Multiscale modeling: Difference between revisions

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In [[engineering]], [[mathematics]], [[physics]], [[chemistry]], [[bioinformatics]], [[computational biology]], [[meteorology]] and [[computer science]], '''multiscale modeling''' or '''multiscale mathematics''' is the field of solving problems which have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids,<ref>{{Cite journal|last=Chen|first=Shiyi|last2=Doolen|first2=Gary D.|date=1998-01-01|title=Lattice Boltzmann Method for Fluid Flows|url=http://dx.doi.org/10.1146/annurev.fluid.30.1.329|journal=Annual Review of Fluid Mechanics|volume=30|issue=1|pages=329–364|doi=10.1146/annurev.fluid.30.1.329}}</ref><ref name="Steinhauser 20082">{{cite book|title=Multiscale Modeling of Fluids and Solids - Theory and Applications|year=2017|isbn=978-3662532225|first1=M. O.|last1=Steinhauser}}</ref> solids,<ref name="Steinhauser 20082" /><ref>{{Cite journal|last=Oden|first=J. Tinsley|last2=Vemaganti|first2=Kumar|last3=Moës|first3=Nicolas|date=1999-04-16|title=Hierarchical modeling of heterogeneous solids|url=http://www.sciencedirect.com/science/article/pii/S0045782598002242|journal=Computer Methods in Applied Mechanics and Engineering|volume=172|issue=1|pages=3–25|doi=10.1016/S0045-7825(98)00224-2|bibcode=1999CMAME.172....3O}}</ref> polymers,<ref>{{Cite journal|last=Zeng|first=Q. H.|last2=Yu|first2=A. B.|last3=Lu|first3=G. Q.|date=2008-02-01|title=Multiscale modeling and simulation of polymer nanocomposites|url=http://www.sciencedirect.com/science/article/pii/S0079670007001049|journal=Progress in Polymer Science|volume=33|issue=2|pages=191–269|doi=10.1016/j.progpolymsci.2007.09.002}}</ref><ref name="Baeurle 20092">{{cite journal|year=2008|title=Multiscale modeling of polymer materials using field-theoretic methodologies: A survey about recent developments|journal=Journal of Mathematical Chemistry|volume=46|issue=2|pages=363–426|doi=10.1007/s10910-008-9467-3|last1=Baeurle|first1=S. A.}}</ref> proteins,<ref>{{Cite journal|last=Kmiecik|first=Sebastian|last2=Gront|first2=Dominik|last3=Kolinski|first3=Michal|last4=Wieteska|first4=Lukasz|last5=Dawid|first5=Aleksandra Elzbieta|last6=Kolinski|first6=Andrzej|date=2016-06-22|title=Coarse-Grained Protein Models and Their Applications|url=http://dx.doi.org/10.1021/acs.chemrev.6b00163|journal=Chemical Reviews|doi=10.1021/acs.chemrev.6b00163|issn=0009-2665|pmid=27333362|volume=116|pages=7898–936}}</ref><ref name=":0">{{Cite journal|last=Levitt|first=Michael|date=2014-09-15|title=Birth and Future of Multiscale Modeling for Macromolecular Systems (Nobel Lecture)|url=http://onlinelibrary.wiley.com/doi/10.1002/anie.201403691/abstract|journal=Angewandte Chemie International Edition|language=en|volume=53|issue=38|pages=10006–10018|doi=10.1002/anie.201403691|issn=1521-3773|pmid=25100216}}</ref><ref name=":1" /><ref name=":2" /> [[nucleic acids]]<ref name="de Pablo 20112">{{cite journal|year=2011|title=Coarse-Grained Simulations of Macromolecules: From DNA to Nanocomposites|journal=Annual Review of Physical Chemistry|volume=62|pages=555–74|doi=10.1146/annurev-physchem-032210-103458|pmid=21219152|last1=De Pablo|first1=Juan J.}}</ref> as well as various physical and chemical phenomena (like adsorption, chemical reactions, [[diffusion]]).<ref name=":1" /><ref name="Knizhnik2">{{cite journal|last2=Bagaturyants|first2=A.A.|last3=Belov|first3=I.V.|last4=Potapkin|first4=B.V.|last5=Korkin|first5=A.A.|year=2002|title=An integrated kinetic Monte Carlo molecular dynamics approach for film growth modeling and simulation: ZrO2 deposition on Si surface|journal=Computational Materials Science|volume=24|pages=128–132|doi=10.1016/S0927-0256(02)00174-X|last1=Knizhnik|first1=A.A.}}</ref><ref name="Adams2">{{cite journal|last2=Astapenko|first2=V.|last3=Chernysheva|first3=I.|last4=Chorkov|first4=V.|last5=Deminsky|first5=M.|last6=Demchenko|first6=G.|last7=Demura|first7=A.|last8=Demyanov|first8=A.|last9=Dyatko|first9=N.|year=2007|title=Multiscale multiphysics nonempirical approach to calculation of light emission properties of chemically active nonequilibrium plasma: Application to Ar GaI3 system|journal=Journal of Physics D: Applied Physics|volume=40|issue=13|pages=3857–3881|bibcode=2007JPhD...40.3857A|doi=10.1088/0022-3727/40/13/S06|author1=Adamson|first1=S.|last10=Eletzkii|first10=A|last11=Knizhnik|first11=A|last12=Kochetov|first12=I|last13=Napartovich|first13=A|last14=Rykova|first14=E|last15=Sukhanov|first15=L|last16=Umanskii|first16=S|last17=Vetchinkin|first17=A|last18=Zaitsevskii|first18=A|last19=Potapkin|first19=B|display-authors=8}}</ref>

==History==

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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.<ref>{{Cite journal|title = Quasicontinuum Analysis of Defects in Solids|url = http://www.tandfonline.com/doi/abs/10.1080/01418619608243000#.VmnyPTYdWLk|journal = Taylor and Francis|date = 1996-09-27|pages = 1529–1563|volume = 73|issue = 6|doi = 10.1080/01418619608243000|first = E.B.|last =Tadmore|first2 = M.|last2 = Ortiz|first3 = R.|last3 = Phillips|bibcode = 1996PMagA..73.1529T }}</ref> [[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.<ref name=":0" /><ref name=":1">{{Cite journal|last=Karplus|first=Martin|date=2014-09-15|title=Development of Multiscale Models for Complex Chemical Systems: From H+H2 to Biomolecules (Nobel Lecture)|url=http://onlinelibrary.wiley.com/doi/10.1002/anie.201403924/abstract|journal=Angewandte Chemie International Edition|language=en|volume=53|issue=38|pages=9992–10005|doi=10.1002/anie.201403924|issn=1521-3773}}</ref><ref name=":2">{{Cite journal|last=Warshel|first=Arieh|date=2014-09-15|title=Multiscale Modeling of Biological Functions: From Enzymes to Molecular Machines (Nobel Lecture)|url=http://onlinelibrary.wiley.com/doi/10.1002/anie.201403689/abstract|journal=Angewandte Chemie International Edition|language=en|volume=53|issue=38|pages=10020–10031|doi=10.1002/anie.201403689|issn=1521-3773|pmid=25060243|pmc=4948593}}</ref>

==Areas of research==

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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]]. Multiscale decision-making 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. 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 ~ {{val|500|u=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 ~ {{val|100|u=km}}, 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 time we do not lose much information, with the help of making some rational guesses, a process called Parametrization.

Besides the many specific applications, one area of research is methods for the accurate and efficient solution of multiscale modeling problems. The primary areas of mathematical and algorithmic development include: