E. K. O. Hellén

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 (≫wf,tf) is irrelevant. With increasing coverage c, a crossover occurs at c=c0≈1+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.

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 “rough,” 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.

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, , lx = 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 more efficient the larger the moving clusters are.

Persistence in cluster-cluster aggregation

Persistence is considered in one-dimensional diffusion-limited cluster-cluster aggregation when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). The probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences. The cluster persistence gives the probability of a cluster remaining intact. The empty site and cluster persistences are universal whereas the filled site depends on the initial concentration. For gamma>0 the universal persistences decay algebraically with the exponent 2/(2-gamma). For the empty site case the exponent remains the same for gamma<0 but the cluster persistence shows a stretched exponential behavior as it is related to the small s behavior of the cluster size distribution. The scaling of the intervals between persistent regions demonstrates the presence of two length scales: the one related to the distances between clusters and that between the persistent regions.

Cluster survival and polydispersity in aggregation

We study the probability, PS(t), of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as D(s) ~ sγ. PS(t) exhibits a stretched exponential decay for γ < 0 and the power laws t−3/2 for γ = 0, and t−2/(2 − γ) for 0 < γ < 2. A random walk picture explains the discontinuous and non-monotonic behavior of the exponent. The decay of PS(t) determines the polydispersity exponent, τ, which describes the size distribution for small clusters. Surprisingly, τ(γ) is a constant τ = 0 for 0 < γ < 2.

Multilayer cooperative sequential adsorption

Cooperative sequential adsorption is here extended to multilayer coverages. We discuss two different growth rules with cooperativity either restricted to only the first layer of coverage or applied in all layers. The unrestricted variant is considered in the case where lateral growth dominates over the nucleation of terraces. The limit of completely suppressed nucleation corresponds to a morphological transition to a flat interface from one governed by the Kardar–Parisi–Zhang equation. With the restricted growth rule we find interesting behavior resulting from a competition between lateral growth at the first layer and growth on the top of nucleated islands. There is an intermediate regime between random deposition at the submonolayer coverage and asymptotic random deposition behavior. In this regime the kinetic roughening can be studied by applying sequential adsorption rate equations for cluster lengths in the first layer, with an additional geometric argument.