A Review of Multiscale Analysis: Examples from Systems Biology, Materials Engineering, and Other Fluid–Surface Interacting Systems

Abstract

Multiscale simulation is an emerging scientific field that spans many disciplines, including physics, chemistry, mathematics, statistics, chemical engineering, mechanical engineering, and materials science. This review paper first defines this new scientific field and outlines its objectives. An overview of deterministic, continuum models and discrete, particle models is then given. Among discrete, particle models, emphasis is placed on Monte Carlo stochastic simulation methods in well-mixed and spatially distributed systems. Next, a classification of multiscale methods is carried out based on separation of length and time scales and the computational and mathematical approach taken. Broadly speaking, hybrid simulation and coarse graining or mesoscopic modeling are identified as two general and complementary approaches of multiscale modeling. The former is further classified into onion- and multigrid-type simulation depending on length scales and the presence or not of gradients. Several approaches, such as the net event, the probability weighted, the Poisson and binomial τ-leap, and the hybrid, are discussed for acceleration of stochastic simulation. In order to demonstrate the unifying principles of multiscale simulation, examples from different areas are discussed, including systems biology, materials growth and other reacting systems, fluids, and statistical mechanics. While the classification is general and examples from other scales and tools are touched upon, in this review emphasis is placed on stochastic models, their coarse graining, and their integration with continuum deterministic models, i.e., on the coupling of mesoscopic and macroscopic scales. The concept of hierarchical multiscale modeling is discussed in some length. Finally, the importance of systems-level tools such as sensitivity analysis, parameter estimation, optimization, control, model reduction, and bifurcation in multiscale analysis is underscored.