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Concept
Multiscale modeling
Summary
Multiscale modeling or multiscale mathematics is the field of solving problems that have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids, solids, polymers, proteins, nucleic acids as well as various physical and chemical phenomena (like adsorption, chemical reactions, diffusion).
An example of such problems involve the Navier–Stokes equations for incompressible fluid flow.
In a wide variety of applications, the stress tensor is given as a linear function of the gradient . Such a choice for has been proven to be sufficient for describing the dynamics of a broad range of fluids. However, its use for more complex fluids such as polymers is dubious. In such a case, it may be necessary to use multiscale modeling to accurately model the system such that the stress tensor can be extracted without requiring the computational cost of a full microscale simulation.
Horstemeyer 2009, 2012 presented a historical review of the different disciplines (mathematics, physics, and materials science) for solid materials related to multiscale materials modeling.
The aforementioned DOE multiscale modeling efforts were hierarchical in nature. The first concurrent multiscale model occurred when Michael Ortiz (Caltech) took the molecular dynamics code, Dynamo, (developed by Mike Baskes at Sandia National Labs) and with his students embedded it into a finite element code for the first time. Martin Karplus, Michael Levitt, Arieh Warshel 2013 were awarded a Nobel Prize in Chemistry for the development of a multiscale model method using both classical and quantum mechanical theory which were used to model large complex chemical systems and reactions.
In physics and chemistry, multiscale modeling is aimed at the calculation of material properties or system behavior on one level using information or models from different levels. On each level, particular approaches are used for the description of a system.
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