21 research outputs found
Particle Survival and Polydispersity in Aggregation
We study the probability, , of a cluster to remain intact in
one-dimensional cluster-cluster aggregation when the cluster diffusion
coefficient scales with size as . exhibits a
stretched exponential decay for and the power-laws for
, and for . A random walk picture
explains the discontinuous and non-monotonic behavior of the exponent. The
decay of determines the polydispersity exponent, , which
describes the size distribution for small clusters. Surprisingly,
is a constant for .Comment: submitted to Europhysics Letter
No self-similar aggregates with sedimentation
Two-dimensional cluster-cluster aggregation is studied when clusters move
both diffusively and sediment with a size dependent velocity. Sedimentation
breaks the rotational symmetry and the ensuing clusters are not self-similar
fractals: the mean cluster width perpendicular to the field direction grows
faster than the height. The mean width exhibits power-law scaling with respect
to the cluster size, ~ s^{l_x}, l_x = 0.61 +- 0.01, but the mean height
does not. The clusters tend to become elongated in the sedimentation direction
and the ratio of the single particle sedimentation velocity to single particle
diffusivity controls the degree of orientation. These results are obtained
using a simulation method, which becomes the more efficient the larger the
moving clusters are.Comment: 10 pages, 10 figure
Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation
The persistence probability, , of a cluster to remain unaggregated is
studied in cluster-cluster aggregation, when the diffusion coefficient of a
cluster depends on its size as . In the mean-field the
problem maps to the survival of three annihilating random walkers with
time-dependent noise correlations. For the motion of persistent
clusters becomes asymptotically irrelevant and the mean-field theory provides a
correct description. For the spatial fluctuations remain relevant
and the persistence probability is overestimated by the random walk theory. The
decay of persistence determines the small size tail of the cluster size
distribution. For the distribution is flat and, surprisingly,
independent of .Comment: 11 pages, 6 figures, RevTeX4, submitted to Phys. Rev.
The electric field close to an undulating interface
The electric potential close to a boundary between two dielectric material layers reflects the geometry of such an interface. The local variations arise from the combination of material parameters and from the nature of the inhomogeneity. Here, the arising electric field is considered for both a sinusoidally varying boundary and for a ârough,â Gaussian test case. We discuss the applicability of a one-dimensional model with the varying layer thickness as a parameter and the generic scaling of the results. As an application we consider the effect of paper roughness on toner transfer in electrophotographic printing.Peer reviewe
Persistence in Cluster--Cluster Aggregation
Persistence is considered in diffusion--limited cluster--cluster aggregation,
in one dimension and when the diffusion coefficient of a cluster depends on its
size as . The empty and filled site persistences are
defined as the probabilities, that a site has been either empty or covered by a
cluster all the time whereas the cluster persistence gives the probability of a
cluster to remain intact. The filled site one is nonuniversal. The empty site
and cluster persistences are found to be universal, as supported by analytical
arguments and simulations. The empty site case decays algebraically with the
exponent . The cluster persistence is related to the
small behavior of the cluster size distribution and behaves also
algebraically for while for the behavior is
stretched exponential. In the scaling limit and with fixed the distribution of intervals of size between
persistent regions scales as , where is the average interval size and . For finite the
scaling is poor for , due to the insufficient separation of the two
length scales: the distances between clusters, , and that between
persistent regions, . For the size distribution of persistent regions
the time and size dependences separate, the latter being independent of the
diffusion exponent but depending on the initial cluster size
distribution.Comment: 14 pages, 12 figures, RevTeX, submitted to Phys. Rev.
Coarsening of Sand Ripples in Mass Transfer Models with Extinction
Coarsening of sand ripples is studied in a one-dimensional stochastic model,
where neighboring ripples exchange mass with algebraic rates, , and ripples of zero mass are removed from the system. For ripples vanish through rare fluctuations and the average ripples mass grows
as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as
or depending on the symmetry of the mass transfer, and
asymptotically the system is characterized by a product measure. The stationary
ripple mass distribution is obtained exactly. For ripple evolution
is linearly unstable, and the noise in the dynamics is irrelevant. For the problem is solved on the mean field level, but the mean-field theory
does not adequately describe the full behavior of the coarsening. In
particular, it fails to account for the numerically observed universality with
respect to the initial ripple size distribution. The results are not restricted
to sand ripple evolution since the model can be mapped to zero range processes,
urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.
Porous structure of thick fiber webs
The bulk properties and stochastic pore geometry of finite-thickness fiber webs are studied using a realistic model for the sedimentation of flexible fibers [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)]. The resulting web structure is controlled by a dimensionless number F=Tfwf/tf, where Tf is fiber flexibility, wf fiber width, and tf fiber thickness. The fiber length (â«wf,tf) is irrelevant. With increasing coverage cÌ, a crossover occurs at cÌ=c0â1+2F from a vacancy-controlled two-dimensional (2D) structure to a pore-controlled 3D structure. The 3D structures are isomorphic in that the pore dimensions are exponentially distributed, with the decay rate dependent only on F.Peer reviewe
Failure of planar fiber networks
We study the failure of planar random fiber networks with computer simulations. The networks are grown by adding flexible fibers one by one on a growing deposit [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)], a process yielding realistic three dimensional network structures. The network thus obtained is mapped to an electrical analogue of the elastic problem, namely to a random fuse network with separate bond elements for the fiber-to-fiber contacts. The conductivity of the contacts (corresponding to the efficiency of stress transfer between fibers) is adjustable. We construct a simple effective medium theory for the current distribution and conductivity of the networks as a function of intra-fiber current transfer efficiency. This analysis compares favorably with the computed conductivity and with the fracture properties of fiber networks with varying fiber flexibility and network thickness. The failure characteristics are shown to obey scaling behavior, as expected of a disordered brittlematerial, which is explained by the high current end of the current distribution saturating in thick enough networks. For bond breaking, fracture load and strain can be estimated with the effective medium theory. For fiber breaking, we find the counter-intuitive result that failure is more likely to nucleate far from surfaces, as the stress is transmitted more effectively to the fibers in the interior.Peer reviewe
Dynamic Scaling in One-Dimensional Cluster-Cluster Aggregation
We study the dynamic scaling properties of an aggregation model in which
particles obey both diffusive and driven ballistic dynamics. The diffusion
constant and the velocity of a cluster of size follow
and , respectively. We determine the dynamic exponent and
the phase diagram for the asymptotic aggregation behavior in one dimension in
the presence of mixed dynamics. The asymptotic dynamics is dominated by the
process that has the largest dynamic exponent with a crossover that is located
at . The cluster size distributions scale similarly in all
cases but the scaling function depends continuously on and .
For the purely diffusive case the scaling function has a transition from
exponential to algebraic behavior at small argument values as changes
sign whereas in the drift dominated case the scaling function decays always
exponentially.Comment: 6 pages, 6 figures, RevTeX, submitted to Phys. Rev.
Persistence properties of a system of coagulating and annihilating random walkers
We study a d-dimensional system of diffusing particles that on contact either
annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1).
In 1-dimension, the system models the zero temperature Glauber dynamics of
domain walls in the q-state Potts model. We calculate P(m,t), the probability
that a randomly chosen lattice site contains a particle whose ancestors have
undergone exactly (m-1) coagulations. Using perturbative renormalization group
analysis for d < 2, we show that, if the number of coagulations m is much less
than the typical number M(t), then P(m,t) ~ m^(z/d) t^(-theta), with theta=d Q
+ Q(Q-1/2) epsilon + O(epsilon^2), z=(2Q-1) epsilon + (2 Q-1) (Q-1)(1/2+A Q)
epsilon^2 +O(epsilon^3), where Q=(q-1)/q, epsilon =2-d and A =-0.006. M(t) is
shown to scale as t^(d/2-delta), where delta = d (1 -Q)+(Q-1)(Q-1/2) epsilon+
O(epsilon^2). In two dimensions, we show that P(m,t) ~ ln(t)^(Q(3-2Q))
ln(m)^((2Q-1)^2) t^(-2Q) for m << t^(2 Q-1). The 1-dimensional results
corresponding to epsilon=1 are compared with results from Monte Carlo
simulations.Comment: 12 pages, revtex, 5 figure