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# Multiscale modeling

In engineering, mathematics, physics, meteorology and computer science, multiscale modeling is the field of solving physical problems which have important features at multiple scales, particularly multiple spatial and(or) temporal scales. Important problems include scale linking (Baeurle 2009[1], de Pablo 2011[2], Knizhnik 2002[3], Adamson 2007[4]). Horstemeyer 2009[5] presented historical review of the different disciplines (solid mechanics, numerical methods, mathematics, physics, and materials science) for solid materials related to multiscale materials modeling.

Multiscale modeling in physics is aimed to calculation of material properties or system behaviour on one level using information or models from different levels. On each level particular approaches are used for description of a system. Following levels are usually distinguished: level of quantum mechanical models (information about electrons is included), level of molecular dynamics models (information about individual atoms is included), mesoscale or nano level (information about groups of atoms and molecules is included), level of continuum models, level of device models. Each level addresses a phenomenon over a specific window of length and time. Multiscale modeling is particularly important in integrated computational materials engineering since it allows to predict material properties or system behaviour based on knowledge of the atomistic structure and properties of elementary processes.

In Operations Research, multiscale modeling addresses challenges for decision makers which come from multiscale phenomena across organizational, temporal and spatial scales. This theory fuses decision theory and multiscale mathematics and is referred to as Multiscale decision making. The Multiscale decision making approach draws upon the analogies between physical systems and complex man-made systems.

In Meteorology, multiscale modeling is the modeling of interaction between weather systems of different spatial and temporal scales that produces the weather that we experience finally. The most challenging task is to model the way through which the weather systems interact as models cannot see beyond the limit of the model grid size. In other words, to run an atmospheric model that is having a grid size (very small ~ 500 m) which can see each possible cloud structure for the whole globe is computationally very expensive. On the other hand, a computationally feasible Global climate model (GCM, with grid size ~ 100km, cannot see the smaller cloud systems. So we need to come to a balance point so that the model becomes computationally feasible and at the same we do not lose much information, with the help of making some rational guesses, a process called Parametrization.

## References

1. ^ Baeurle, S.A. (2009). "Multiscale modeling of polymer materials using field-theoretic methodologies: a survey about recent developments". J. Math. Chem. 46 (2): 363–426. doi:10.1007/s10910-008-9467-3.
2. ^ de Pablo, J.J. (2011). "Coarse-grained simulations of macromolecules: From DNA to nanocomposites". Annu. Rev. Phys. Chem. 62 (1): 555–574. doi:10.1146/annurev-physchem-032210-103458.
3. ^ Knizhnik, A.A.; Bagaturyants, A.A.; Belov, I.V.; Potapkin, B.V. and Korkin, A.A. (2002). "An integrated kinetic Monte Carlo molecular dynamics approach for film growth modeling and simulation: ZrO2 deposition on Si(1 0 0) surface". Computational Materials Science 24 (1-2): 128–132. doi:10.1016/S0927-0256(02)00174-X.
4. ^ Adamson, S.; Astapenko, V.; Chernysheva, I. et al. (2007). "Multiscale multiphysics non empirical approach to calculation of light emission properties of chemically active non-equilibrium plasma: application to Ar–GaI3 system". J. Phys. D: Appl. Phys. 40 (13): 3857–3881. Bibcode 2007JPhD...40.3857A. doi:10.1088/0022-3727/40/13/S06.
5. ^ Horstemeyer M.F., "Multiscale Modeling: A Review," Practical Aspects of Computational Chemistry, ed. J. Leszczynski and M.K. Shukla, Springer Science+Business Media, pp. 87-135, 2009

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