A stochastic atomic-scale lattice-based numerical method based on the Exact Lattice First Passage Time method was developed for the simulation of the early stages of kinetically controlled electrochemical nucleation and growth. Electrochemical reaction and surface diffusion on a hexagonal lattice was accounted for in a pristine physical model system that included edge diffusion along steps, and movement over step edges with Ehrlich-Schwöbel barrier. Five cases were investigated: homoexpitaxy, heteroepitaxy, multi-layer growth, terraces, and confined regions. For each, the influence of the physical parameters, deposition conditions, and system geometry on growth morphology was investigated. Simulation based studies of multilayer surface morphology were able to distinguish between layer-by-layer and island growth modes. On stepped terraces, parameter regions associated with he surface diffusion to deposition flux ratio (D/F) and the Ehrlich-Schwöbel barrier were identified under which deposition occurred either at the step edge or by nucleation and growth of islands on the terraces. The probability of growing single crystals in a small confined region was found to scale with D/F and the radius squared. © 2014 The Electrochemical Society.

We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096 × 4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands. © 2013 Elsevier Inc.

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.