We present a versatile cooperative three-state model with adsorption and evaporation defined on different topologies: two- and three-dimensional lattices and Cayley trees. We discuss this model in the context of two main applications: silica and titania self-assembled optical coatings on glass substrates and drug encapsulation of two different types of nanoparticles on tree-like synthetic polymers called dendrimers and described mathematically as Cayley trees. We present analytical and Monte Carlo simulation results for these different topologies and discuss other possible extensions of the model to social sciences.
As the political landscape becomes increasingly complex, the classic paradigms used in political science have failed to remain relevant and other methods of study are needed. We introduce a population dynamics model and a multi-temperature kinetic Ising model to analyze the partisanship dynamics of the US Senate. We use Monte Carlo simulations, mean field theory and numerical analysis of the master equation of a system of 100 senators (agents) separated into various categories based on their political leanings and interactions with each other. Results show an interesting development of partisanship between the agents after a short time. The model can be extended to other cooperative stochastic systems in physics and social sciences.
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