulent, neutrino-heated
postshock layer (some 10 to several 100) are in the ballpark of expected
neutrino-drag effects on the relevant length scales in the turbulent postshock
layer. We provide a formal derivation and quantitative assessment of the
neutrino drag terms in an appendix.Comment: 37 pages, 14 figures, 4 tables; revised version with neutrino drag
discussion extended for numerical evaluation; accepted by Ap
Efficient prediction of broadband trailing edge noise and application to porous edge treatment
Trailing edge noise generated by turbulent flow traveling past an edge of an
airfoil is one of the most essential aeroacoustic sound generation mechanisms.
It is of great interest for noise problems in various areas of industrial
application. First principle based CAA with short response time are needed in
the industrial design process for reliable prediction of spectral differences
in turbulent-boundary-layer trailing-edge noise due to design modifications. In
this paper, an aeroacoustic method is studied, resting on a hybrid CFD/CAA
procedure. In a first step RANS simulation provides a time-averaged solution,
including the mean-flow and turbulence statistics such as length-scale,
time-scale and turbulence kinetic energy. Based on these, fluctuating sound
sources are then stochastically generated by the Fast Random Particle-Mesh
Method to simulate in a second CAA step broadband aeroacoustic sound. From
experimental findings it is well known that porous trailing edges significantly
lower trailing edge noise level over a large range of frequencies reaching up
to 8dB reduction. Furthermore, sound reduction depends on the porous material
parameters, e.g. geometry, porosity, permeability and pore size. The paper
presents first results for an extended hybrid CFD/CAA method including porous
materials with prescribed parameters. To incorporate the effect of porosity, an
extended formulation of the Acoustic Perturbation Equations with source terms
is derived based on a reformulation of the volume averaged Navier-Stokes
equations into perturbation form. Proper implementation of the Darcy and
Forchheimer terms is verified for sound propagation in homogeneous and
anisotropic porous medium. Sound generation is studied for a generic symmetric
NACA0012 airfoil without lift to separate secondary effects of lift and camber
on sound from those of the basic edge noise treatments.Comment: 37 page
On statistical equilibrium in helical fluid flows
International audienceThe statistical mechanics of 3-D helical flows is re-examined for a continuum truncated at a top wavenumber. Based on the principle of equipartition of the flow enstrophy between helical modes, the emerging (i) energy spectrum law "?2" and (ii) formal mathematical analogy between the helicity and the thermodynamic entropy are discussed. It is noted that the "?2" scaling law is consistent with both spectral equilibrium and spectral cascade paradigms. In an attempt to apply the obtained results to a turbulent flow regime within the Earth's outer liquid core, where the net helicity of a turbulent flow component is presumably explained by Earth's rotation, it has been noticed that it is the energy spectral law "?1", but not "?2", which is likely realized there and within the logarithmic accuracy corresponds to the case of the velocity structure function [u(l)]2 independency on the spatial scale l, the latter is consistent with observations. It is argued that the "?1" scaling law can also be interpreted in terms of the spectral equilibrium and it is emphasized that the causes of the likely dominance of the spectral law "?1" over the spectral law "?2" in this geophysical application deserve further investigation and clarification
Selection theorem for systems with inheritance
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic
systems is studied. A non-linear kinetic system with conservation of supports
for distributions has generically finite-dimensional asymptotics. Such systems
are apparent in many areas of biology, physics (the theory of parametric wave
interaction), chemistry and economics. This conservation of support has a
biological interpretation: inheritance. The finite-dimensional asymptotics
demonstrates effects of "natural" selection. Estimations of the asymptotic
dimension are presented. After some initial time, solution of a kinetic
equation with conservation of support becomes a finite set of narrow peaks that
become increasingly narrow over time and move increasingly slowly. It is
possible that these peaks do not tend to fixed positions, and the path covered
tends to infinity as t goes to infinity. The drift equations for peak motion
are obtained. Various types of distribution stability are studied: internal
stability (stability with respect to perturbations that do not extend the
support), external stability or uninvadability (stability with respect to
strongly small perturbations that extend the support), and stable realizability
(stability with respect to small shifts and extensions of the density peaks).
Models of self-synchronization of cell division are studied, as an example of
selection in systems with additional symmetry. Appropriate construction of the
notion of typicalness in infinite-dimensional space is discussed, and the
notion of "completely thin" sets is introduced.
Key words: Dynamics; Attractor; Evolution; Entropy; Natural selectionComment: 46 pages, the final journal versio
Equilibration of a baroclinic planetary atmosphere toward the limit of vanishing bottom friction
This is the author accepted manuscript. The final version is available from the American Meteorological Society via the DOI in this record.This paper discusses whether and how a baroclinic atmosphere can equilibrate with very small bottom friction in a dry, primitive equation, general circulation model. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and it is damped by a linear friction near the lower boundary. When friction is decreased by four orders of magnitude, kinetic energy dissipation by friction gradually becomes negligible,while “energy recycling” becomes dominant. In this limit kinetic energy is converted back into potential energy at the largest scales, thus closing the energy cycle without significant frictional dissipation. The momentum fluxes are of opposite sign in the upper and lower atmosphere: in the upper atmosphere, eddies converge momentum into the westerly jets, however, in the lower atmosphere, the eddies diverge momentum out of the westerly jets. The secondary circulation driven by the meridional eddy momentum fluxes thus acts to increase the baroclinicity of the westerly jet. This regime may be relevant for the Jovian atmosphere, where the frictional time scale may be much larger than the radiative damping time scale.This work was funded by the NSF under grant
656 AGS-1144302 and the NOAA under grant NA08OAR4320752
Primordial magnetic fields
Large scale magnetic fields represent a triple point where cosmology,
high-energy physics and astrophysics meet for different but related purposes.
After reviewing the implications of large scale magnetic fields in these
different areas, the role of primordial magnetic fields is discussed in various
physical processes occurring prior to the decoupling epoch with particular
attention to the big bang nucleosynthesis (BBN) epoch and to the electroweak
(EW) epoch. The generation of matter--antimatter isocurvature fluctuations,
induced by hypermagnetic fields, is analyzed in light of a possible increase of
extra-relativistic species at BBN. It is argued that stochastic GW backgrounds
can be generated by hypermagnetic fields at the LISA frequency. The problem of
the origin of large scale magnetic fields is also scrutinized.Comment: 41 pages in Latex style, 5 figure
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