Overview of Discrete, Particle Models

Discrete models treat individual atoms, molecules, or particles and can be deterministic or stochastic. Examples of the former include MD simulations. Examples of the latter are various MC methods, BD, DPD, DSMC, and LB simulations. There are different ensembles in which these simulations can be performed, depending on the quantities that one is interested in computing. 

Different techniques are suitable for different tasks. For example, BD focuses on molecules and particles in solution where the solvent is implicitly lumped into a friction force. On the other hand, DSMC and LB are typically applied to various fluid-related problems. MD is the only fundamental, first principles tool where the equations of motion are solved using as input an interparticle potential. MC methods map the system description into a stochastic Markov-based framework. MD and MC are often thought of as molecular modeling tools, whereas the rest are mesoscopic tools (lattice MC is also a mesoscopic tool). 

Obviously, the spectrum of mesoscale, particle-based tools is too vast to be covered in a single paper. Therefore, in this and the subsequent sections, I mainly elaborate on MC methods to illustrate various aspects of multiscale modeling and simulation. Below, the modeling hierarchy for stochastic well-mixed chemically reacting systems is first outlined, followed by a brief introduction to MC methods. 

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