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 ($k^2$). 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 $45^\circ$ ($30^\circ$) 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 $k^\nu$, was proposed. The exponent $\nu$ has a nonuniversal critical value $\nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $\nu<\nu_c$ and the rotated one (diagonal) for $\nu>\nu_c$. The values $\nu_c = 1.395\pm0.005$ and $\nu_c = 0.82\pm 0.01$ 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 $\nu=2$ (\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 $ds/dt=As^\beta$. 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$\times10^3$ s of the late evolution of a $23 \rm M_\odot$ 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 $P_{ba}$, or random ones, with probability $P_{rw}=1-P_{ba}$. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of $P_{ba}$ continuously increases from $d_f\approx 1.72$ (DLA dimensionality) for $P_{ba}=0$ to $d_f\approx 2$ (BA dimensionality) for $P_{ba}=1$. However, the lacunarity and the active zone width exhibt a distinct behavior: they are convex functions of $P_{ba}$ with a maximum at $P_{ba}\approx1/2$. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{ba}$ and rapidly vanishes for $P_{ba}>1/2$, 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