1,227 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
Smoluchowski's equation for cluster exogenous growth
We introduce an extended Smoluchowski equation describing coagulation
processes for which clusters of mass s grow between collisions with
. A physical example, dropwise condensation is provided, and
its collision kernel K is derived. In the general case, the gelation criterion
is determined. Exact solutions are found and scaling solutions are
investigated. Finally we show how these results apply to nucleation of discs on
a planeComment: Revtex, 4 pages (multicol.sty), 1 eps figures (uses epsfig
Amalgams of Inverse Semigroups and C*-algebras
An amalgam of inverse semigroups [S,T,U] is full if U contains all of the
idempotents of S and T. We show that for a full amalgam [S,T,U], the C*-algebra
of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam
of C*(S) and C*(T) over C*(U). Using this result, we describe certain
amalgamated free products of C*-algebras, including finite-dimensional
C*-algebras, the Toeplitz algebra, and the Toeplitz C*-algebras of graphs
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
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