216 research outputs found
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
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.
Identification of Changes Needed in Supermarket Design for Energy Demand Reduction
Supermarkets use 3 percent of UK energy. To satisfy building regulations supermarket buildings are modeled in considerable detail. Lighting, occupancy, and small electrical energy impacts are included in this modeling. However, refrigeration energy is not, as it is classified as process energy rather than building related. Refrigeration energy, which can be very significant, is therefore currently unregulated and as a result, heat transfers related to refrigeration cabinets are typically not incorporated in modeling of the building at design stage. This paper explores the comparative energy demands of supermarket stores modeled, using a simple first order dynamic model, executed on Excel, and optimized firstly with, and secondly without, the cooling effect of refrigeration cabinets included in the model. A recently built supermarket is modeled. Results suggest that the energy demand of a new store could be reduced by 15 to 25 percent by improvement of the building envelope design with process energy included in the modeling
Statistics and Characteristics of Spatio-Temporally Rare Intense Events in Complex Ginzburg-Landau Models
We study the statistics and characteristics of rare intense events in two
types of two dimensional Complex Ginzburg-Landau (CGL) equation based models.
Our numerical simulations show finite amplitude collapse-like solutions which
approach the infinite amplitude solutions of the nonlinear Schr\"{o}dinger
(NLS) equation in an appropriate parameter regime. We also determine the
probability distribution function (PDF) of the amplitude of the CGL solutions,
which is found to be approximately described by a stretched exponential
distribution, , where . This
non-Gaussian PDF is explained by the nonlinear characteristics of individual
bursts combined with the statistics of bursts. Our results suggest a general
picture in which an incoherent background of weakly interacting waves,
occasionally, `by chance', initiates intense, coherent, self-reinforcing,
highly nonlinear events.Comment: 7 pages, 9 figure
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
Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse
Radiative transfer plays a major role in the process of star formation. Many
simulations of gravitational collapse of a cold gas cloud followed by the
formation of a protostellar core use a grey treatment of radiative transfer
coupled to the hydrodynamics. However, dust opacities which dominate extinction
show large variations as a function of frequency. In this paper, we used
frequency-dependent radiative transfer to investigate the influence of the
opacity variations on the properties of Larson's first core. We used a
multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the
spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust
opacities for five different temperature ranges were used to compute Planck and
Rosseland means inside each frequency group. The results are very consistent
with previous studies and only small differences were observed between the grey
and multigroup simulations. For a same central density, the multigroup
simulations tend to produce first cores with a slightly higher radius and
central temperature. We also performed simulations of the collapse of a 10 and
0.1 solar mass cloud, which showed the properties of the first core to be
independent of the initial cloud mass, with again no major differences between
grey and multigroup models. For Larson's first collapse, where temperatures
remain below 2000 K, the vast majority of the radiation energy lies in the IR
regime and the system is optically thick. In this regime, the grey
approximation does a good job reproducing the correct opacities, as long as
there are no large opacity variations on scales much smaller than the width of
the Planck function. The multigroup method is however expected to yield more
important differences in the later stages of the collapse when high energy (UV
and X-ray) radiation is present and matter and radiation are strongly
decoupled.Comment: 9 pages, 5 figures, accepted for publication in A&
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
Analytic solutions and Singularity formation for the Peakon b--Family equations
Using the Abstract Cauchy-Kowalewski Theorem we prove that the -family
equation admits, locally in time, a unique analytic solution. Moreover, if the
initial data is real analytic and it belongs to with , and the
momentum density does not change sign, we prove that the
solution stays analytic globally in time, for . Using pseudospectral
numerical methods, we study, also, the singularity formation for the -family
equations with the singularity tracking method. This method allows us to follow
the process of the singularity formation in the complex plane as the
singularity approaches the real axis, estimating the rate of decay of the
Fourier spectrum
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
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