We investigate, both theoretically and experimentally, the drift, diffusion, and recombination of excitons in the strain field of an edge threading dislocation intersecting the GaN{0001} surface. We calculate and measure hyperspectral cathodoluminescence maps around the dislocation outcrop for temperatures between 10 to 200 K. Contrary to common belief, the cathodoluminescence intensity contrast is only weakly affected by exciton diffusion, but is caused primarily by exciton dissociation in the piezoelectric field at the dislocation outcrop. Hence, the extension of the dark spots around dislocations in the luminescence maps cannot be used to determine the exciton diffusion length. However, the cathodoluminescence energy contrast, reflecting the local bandgap variation in the dislocation strain field, does sensitively depend on the exciton diffusion length and hence enables its experimental determination. arXiv:1906.05645v1 [cond-mat.mtrl-sci]

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In this paper, the investigations on stochastic cellular automata models of stable oscillations and autowaves in active media are summarized to formulate a concept of stochastic cellular automaton (CA) corresponding to asynchronous CAs with probabilistic transition rules. A formal description of a stochastic CA and a stochastic CA model is given. The properties and methods of synthesis of CA models for a specified set of elementary physical and chemical transformations are described. Some possibilities of simulating autowave and oscillatory processes are demonstrated using, as an example, a carbon monoxide oxidation reaction on a platinum catalyst with surface restructuring. The CA-simulation has made it possible to reveal the range of reaction parameter values with stable oscillations of reagent concentrations and to observe autowaves on the platinum surface. Special attention is given to providing a highly efficient parallel implementation of the stochastic CA algorithm. For this, the asynchronous mode must be preliminarily transformed to a block-synchronous one. Its equivalence to the asynchronous mode is justified. This is done for the CA reaction model by a comparative statistical analysis of the simulation results.

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