Mesoscopic scale
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In physics and chemistry, the mesoscopic scale refers to the length scale at which one can reasonably discuss the properties of a material or phenomenon without having to discuss the behavior of individual atoms, and concepts of averages such as density and temperature are useful. For solids and liquids this is typically a few to ten nanometers, and involves averaging over a few thousand atoms or molecules. Hence, the mesoscopic scale is roughly identical to the nanoscopic scale for most solids.
The prefix meso- comes from the Greek word mesos, meaning middle. The mesoscopic scale thus lies between the macroscopic scale of the world we live in, and the atomic scale in which each atom is considered separately resolved. Thus the mesoscale fills the middle ground between single discrete elements or large statistical collections. As an analogy, psychologists focus mainly on the behavior and mental processes of the individual while sociologists study the behavior of large societal groups, but a situation where only 3 people are interacting can be considered mesoscale.
For practical purposes, the mesoscopic scale is the size at which it becomes reasonable to talk about the average density, charge or other characteristics of a material, and where statistical properties such as temperature and entropy have meaning. Because dealing with individual atoms can easily become mathematically unwieldy, scientists often perform calculations by averaging over structure "at the mesoscopic scale", meaning they replace the discrete structure of atoms with a continuous distribution of mass, charge, etc, whose values are taken as equal to that from averaging over several thousands atoms in that vicinity. For many problems, such mesoscopic averaging allows one to very accurately predict macroscopic behavior and properties.
For technical purposes, the mesoscopic scale is the size at which the expected fluctuations of the averaged properties due to the motion and behavior of individual particles can be reduced to below some desirable threshold (often a few percent), and must be rigorously established within the context of any particular problem.
