24,550 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
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
Exact solution for the energy density inside a one-dimensional non-static cavity with an arbitrary initial field state
We study the exact solution for the energy density of a real massless scalar
field in a two-dimensional spacetime, inside a non-static cavity with an
arbitrary initial field state, taking into account the Neumann and Dirichlet
boundary conditions. This work generalizes the exact solution proposed by Cole
and Schieve in the context of the Dirichlet boundary condition and vacuum as
the initial state. We investigate diagonal states, examining the vacuum and
thermal field as particular cases. We also study non-diagonal initial field
states, taking as examples the coherent and Schrodinger cat states.Comment: 10 pages, 8 figure
Avaliação da composição da uva e do vinho varietal 'Tempranillo' segundo a época de produção, na região do Vale do Submédio São Francisco.
O Vale do Submédio do São Francisco é a segunda região produtora de vinhos finos do Brasil, sendo responsável por 15% da produção nacional, com oito milhões de litros/ano
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
Explicit parametrization of more than one vector-like quark of Nelson-Barr type
Nelson-Barr models solve the strong CP problem based on spontaneous CP
violation and generically requires vector-like quarks (VLQs) mixing with
standard quarks to transmit the CP violation. We devise an explicit
parametrization for the case of two VLQs of either down-type or up-type and
quantitatively study several aspects including the hierarchy of the VLQ Yukawas
and their irreducible contribution to . In particular, with the
use of the parametrization, we show that a big portion of the parameter space
for two up-type VLQs at the TeV scale is still allowed by the constraint on
, although this case had been previously shown to be very
restricted based on estimates
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