Multiscale modeling: Difference between revisions

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{{Short description|Mathematical field}}

{{Over-quotation|date=August 2019}}

[[File:Holec2016P40.svg|thumb|Modeling approaches and their scales]]

'''Multiscale modeling''' or '''multiscale mathematics''' is the [[Branches of science|field]] of solving problems that have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids,<ref>{{Cite journal|last1=Chen|first1=Shiyi|last2=Doolen|first2=Gary D.|date=1998-01-01|title=Lattice Boltzmann Method for Fluid Flows|journal=Annual Review of Fluid Mechanics|volume=30|issue=1|pages=329–364|doi=10.1146/annurev.fluid.30.1.329|bibcode=1998AnRFM..30..329C}}</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|publisher=Springer }}</ref><ref>{{Cite journal |last1=Martins |first1=Ernane de Freitas |last2=da Silva |first2=Gabriela Dias |last3=Salvador |first3=Michele Aparecida |last4=Baptista |first4=Alvaro David Torrez |last5=de Almeida |first5=James Moraes |last6=Miranda |first6=Caetano Rodrigues |date=2019-10-28 |title=Uncovering the Mechanisms of Low-Salinity Water Injection EOR Processes: A Molecular Simulation Viewpoint |url=https://onepetro.org/OTCBRASIL/proceedings/19OTCB/3-19OTCB/Rio%20de%20Janeiro,%20Brazil/180751 |journal=Otc-29885-Ms |publisher=OTC |doi=10.4043/29885-MS|url-access=subscription }}</ref> solids,<ref name="Steinhauser 20082" /><ref>{{Cite journal|last1=Oden|first1=J. Tinsley|last2=Vemaganti|first2=Kumar|last3=Moës|first3=Nicolas|date=1999-04-16|title=Hierarchical modeling of heterogeneous solids|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|url=https://hal.science/hal-04243925 }}</ref> polymers,<ref>{{Cite journal|last1=Zeng|first1=Q. H.|last2=Yu|first2=A. B.|last3=Lu|first3=G. Q.|date=2008-02-01|title=Multiscale modeling and simulation of polymer nanocomposites|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.|s2cid=117867762 }}</ref> proteins,<ref>{{Cite journal|last1=Kmiecik|first1=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|journal=Chemical Reviews|doi=10.1021/acs.chemrev.6b00163|issn=0009-2665|pmid=27333362|volume=116|issue=14|pages=7898–936|doi-access=free}}</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)|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.|bibcode=2011ARPC...62..555D}}</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|issue=1–2|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|last1=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|s2cid=97819264 |display-authors=8}}</ref><ref>{{Cite journal |last1=da Silva |first1=Gabriela Dias |last2=de Freitas Martins |first2=Ernane |last3=Salvador |first3=Michele Aparecida |last4=Baptista |first4=Alvaro David Torrez |last5=de Almeida |first5=James Moraes |last6=Miranda |first6=Caetano Rodrigues |date=2019 |title=From Atoms to Pre-salt Reservoirs: Multiscale Simulations of the Low-Salinity Enhanced Oil Recovery Mechanisms |url=http://link.springer.com/10.1007/s41050-019-00014-1 |journal=Polytechnica |language=en |volume=2 |issue=1–2 |pages=30–50 |doi=10.1007/s41050-019-00014-1 |bibcode=2019Polyt...2...30D |issn=2520-8497|url-access=subscription }}</ref>

An example of such problems involve the [[Navier–Stokes equations|Navier-Stokes equations]] for incompressible fluid flow.

<math>\begin{array}{lcl} \rho_0(\partial_t\mathbf{u}+(\mathbf{u}\cdot\nabla)\mathbf{u})=\nabla\cdot\tau,

\\ \nabla\cdot\mathbf{u}=0. \end{array}</math>

In a wide variety of applications, the stress tensor <math>\tau</math> is given as a linear function of the gradient <math>\nabla u</math>. Such a choice for <math>\tau</math> 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.<ref>{{Cite book |last=E |first=Weinan |url=https://www.worldcat.org/oclc/721888752 |title=Principles of multiscale modeling |date=2011 |publisher=Cambridge University Press |isbn=978-1-107-09654-7 |___location=Cambridge |oclc=721888752}}</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 [[Michael Baskes|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|journal = Philosophical Magazine A|date = 1996-09-27|pages = 1529–1563|volume = 73|issue = 6|doi = 10.1080/01418619608243000|first1 = E.B.|last1 =Tadmore|first2 = M.|last2 = Ortiz|first3 = R.|last3 = Phillips|bibcode = 1996PMagA..73.1529T }}</ref> [[Martin Karplus]], [[Michael Levitt (biophysicist)|Michael Levitt]], and [[Arieh Warshel]] 2013received were awarded athe Nobel Prize in Chemistry in 2013 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)|journal=Angewandte Chemie International Edition|language=en|volume=53|issue=38|pages=9992–10005|doi=10.1002/anie.201403924|pmid=25066036|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)|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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* [[Equation-free modeling]]

* [[Integrated computational materials engineering]]

* [[Multilevel model]]

* [[Multiphysics]]

* [[Multiresolution analysis]]

* [[Space mapping]]

* [[Multiscale Reservoir Modeling]]

==References==

<references>

<ref name="Horstemeyer 2009">

{{cite book |first1=M. F. |last1=Horstemeyer |year=2009 |chapter=Multiscale Modeling: A Review |chapter-url=https://books.google.com/books?id=esOANcsz5w8C&pg=PA87 |pages=87–135 |editor1-first=Jerzy |editor1-last=Leszczyński |editor2-first=Manoj K. |editor2-last=Shukla |title=Practical Aspects of Computational Chemistry: Methods, Concepts and Applications |publisher=Springer |isbn=978-90-481-2687-3}}

</ref>

<ref name="Horstemeyer 2012">

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==Further reading==

*{{cite journal |pmid=19136256 |year=2009 |last1=Hosseini |first1=SA |last2=Shah |first2=N |title=Multiscale modelling of hydrothermal biomass pretreatment for chip size optimization |volume=100 |issue=9 |pages=2621–8 |doi=10.1016/j.biortech.2008.11.030 |journal=Bioresource Technology|bibcode=2009BiTec.100.2621H }}

*{{cite journal |bibcode=2009BAMS...90..515T |title=A Multiscale Modeling System: Developments, Applications, and Critical Issues |last1=Tao |first1=Wei-Kuo |last2=Chern |first2=Jiun-Dar |last3=Atlas |first3=Robert |last4=Randall |first4=David |last5=Khairoutdinov |first5=Marat |last6=Li |first6=Jui-Lin |last7=Waliser |first7=Duane E. |last8=Hou |first8=Arthur |last9=Lin |first9=Xin |last10=Jiang |first10=Jonathan |last11=Hou |first11=Arthur |last12=Lin |first12=Xin |last13=Peters-Lidard |first13=Christa |volume=90 |year=2009 |pages=515–534 |journal=Bulletin of the American Meteorological Society |doi=10.1175/2008BAMS2542.1 |issue=4|display-authors=8 |hdl=2060/20080039624 |hdl-access=free }}

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* [https://web.archive.org/web/20080220104618/http://www.mmm2008.org/bin/view.pl/Main/WebHome Multiscale Materials Modeling: Fourth International Conference, Tallahassee, FL, USA]

* [http://www.biocomp.chem.uw.edu.pl/multiscale_modeling.php Multiscale Modeling Tools for Protein Structure Prediction and Protein Folding Simulations, Warsaw, Poland]

* [http://www.e-xstream.com/applications/material-engineering/about-material-engineering Multiscale modeling for Materials Engineering: Set-up of quantitative micromechanical models]

* [https://web.archive.org/web/20190812193431/http://multiscale-modelling.eu/ Multiscale Material Modelling on High Performance Computer Architectures, MMM@HPC project]

* [http://www.modelingmaterials.org ''Modeling Materials: Continuum, Atomistic and Multiscale Techniques'' (E. B. Tadmor and R. E. Miller, Cambridge University Press, 2011)]