966 research outputs found
Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?
In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an
algorithm aiming to generate isotropic clusters of the on-lattice
diffusion-limited aggregation (DLA) model was proposed. The procedure consists
of aggregation probabilities proportional to the squared number of occupied
sites (). In the present work, we analyzed this algorithm using the noise
reduced version of the DLA model and large scale simulations. In the noiseless
limit, instead of isotropic patterns, a () rotation in the
anisotropy directions of the clusters grown on square (triangular) lattices was
observed. A generalized algorithm, in which the aggregation probability is
proportional to , was proposed. The exponent has a nonuniversal
critical value , for which the patterns generated in the noiseless limit
exhibit the original (axial) anisotropy for and the rotated one
(diagonal) for . The values and were found for square and triangular lattices, respectively.
Moreover, large scale simulations show that there are a nontrivial relation
between noise reduction and anisotropy direction. The case (\bogo's
rule) is an example where the patterns exhibit the axial anisotropy for small
and the diagonal one for large noise reduction.Comment: 12 pages, 8 figure
Multifractal Dimensions for Branched Growth
A recently proposed theory for diffusion-limited aggregation (DLA), which
models this system as a random branched growth process, is reviewed. Like DLA,
this process is stochastic, and ensemble averaging is needed in order to define
multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys.
Rev. A46, 7793 (1992)], annealed average dimensions were computed for this
model. In this paper, we compute the quenched average dimensions, which are
expected to apply to typical members of the ensemble. We develop a perturbative
expansion for the average of the logarithm of the multifractal partition
function; the leading and sub-leading divergent terms in this expansion are
then resummed to all orders. The result is that in the limit where the number
of particles n -> \infty, the quenched and annealed dimensions are {\it
identical}; however, the attainment of this limit requires enormous values of
n. At smaller, more realistic values of n, the apparent quenched dimensions
differ from the annealed dimensions. We interpret these results to mean that
while multifractality as an ensemble property of random branched growth (and
hence of DLA) is quite robust, it subtly fails for typical members of the
ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl
Active Carbon and Oxygen Shell Burning Hydrodynamics
We have simulated 2.5 s of the late evolution of a star with full hydrodynamic behavior. We present the first simulations
of a multiple-shell burning epoch, including the concurrent evolution and
interaction of an oxygen and carbon burning shell. In addition, we have evolved
a 3D model of the oxygen burning shell to sufficiently long times (300 s) to
begin to assess the adequacy of the 2D approximation. We summarize striking new
results: (1) strong interactions occur between active carbon and oxygen burning
shells, (2) hydrodynamic wave motions in nonconvective regions, generated at
the convective-radiative boundaries, are energetically important in both 2D and
3D with important consequences for compositional mixing, and (3) a spectrum of
mixed p- and g-modes are unambiguously identified with corresponding adiabatic
waves in these computational domains. We find that 2D convective motions are
exaggerated relative to 3D because of vortex instability in 3D. We discuss the
implications for supernova progenitor evolution and symmetry breaking in core
collapse.Comment: 5 pages, 4 figures in emulateapj format. Accepted for publication in
ApJ Letters. High resolution figure version available at
http://spinach.as.arizona.ed
Aggregation in a mixture of Brownian and ballistic wandering particles
In this paper, we analyze the scaling properties of a model that has as
limiting cases the diffusion-limited aggregation (DLA) and the ballistic
aggregation (BA) models. This model allows us to control the radial and angular
scaling of the patterns, as well as, their gap distributions. The particles
added to the cluster can follow either ballistic trajectories, with probability
, or random ones, with probability . The patterns were
characterized through several quantities, including those related to the radial
and angular scaling. The fractal dimension as a function of
continuously increases from (DLA dimensionality) for
to (BA dimensionality) for . However, the
lacunarity and the active zone width exhibt a distinct behavior: they are
convex functions of with a maximum at . Through the
analysis of the angular correlation function, we found that the difference
between the radial and angular exponents decreases continuously with increasing
and rapidly vanishes for , in agreement with recent
results concerning the asymptotic scaling of DLA clusters.Comment: 7 pages, 6 figures. accepted for publication on PR
Young stars and dust in AFGL437: NICMOS/HST polarimetric imaging of an outflow source
We present near infrared broad band and polarimetric images of the compact
star forming cluster AFGL437 obtained with the NICMOS instrument aboard HST.
Our high resolution images reveal a well collimated bipolar reflection
nebulosity in the cluster and allow us to identify WK34 as the illuminating
source. The scattered light in the bipolar nebulosity centered on this source
is very highly polarized (up to 79%). Such high levels of polarization implies
a distribution of dust grains lacking large grains, contrary to the usual dust
models of dark clouds. We discuss the geometry of the dust distribution giving
rise to the bipolar reflection nebulosity and make mass estimates for the
underlying scattering material. We find that the most likely inclination of the
bipolar nebulosity, south lobe inclined towards Earth, is consistent with the
inclination of the large scale CO molecular outflow associated with the
cluster, strengthening the identification of WK34 as the source powering it.Comment: 26 pages, 10 figues. Accepted for publication in the Astrophysical
Journa
The Impact of Hydrodynamic Mixing on Supernova Progenitors
Recent multidimensional hydrodynamic simulations have demonstrated the
importance of hydrodynamic motions in the convective boundary and radiative
regions of stars to transport of energy, momentum, and composition. The impact
of these processes increases with stellar mass. Stellar models which
approximate this physics have been tested on several classes of observational
problems. In this paper we examine the implications of the improved treatment
on supernova progenitors. The improved models predict substantially different
interior structures. We present pre-supernova conditions and simple explosion
calculations from stellar models with and without the improved mixing treatment
at 23 solar masses. The results differ substantially.Comment: 12 pages, 2 figures, accepted for publication in the Astrophysical
Journal Letter
Multilayer parking with screening on a random tree
In this paper we present a multilayer particle deposition model on a random
tree. We derive the time dependent densities of the first and second layer
analytically and show that in all trees the limiting density of the first layer
exceeds the density in the second layer. We also provide a procedure to
calculate higher layer densities and prove that random trees have a higher
limiting density in the first layer than regular trees. Finally, we compare
densities between the first and second layer and between regular and random
trees.Comment: 15 pages, 2 figure
A pseudo-spectral approach to inverse problems in interface dynamics
An improved scheme for computing coupling parameters of the
Kardar-Parisi-Zhang equation from a collection of successive interface
profiles, is presented. The approach hinges on a spectral representation of
this equation. An appropriate discretization based on a Fourier representation,
is discussed as a by-product of the above scheme. Our method is first tested on
profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it
is shown to reproduce the input parameters very accurately. When applied to
microscopic models of growth, it provides the values of the coupling parameters
associated with the corresponding continuum equations. This technique favorably
compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys.
Rev.
Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models
The competitive growth models involving only one kind of particles (CGM), are
a mixture of two processes one with probability and the other with
probability . The dependance produce crossovers between two different
regimes. We demonstrate that the coefficients of the continuous equation,
describing their universality classes, are quadratic in (or ). We show
that the origin of such dependance is the existence of two different average
time rates. Thus, the quadratic dependance is an universal behavior of all
the CGM. We derive analytically the continuous equations for two CGM, in 1+1
dimensions, from the microscopic rules using a regularization procedure. We
propose generalized scalings that reproduce the scaling behavior in each
regime. In order to verify the analytic results and the scalings, we perform
numerical integrations of the derived analytical equations. The results are in
excellent agreement with those of the microscopic CGM presented here and with
the proposed scalings.Comment: 9 pages, 3 figure
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