24,724 research outputs found
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
Optimized cross-slot flow geometry for microfluidic extension rheometry
A precision-machined cross-slot flow geometry with a shape that has been optimized by numerical simulation of the fluid kinematics is fabricated and used to measure the extensional viscosity of a dilute polymer solution. Full-field birefringence microscopy is used to monitor the evolution and growth of macromolecular anisotropy along the stagnation point streamline, and we observe the formation of a strong and uniform birefringent strand when the dimensionless flow strength exceeds a critical Weissenberg number Wicrit 0:5. Birefringence and bulk pressure drop measurements provide self consistent estimates of the planar extensional viscosity of the fluid over a wide range of deformation rates (26 s1 "_ 435 s1) and are also in close agreement with numerical simulations performed by using a finitely extensible nonlinear elastic dumbbell model
Morphological transition between diffusion-limited and ballistic aggregation growth patterns
In this work, the transition between diffusion-limited and ballistic
aggregation models was revisited using a model in which biased random walks
simulate the particle trajectories. The bias is controlled by a parameter
, which assumes the value (1) for ballistic
(diffusion-limited) aggregation model. Patterns growing from a single seed were
considered. In order to simulate large clusters, a new efficient algorithm was
developed. For , the patterns are fractal on the small length
scales, but homogeneous on the large ones. We evaluated the mean density of
particles in the region defined by a circle of radius centered
at the initial seed. As a function of , reaches the asymptotic
value following a power law
with a universal exponent , independent of . The
asymptotic value has the behavior , where . The characteristic crossover length that determines the transition
from DLA- to BA-like scaling regimes is given by ,
where , while the cluster mass at the crossover follows a power
law , where . We deduce the
scaling relations \beta=\n u\gamma and between these
exponents.Comment: 7 pages, 8 figure
Error threshold in the evolution of diploid organisms
The effects of error propagation in the reproduction of diploid organisms are
studied within the populational genetics framework of the quasispecies model.
The dependence of the error threshold on the dominance parameter is fully
investigated. In particular, it is shown that dominance can protect the
wild-type alleles from the error catastrophe. The analysis is restricted to a
diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge
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