71,286 research outputs found
Radiative transfer in very optically thick circumstellar disks
In this paper we present two efficient implementations of the diffusion
approximation to be employed in Monte Carlo computations of radiative transfer
in dusty media of massive circumstellar disks. The aim is to improve the
accuracy of the computed temperature structure and to decrease the computation
time. The accuracy, efficiency and applicability of the methods in various
corners of parameter space are investigated. The effects of using these methods
on the vertical structure of the circumstellar disk as obtained from
hydrostatic equilibrium computations are also addressed. Two methods are
presented. First, an energy diffusion approximation is used to improve the
accuracy of the temperature structure in highly obscured regions of the disk,
where photon counts are low. Second, a modified random walk approximation is
employed to decrease the computation time. This modified random walk ensures
that the photons that end up in the high-density regions can quickly escape to
the lower density regions, while the energy deposited by these photons in the
disk is still computed accurately. A new radiative transfer code, MCMax, is
presented in which both these diffusion approximations are implemented. These
can be used simultaneously to increase both computational speed and decrease
statistical noise. We conclude that the diffusion approximations allow for fast
and accurate computations of the temperature structure, vertical disk structure
and observables of very optically thick circumstellar disks.Comment: Accepted for publication in A&
Probabilistic Numerics and Uncertainty in Computations
We deliver a call to arms for probabilistic numerical methods: algorithms for
numerical tasks, including linear algebra, integration, optimization and
solving differential equations, that return uncertainties in their
calculations. Such uncertainties, arising from the loss of precision induced by
numerical calculation with limited time or hardware, are important for much
contemporary science and industry. Within applications such as climate science
and astrophysics, the need to make decisions on the basis of computations with
large and complex data has led to a renewed focus on the management of
numerical uncertainty. We describe how several seminal classic numerical
methods can be interpreted naturally as probabilistic inference. We then show
that the probabilistic view suggests new algorithms that can flexibly be
adapted to suit application specifics, while delivering improved empirical
performance. We provide concrete illustrations of the benefits of probabilistic
numeric algorithms on real scientific problems from astrometry and astronomical
imaging, while highlighting open problems with these new algorithms. Finally,
we describe how probabilistic numerical methods provide a coherent framework
for identifying the uncertainty in calculations performed with a combination of
numerical algorithms (e.g. both numerical optimisers and differential equation
solvers), potentially allowing the diagnosis (and control) of error sources in
computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl
Tethered Monte Carlo: computing the effective potential without critical slowing down
We present Tethered Monte Carlo, a simple, general purpose method of
computing the effective potential of the order parameter (Helmholtz free
energy). This formalism is based on a new statistical ensemble, closely related
to the micromagnetic one, but with an extended configuration space (through
Creutz-like demons). Canonical averages for arbitrary values of the external
magnetic field are computed without additional simulations. The method is put
to work in the two dimensional Ising model, where the existence of exact
results enables us to perform high precision checks. A rather peculiar feature
of our implementation, which employs a local Metropolis algorithm, is the total
absence, within errors, of critical slowing down for magnetic observables.
Indeed, high accuracy results are presented for lattices as large as L=1024.Comment: 32 pages, 8 eps figures. Corrected Eq. (36), which is wrong in the
published pape
Nucleon Polarisabilities at and Beyond Physical Pion Masses
We examine the results of Chiral Effective Field Theory (EFT) for the
scalar- and spin-dipole polarisabilities of the proton and neutron, both for
the physical pion mass and as a function of . This provides chiral
extrapolations for lattice-QCD polarisability computations. We include both the
leading and sub-leading effects of the nucleon's pion cloud, as well as the
leading ones of the resonance and its pion cloud. The analytic
results are complete at NLO in the -counting for pion masses close
to the physical value, and at leading order for pion masses similar to the
Delta-nucleon mass splitting. In order to quantify the truncation error of our
predictions and fits as \% degree-of-belief intervals, we use a Bayesian
procedure recently adapted to EFT expansions. At the physical point, our
predictions for the spin polarisabilities are, within respective errors, in
good agreement with alternative extractions using experiments and
dispersion-relation theory. At larger pion masses we find that the chiral
expansion of all polarisabilities becomes intrinsically unreliable as
approaches about MeV---as has already been seen in other observables.
EFT also predicts a substantial isospin splitting above the physical
point for both the electric and magnetic scalar polarisabilities; and we
speculate on the impact this has on the stability of nucleons. Our results
agree very well with emerging lattice computations in the realm where EFT
converges. Curiously, for the central values of some of our predictions, this
agreement persists to much higher pion masses. We speculate on whether this
might be more than a fortuitous coincidence.Comment: 39 pages LaTeX2e (pdflatex) including 12 figures as 16 .pdf files
using includegraphics. Version approved for publication in EPJA includes
modifications, clarifications and removal of typographical errors in
refereeing and publication proces
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