Statistics of interfacial fluctuations of radially growing clusters

Universal fluctuations of global geometrical measurements in planar clusters

We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from simulations of both continuous and discrete models of kinetically rough interfaces, including several universality classes, such as Kardar-Parisi-Zhang. We mostly focus on the scaling behavior with time of the sample-to-sample deviation for those global magnitudes, but we have also characterized their histograms and correlations.

Eden model with nonlocal growth rules and kinetic roughening in biological systems

We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. The concentration of nutrients necessary for replication is assumed to be proportional to the voids connecting the replicating cells to the outer region, introducing therefore a nonlocal dependence on the replication rule. Our simulations point out that the Kadar-Parisi-Zhang (KPZ) universality class is a transient that can last for long periods in plentiful environments. For conditions of nutrient scarcity, we observe a crossover from regular KPZ to unstable growth, passing by a transient consistent with the quenched KPZ class at the pinning transition. Our analysis sheds light on results reporting on the universality class of kinetic roughening in akin experiments of biological growth.

Diffusion in an expanding medium: Fokker-Planck equation, Green's function, and first-passage properties

We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical expression for the Green's function (propagator) and investigate both analytically and numerically how this function and the associated moments behave. We also study first-passage properties in expanding hyperspherical geometries. We show that in all cases the behavior is determined to a great extent by the so-called Brownian conformal time τ(t), which we define via the relation τ[over ̇]=1/a^{2}, where a(t) is the expansion scale factor. If the medium expansion is driven by a power law [a(t)∝t^{γ} with γ>0], then we find interesting crossover effects in the mixing effectiveness of the diffusion process when the characteristic exponent γ is varied. Crossover effects are also found at the level of the survival probability and of the moments of the first passage-time distribution with two different regimes separated by the critical value γ=1/2. The case of an exponential scale factor is analyzed separately both for expanding and contracting media. In the latter situation, a stationary probability distribution arises in the long-time limit.

Anomalous surface relaxations of branched-polymer melts

The dynamics of thermally stimulated surface fluctuations of 100 nm thick films of long-branched polymers are measured for the first time. In contrast to comparable films of linear or cyclic chains that show no change in viscosity upon confinement, films of 6-pom, 6-star, and 6-end end-branched stars show viscosities, inferred from x-ray photon correlation spectroscopy, as much as 100 times higher than in the bulk. This difference varies in magnitude with chain architecture. Branching has a profound effect on confinement, even for these unentangled chains.