161 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
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
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
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
with , 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 , an explicit convergence rate is obtained
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.
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
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
How to Cost the Implementation of Major System Change for Economic Evaluations: Case Study Using Reconfigurations of Specialist Cancer Surgery in Part of London, England.
BACKGROUND: Studies have been published regarding the impact of major system change (MSC) on care quality and outcomes, but few evaluate implementation costs or include them in cost-effectiveness analysis (CEA). This is despite large potential costs of MSC: change planning, purchasing or repurposing assets, and staff time. Implementation costs can influence implementation decisions. We describe our framework and principles for costing MSC implementation and illustrate them using a case study. METHODS: We outlined MSC implementation stages and identified components, using a framework conceived during our work on MSC in stroke services. We present a case study of MSC of specialist surgery services for prostate, bladder, renal and oesophagogastric cancers, focusing on North Central and North East London and West Essex. Health economists collaborated with qualitative researchers, clinicians and managers, identifying key reconfiguration stages and expenditures. Data sources (n = approximately 100) included meeting minutes, interviews, and business cases. National Health Service (NHS) finance and service managers and clinicians were consulted. Using bottom-up costing, items were identified, and unit costs based on salaries, asset costs and consultancy fees assigned. Itemised costs were adjusted and summed. RESULTS: Cost components included options appraisal, bidding process, external review; stakeholder engagement events; planning/monitoring boards/meetings; and making the change: new assets, facilities, posts. Other considerations included hospital tariff changes; costs to patients; patient population; and lifetime of changes. Using the framework facilitated data identification and collection. The total adjusted implementation cost was estimated at £7.2 million, broken down as replacing robots (£4.0 million), consultancy fees (£1.9 million), staff time costs (£1.1 million) and other costs (£0.2 million). CONCLUSIONS: These principles can be used by funders, service providers and commissioners planning MSC and researchers evaluating MSC. Health economists should be involved early, alongside qualitative and health-service colleagues, as retrospective capture risks information loss. These analyses are challenging; many cost factors are difficult to identify, access and measure, and assumptions regarding lifetime of the changes are important. Including implementation costs in CEA might make MSC appear less cost effective, influencing future decisions. Future work will incorporate this implementation cost into the full CEAs of the London Cancer MSC. TRIAL REGISTRATION: Not applicable
Moment Closure - A Brief Review
Moment closure methods appear in myriad scientific disciplines in the
modelling of complex systems. The goal is to achieve a closed form of a large,
usually even infinite, set of coupled differential (or difference) equations.
Each equation describes the evolution of one "moment", a suitable
coarse-grained quantity computable from the full state space. If the system is
too large for analytical and/or numerical methods, then one aims to reduce it
by finding a moment closure relation expressing "higher-order moments" in terms
of "lower-order moments". In this brief review, we focus on highlighting how
moment closure methods occur in different contexts. We also conjecture via a
geometric explanation why it has been difficult to rigorously justify many
moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in
mathematics, physics, chemistry and quantitative biolog
Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
The aim of this paper is the accurate numerical study of the KP equation. In
particular we are concerned with the small dispersion limit of this model,
where no comprehensive analytical description exists so far. To this end we
first study a similar highly oscillatory regime for asymptotically small
solutions, which can be described via the Davey-Stewartson system. In a second
step we investigate numerically the small dispersion limit of the KP model in
the case of large amplitudes. Similarities and differences to the much better
studied Korteweg-de Vries situation are discussed as well as the dependence of
the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at
http://www.mis.mpg.de/preprints/index.html
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