A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae at each order by using results from previous orders. In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases. We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process-dependent and our heat current depends on the gradients of both temperature and density. On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper. In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page

Radiative Transfer in Star Formation: Testing FLD and Hybrid Methods

We perform a comparison between two radiative transfer algorithms commonly employed in hydrodynamical calculations of star formation: grey flux limited diffusion and the hybrid scheme, in addition we compare these algorithms to results from the Monte-Carlo radiative transfer code MOCASSIN. In disc like density structures the hybrid scheme performs significantly better than the FLD method in the optically thin regions, with comparable results in optically thick regions. In the case of a forming high mass star we find the FLD method significantly underestimates the radiation pressure by a factor of ~100.Comment: 4 Pages; to appear in the proceedings of 'The Labyrinth of Star Formation', Crete, 18-22 June 201

Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions

The paper is concerned with the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When the initial vorticity is in the Lebesgue space $L^q$ with $2<q\le\infty$, we show the degenerate viscous lake equations possess a unique global solution and the solution converges to a corresponding weak solution of the inviscid lake equations. In the special case when the vorticity is in $L^\infty$, an explicit convergence rate is obtained

Assessing the risk of climate change for buildings: A comparison between multi-year and probabilistic reference year simulations

Copyright © 2011 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Building and Environment . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Building and Environment Vol. 46 (2011), DOI: 10.1016/j.buildenv.2010.12.018Given a changing climate, there is a need to provide data for future years so that practicing engineers can investigate the impact of climate change on particular designs and examine any risk the client might be exposed to. In addition, such files are of use to building scientists in developing generic solutions to problems such as elevated internal temperatures and poor thermal comfort. With the release of the UK Climate Projections (UKCP09) [1], and the publication of a methodology for the creation of probabilistic future reference years using the UKCP09 weather generator [2], it is possible to model future building performance. However, the collapse of the distribution of possibilities inherent in the UKCP09 method into a single reference year or a small number of reference years, potentially means the loss of most of the information about the potential range of the response of the building and of the risk occupants might be subject to. In this paper we model for the first time the internal conditions and energy use of a building with all 3000 example years produced by the UKCP09 weather generator in an attempt to study the full range of response and risk. The resultant histograms and cumulative distribution functions are then used to examine whether single reference years can be used to answer questions about response and risk under a changing climate, or whether a more probabilistic approach is unavoidable

Fluctuation-Response Relations for Multi-Time Correlations

We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control term'' added as a modification to the master equation for statistical distributions. The proof of the relations is based upon a variational characterization of the generating functional of the time-correlations. The same fluctuation-response relations are preserved within moment-closures for the statistical dynamical system, when these are constructed via the variational Rayleigh-Ritz procedure. For the 2-time correlations of the moment-variables themselves, the fluctuation-response relation is equivalent to an ``Onsager regression hypothesis'' for the small fluctuations. For correlations of higher-order, there is a new effect in addition to such linear propagation of fluctuations present instantaneously: the dynamical generation of correlations by nonlinear interaction of fluctuations. In general, we discuss some physical and mathematical aspects of the {\it Ans\"{a}tze} required for an accurate calculation of the time correlations. We also comment briefly upon the computational use of these relations, which is well-suited for automatic differentiation tools. An example will be given of a simple closure for turbulent energy decay, which illustrates the numerical application of the relations.Comment: 28 pages, 1 figure, submitted to Phys. Rev.

Critical Protoplanetary Core Masses in Protoplanetary Disks and the Formation of Short-Period Giant Planets

We study a solid protoplanetary core of 1-10 earth masses migrating through a disk. We suppose the core luminosity is generated as a result of planetesimal accretion and calculate the structure of the gaseous envelope assuming equilibrium. This is a good approximation when the core mass is less than the critical value, M_{crit}, above which rapid gas accretion begins. We model the structure of the protoplanetary nebula as an accretion disk with constant \alpha. We present analytic fits for the steady state relation between disk surface density and mass accretion rate as a function of radius r. We calculate M_{crit} as a function of r, gas accretion rate through the disk, and planetesimal accretion rate onto the core \dot{M}. For a fixed \dot{M}, M_{crit} increases inwards, and it decreases with \dot{M}. We find that \dot{M} onto cores migrating inwards in a time 10^3-10^5 yr at 1 AU is sufficient to prevent the attainment of M_{crit} during the migration process. Only at small radii where planetesimals no longer exist can M_{crit} be attained. At small radii, the runaway gas accretion phase may become longer than the disk lifetime if the core mass is too small. However, massive cores can be built-up through the merger of additional incoming cores on a timescale shorter than for in situ formation. Therefore, feeding zone depletion in the neighborhood of a fixed orbit may be avoided. Accordingly, we suggest that giant planets may begin to form early in the life of the protostellar disk at small radii, on a timescale that may be significantly shorter than for in situ formation. (abridged)Comment: 24 pages (including 9 figures), LaTeX, uses emulateapj.sty, to be published in ApJ, also available at http://www.ucolick.org/~ct/home.htm

Random Walks on a Fluctuating Lattice: A Renormalization Group Approach Applied in One Dimension

We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with dimensionality of the lattice.Comment: PostScript file including 2 figures, total 15 pages, 8 other figures obtainable by mail from D.L. Stei

Nonequilibrium corrections in the pressure tensor due to an energy flux

The physical interpretation of the nonequilibrium corrections in the pressure tensor for radiation submitted to an energy flux obtained in some previous works is revisited. Such pressure tensor is shown to describe a moving equilibrium system but not a real nonequilibrium situation.Comment: 4 pages, REVTeX, Brief Report to appear in PRE Dec 9

Bispectrum speckle interferometry of the massive protostellar outflow source IRAS 23151+5912

We present bispectrum speckle interferometry of the massive protostellar object IRAS 23151+5912 in the near-infrared K' band. The reconstructed image shows the diffuse nebulosity north-east of two point-like sources in unprecedented detail. The comparison of our near-infrared image with mm continuum and CO molecular line maps shows that the brighter of the two point sources lies near the center of the mm peak, indicating that it is a high-mass protostar. The nebulosity coincides with the blue-shifted molecular outflow component. The most prominent feature in the nebulosity is a bow-shock-like arc. We assume that this feature is associated with a precessing jet which has created an inward-pointed cone in the swept-up material. We present numerical jet simulations that reproduce this and several other features observed in our speckle image of the nebulosity. Our data also reveal a linear structure connecting the central point source to the extended diffuse nebulosity. This feature may represent the innermost part of a jet that drives the strong molecular outflow (PA ~80 degr) from IRAS 23151+5912. With the aid of radiative transfer calculations, we demonstrate that, in general, the observed inner structures of the circumstellar material surrounding high-mass stars are strongly influenced by the orientation and symmetry of the bipolar cavity.Comment: accepted by Astronomy & Astrophysics; preprints with high-resolution images can be obtained from http://www.mpifr-bonn.mpg.de/staff/tpreibis/iras23151.htm