14,509 research outputs found
An implementation of radiative transfer in the cosmological simulation code GADGET
We present a novel numerical implementation of radiative transfer in the
cosmological smoothed particle hydrodynamics (SPH) simulation code {\small
GADGET}. It is based on a fast, robust and photon-conserving integration scheme
where the radiation transport problem is approximated in terms of moments of
the transfer equation and by using a variable Eddington tensor as a closure
relation, following the `OTVET'-suggestion of Gnedin & Abel. We derive a
suitable anisotropic diffusion operator for use in the SPH discretization of
the local photon transport, and we combine this with an implicit solver that
guarantees robustness and photon conservation. This entails a matrix inversion
problem of a huge, sparsely populated matrix that is distributed in memory in
our parallel code. We solve this task iteratively with a conjugate gradient
scheme. Finally, to model photon sink processes we consider ionisation and
recombination processes of hydrogen, which is represented with a chemical
network that is evolved with an implicit time integration scheme. We present
several tests of our implementation, including single and multiple sources in
static uniform density fields with and without temperature evolution, shadowing
by a dense clump, and multiple sources in a static cosmological density field.
All tests agree quite well with analytical computations or with predictions
from other radiative transfer codes, except for shadowing. However, unlike most
other radiative transfer codes presently in use for studying reionisation, our
new method can be used on-the-fly during dynamical cosmological simulation,
allowing simultaneous treatments of galaxy formation and the reionisation
process of the Universe.Comment: 21 pages, 17 figures, published in MNRA
Random real trees
We survey recent developments about random real trees, whose prototype is the
Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain
the formalism of real trees, which yields a neat presentation of the theory and
in particular of the relations between discrete Galton-Watson trees and
continuous random trees. We then discuss the particular class of self-similar
random real trees called stable trees, which generalize the CRT. We review
several important results concerning stable trees, including their branching
property, which is analogous to the well-known property of Galton-Watson trees,
and the calculation of their fractal dimension. We then consider spatial trees,
which combine the genealogical structure of a real tree with spatial
displacements, and we explain their connections with superprocesses. In the
last section, we deal with a particular conditioning problem for spatial trees,
which is closely related to asymptotics for random planar quadrangulations.Comment: 25 page
Measuring the saturation scale in nuclei
The saturation momentum seeing in the nuclear infinite momentum frame is
directly related to transverse momentum broadening of partons propagating
through the medium in the nuclear rest frame. Calculation of broadening within
the color dipole approach including the effects of saturation in the nucleus,
gives rise to an equation which describes well data on broadening in Drell-Yan
reaction and heavy quarkonium production.Comment: 11 pages, 5 figures, based on the talk presented by B.K. at the INT
workshop "Physics at a High Energy Electron Ion Collider", Seattle, October
200
Proximity Action theory of superconductive nanostructures
We review a novel approach to the superconductive proximity effect in
disordered normal-superconducting (N-S) structures. The method is based on the
multicharge Keldysh action and is suitable for the treatment of interaction and
fluctuation effects. As an application of the formalism, we study the subgap
conductance and noise in two-dimensional N-S systems in the presence of the
electron-electron interaction in the Cooper channel. It is shown that singular
nature of the interaction correction at large scales leads to a nonmonotonuos
temperature, voltage and magnetic field dependence of the Andreev conductance.Comment: RevTeX, 6 pages, 5 eps figures. This is a concise review of
cond-mat/0008463; to be published in the Proceedings of the conference
"Mesoscopic and strongly correlated electron systems" (Chernogolovka, Russia,
July 2000
Conservative 3+1 General Relativistic Variable Eddington Tensor Radiation Transport Equations
We present conservative 3+1 general relativistic variable Eddington tensor
radiation transport equations, including greater elaboration of the momentum
space divergence (that is, the energy derivative term) than in previous work.
These equations are intended for use in simulations involving numerical
relativity, particularly in the absence of spherical symmetry. The independent
variables are the lab frame coordinate basis spacetime position coordinates and
the particle energy measured in the comoving frame. With an eye towards
astrophysical applications---such as core-collapse supernovae and compact
object mergers---in which the fluid includes nuclei and/or nuclear matter at
finite temperature, and in which the transported particles are neutrinos, we
pay special attention to the consistency of four-momentum and lepton number
exchange between neutrinos and the fluid, showing the term-by-term
cancellations that must occur for this consistency to be achieved.Comment: Version accepted by Phys. Rev.
Beyond the Spectral Theorem: Spectrally Decomposing Arbitrary Functions of Nondiagonalizable Operators
Nonlinearities in finite dimensions can be linearized by projecting them into
infinite dimensions. Unfortunately, often the linear operator techniques that
one would then use simply fail since the operators cannot be diagonalized. This
curse is well known. It also occurs for finite-dimensional linear operators. We
circumvent it by developing a meromorphic functional calculus that can
decompose arbitrary functions of nondiagonalizable linear operators in terms of
their eigenvalues and projection operators. It extends the spectral theorem of
normal operators to a much wider class, including circumstances in which poles
and zeros of the function coincide with the operator spectrum. By allowing the
direct manipulation of individual eigenspaces of nonnormal and
nondiagonalizable operators, the new theory avoids spurious divergences. As
such, it yields novel insights and closed-form expressions across several areas
of physics in which nondiagonalizable dynamics are relevant, including
memoryful stochastic processes, open non unitary quantum systems, and
far-from-equilibrium thermodynamics.
The technical contributions include the first full treatment of arbitrary
powers of an operator. In particular, we show that the Drazin inverse,
previously only defined axiomatically, can be derived as the negative-one power
of singular operators within the meromorphic functional calculus and we give a
general method to construct it. We provide new formulae for constructing
projection operators and delineate the relations between projection operators,
eigenvectors, and generalized eigenvectors.
By way of illustrating its application, we explore several, rather distinct
examples.Comment: 29 pages, 4 figures, expanded historical citations;
http://csc.ucdavis.edu/~cmg/compmech/pubs/bst.ht
Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations
We present approaches for the study of fluid-structure interactions subject
to thermal fluctuations. A mixed mechanical description is utilized combining
Eulerian and Lagrangian reference frames. We establish general conditions for
operators coupling these descriptions. Stochastic driving fields for the
formalism are derived using principles from statistical mechanics. The
stochastic differential equations of the formalism are found to exhibit
significant stiffness in some physical regimes. To cope with this issue, we
derive reduced stochastic differential equations for several physical regimes.
We also present stochastic numerical methods for each regime to approximate the
fluid-structure dynamics and to generate efficiently the required stochastic
driving fields. To validate the methodology in each regime, we perform analysis
of the invariant probability distribution of the stochastic dynamics of the
fluid-structure formalism. We compare this analysis with results from
statistical mechanics. To further demonstrate the applicability of the
methodology, we perform computational studies for spherical particles having
translational and rotational degrees of freedom. We compare these studies with
results from fluid mechanics. The presented approach provides for
fluid-structure systems a set of rather general computational methods for
treating consistently structure mechanics, hydrodynamic coupling, and thermal
fluctuations.Comment: 24 pages, 3 figure
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