337,576 research outputs found
Molecular line radiative transfer in protoplanetary disks: Monte Carlo simulations versus approximate methods
We analyze the line radiative transfer in protoplanetary disks using several
approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass
flaring disk model with uniform as well as stratified molecular abundances is
adopted. Radiative transfer in low and high rotational lines of CO, C18O, HCO+,
DCO+, HCN, CS, and H2CO is simulated. The corresponding excitation
temperatures, synthetic spectra, and channel maps are derived and compared to
the results of the Monte Carlo calculations. A simple scheme that describes the
conditions of the line excitation for a chosen molecular transition is
elaborated. We find that the simple LTE approach can safely be applied for the
low molecular transitions only, while it significantly overestimates the
intensities of the upper lines. In contrast, the Full Escape Probability (FEP)
approximation can safely be used for the upper transitions (J_{\rm up} \ga 3)
but it is not appropriate for the lowest transitions because of the maser
effect. In general, the molecular lines in protoplanetary disks are partly
subthermally excited and require more sophisticated approximate line radiative
transfer methods. We analyze a number of approximate methods, namely, LVG, VEP
(Vertical Escape Probability) and VOR (Vertical One Ray) and discuss their
algorithms in detail. In addition, two modifications to the canonical Monte
Carlo algorithm that allow a significant speed up of the line radiative
transfer modeling in rotating configurations by a factor of 10--50 are
described.Comment: 47 pages, 12 figures, accepted for publication in Ap
Corner and finger formation in Hele--Shaw flow with kinetic undercooling regularisation
We examine the effect of a kinetic undercooling condition on the evolution of
a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We
present analytical and numerical evidence that the bubble boundary is unstable
and may develop one or more corners in finite time, for both expansion and
contraction cases. This loss of regularity is interesting because it occurs
regardless of whether the less viscous fluid is displacing the more viscous
fluid, or vice versa. We show that small contracting bubbles are described to
leading order by a well-studied geometric flow rule. Exact solutions to this
asymptotic problem continue past the corner formation until the bubble
contracts to a point as a slit in the limit. Lastly, we consider the evolving
boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The
boundary may either form corners in finite time, or evolve to a single long
finger travelling at constant speed, depending on the strength of kinetic
undercooling. We demonstrate these two different behaviours numerically. For
the travelling finger, we present results of a numerical solution method
similar to that used to demonstrate the selection of discrete fingers by
surface tension. With kinetic undercooling, a continuum of corner-free
travelling fingers exists for any finger width above a critical value, which
goes to zero as the kinetic undercooling vanishes. We have not been able to
compute the discrete family of analytic solutions, predicted by previous
asymptotic analysis, because the numerical scheme cannot distinguish between
solutions characterised by analytic fingers and those which are corner-free but
non-analytic
High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
In this article, we prove that exact representations of dimer and plaquette
valence-bond ket ground states for quantum Heisenberg antiferromagnets may be
formed via the usual coupled cluster method (CCM) from independent-spin product
(e.g. N\'eel) model states. We show that we are able to provide good results
for both the ground-state energy and the sublattice magnetization for dimer and
plaquette valence-bond phases within the CCM. As a first example, we
investigate the spin-half -- model for the linear chain, and we show
that we are able to reproduce exactly the dimerized ground (ket) state at
. The dimerized phase is stable over a range of values for
around 0.5. We present evidence of symmetry breaking by considering
the ket- and bra-state correlation coefficients as a function of . We
then consider the Shastry-Sutherland model and demonstrate that the CCM can
span the correct ground states in both the N\'eel and the dimerized phases.
Finally, we consider a spin-half system with nearest-neighbor bonds for an
underlying lattice corresponding to the magnetic material CaVO (CAVO).
We show that we are able to provide excellent results for the ground-state
energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes
of this model. The exact plaquette and dimer ground states are reproduced by
the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table
RODEO: a new method for planet-disk interaction
In this paper we describe a new method for studying the hydrodynamical
problem of a planet embedded in a gaseous disk. We use a finite volume method
with an approximate Riemann solver (the Roe solver), together with a special
way to integrate the source terms. This new source term integration scheme
sheds new light on the Coriolis instability, and we show that our method does
not suffer from this instability. The first results on flow structure and gap
formation are presented, as well as accretion and migration rates. For Mpl <
0.1 M_J and Mpl > 1.0 M_J (M_J = Jupiter's mass) the accretion rates do not
depend sensitively on numerical parameters, and we find that within the disk's
lifetime a planet can grow to 3-4 M_J. In between these two limits numerics
play a major role, leading to differences of more than 50 % for different
numerical parameters. Migration rates are not affected by numerics at all as
long as the mass inside the Roche lobe is not considered. We can reproduce the
Type I and Type II migration for low-mass and high-mass planets, respectively,
and the fastest moving planet of 0.1 M_J has a migration time of only 2.0 10^4
yr.Comment: Accepted for publication in A&
Efficient Reactive Brownian Dynamics
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle
simulations of reaction-diffusion systems based on the Doi or volume reactivity
model, in which pairs of particles react with a specified Poisson rate if they
are closer than a chosen reactive distance. In our Doi model, we ensure that
the microscopic reaction rules for various association and disassociation
reactions are consistent with detailed balance (time reversibility) at
thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to
separate reaction and diffusion, and solves both the diffusion-only and
reaction-only subproblems exactly, even at high packing densities. To
efficiently process reactions without uncontrolled approximations, SRBD employs
an event-driven algorithm that processes reactions in a time-ordered sequence
over the duration of the time step. A grid of cells with size larger than all
of the reactive distances is used to schedule and process the reactions, but
unlike traditional grid-based methods such as Reaction-Diffusion Master
Equation (RDME) algorithms, the results of SRBD are statistically independent
of the size of the grid used to accelerate the processing of reactions. We use
the SRBD algorithm to compute the effective macroscopic reaction rate for both
reaction- and diffusion-limited irreversible association in three dimensions.
We also study long-time tails in the time correlation functions for reversible
association at thermodynamic equilibrium. Finally, we compare different
particle and continuum methods on a model exhibiting a Turing-like instability
and pattern formation. We find that for models in which particles diffuse off
lattice, such as the Doi model, reactions lead to a spurious enhancement of the
effective diffusion coefficients.Comment: To appear in J. Chem. Phy
A sandpile model for proportionate growth
An interesting feature of growth in animals is that different parts of the
body grow at approximately the same rate. This property is called proportionate
growth. In this paper, we review our recent work on patterns formed by adding
grains at a single site in the abelian sandpile model. These simple models
show very intricate patterns, show proportionate growth, and sometimes having a
striking resemblance to natural forms. We give several examples of such
patterns. We discuss the special cases where the asymptotic pattern can be
determined exactly. The effect of noise in the background or in the rules on
the patterns is also discussed.Comment: 18 pages, 14 figures, to appear in a special issue of JSTAT dedicated
to Statphys2
Trimer-Monomer Mixture Problem on (111) Surface of Diamond Structure
We consider a system of trimers and monomers on the triangular lattice, which
describes the adsorption problem on (111) surface of diamond
structure. We give a mapping to a 3-state vertex model on the square lattice.
We treat the problem by the transfer-matrix method combined with the
density-matrix algorithm, to obtain thermodynamic quantities.Comment: 9 pages, 7 figures, PTPTeX ver. 1.0. To appear Progress of
Theoretical Physics, Jan. 2001. http://www2.yukawa.kyoto-u.ac.jp/~ptpwww/
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