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Concept
Microscale and macroscale models
Summary
Microscale models form a broad class of computational models that simulate fine-scale details, in contrast with macroscale models, which amalgamate details into select categories. Microscale and macroscale models can be used together to understand different aspects of the same problem.
Macroscale models can include ordinary, partial, and integro-differential equations, where categories and flows between the categories determine the dynamics, or may involve only algebraic equations. An abstract macroscale model may be combined with more detailed microscale models. Connections between the two scales are related to multiscale modeling. One mathematical technique for multiscale modeling of nanomaterials is based upon the use of multiscale Green's function.
In contrast, microscale models can simulate a variety of details, such as individual bacteria in biofilms, individual pedestrians in simulated neighborhoods, individual light beams in ray-tracing imagery, individual houses in cities, fine-scale pores and fluid flow in batteries, fine-scale compartments in meteorology, fine-scale structures in particulate systems, and other models where interactions among individuals and background conditions determine the dynamics.
Discrete-event models, individual-based models, and agent-based models are special cases of microscale models. However, microscale models do not require discrete individuals or discrete events. Fine details on topography, buildings, and trees can add microscale detail to meteorological simulations and can connect to what is called mesoscale models in that discipline. Square-meter-sized landscape resolution available from images allows water flow across land surfaces to be modeled, for example, rivulets and water pockets, using gigabyte-sized arrays of detail. Models of neural networks may include individual neurons but may run in continuous time and thereby lack precise discrete events.
Ideas for computational microscale models arose in the earliest days of computing and were applied to complex systems that could not accurately be described by standard mathematical forms.
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