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Content available remote Combined Probabilistic Methods for Droplet Drying Simulations
The rapidly developing 3D printing and the related fabrication of ultra-thin layers in various industries have resulted in the need for theoretical methods for describing large-area systems of growing nanostructures. The specificity of these issues is the presence of multi-particle systems characterized by the coexistence of particles with a wide range of sizes typical for ions, nanoparticles, and their agglomerates. A particular example would be an aqueous nano-colloidal suspension drying on a substrate as a self-assembling deposit. It should be emphasized here that the development of deposit patterning control techniques is one of the most important challenges for the thin film industry. In this paper we show that probabilistic methods can be successfully used to model such systems. To this aim, the combined master equation and Monte Carlo methods were used for computer simulation of a drying droplet in the case of a low concentration salt solution.The novelty of this approach is to show the possibility of computer simulation for a microscopic system while simulating large-scale processes affecting microscopic processes. The numerical results were additionally supported by experimental data.
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function ρ(x, t). Our main goal is to demonstrate a compatibility of a direct solution method (an explicit, albeit numerically assisted, integration of the master equation) with an indirect pathwise procedure, recently proposed in [Physica A 392, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large sample path data, that are generated by means of a properly tailored Gillespie’s algorithm. Their statistical analysis in turn allows to infer the dynamics of ρ(x, t). However, no consistency check has been completed so far to demonstrate that both methods are fully compatible and indeed provide a solution of the same dynamical problem. Presently we remove this gap, with a focus on potential deficiencies (various cutoffs, including those upon the jump size) of approximations involved in simulation routines and solutions protocols.
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