Multiscale modeling
Encyclopedia
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, de Pablo 2011, Knizhnik 2002, Adamson 2007). Horstemeyer 2009 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.
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
and computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, 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, de Pablo 2011, Knizhnik 2002, Adamson 2007). Horstemeyer 2009 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
Integrated computational materials engineering
Integrated Computational Materials Engineering is an approach to design products, the materials that comprise them, and their associated materials processing methods by linking materials models at multiple length scales. Key words are "Integrated", involving integrating models at multiple length...
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
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
, multiscale modeling addresses challenges for decision makers which come from multiscale phenomena across organizational, temporal and spatial scales. This theory fuses decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
and multiscale mathematics
Multiscale mathematics
Multiscale mathematics is a branch of applied and computational mathematics concerned with the accurate and efficient solution of mathematical expressions representing the physical laws of nature across several levels of physical organization and/or spatial/temporal scales.The primary areas of...
and is referred to as Multiscale decision making
Multiscale decision making
Multiscale decision making, also referred to as Multiscale decision theory , is a recently developed approach in operations research that fuses game theory, multi-agent influence diagrams, in particular dependency graphs, and Markov decision processes to solve multiscale challenges across...
. The Multiscale decision making
Multiscale decision making
Multiscale decision making, also referred to as Multiscale decision theory , is a recently developed approach in operations research that fuses game theory, multi-agent influence diagrams, in particular dependency graphs, and Markov decision processes to solve multiscale challenges across...
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
Global climate model
A General Circulation Model is a mathematical model of the general circulation of a planetary atmosphere or ocean and based on the Navier–Stokes equations on a rotating sphere with thermodynamic terms for various energy sources . These equations are the basis for complex computer programs commonly...
(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.
External links
- Multiscale Modeling of Materials (MMM-Tools) Project at Dr. Martin Steinhauser's group at the Fraunhofer-Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, at Freiburg, Germany
- Multiscale Modeling Group: Institute of Physical & Theoretical Chemistry, University of Regensburg, Regensburg, Germany
- Multiscale modeling of hydrothermal biomass pretreatment for chip size optimization
- Multiscale Materials Modeling: Fourth International Conference, Tallahassee, FL, USA
- Multiscale Modeling Tools for Protein Structure Prediction and Protein Folding Simulations, Warsaw, Poland
- A MULTISCALE MODELING SYSTEM : Developments, Applications, and Critical issues
- Multiscale modeling for Integrated Computational Materials Engineering (ICME)
- Multiscale Material Modelling on High Performance Computer Architectures, MMM@HPC project
- Modeling Materials: Continuum, Atomistic and Multiscale Techniques (E. B. Tadmor and R. E. Miller, Cambridge University Press, 2011)
See also
- Computational mechanicsComputational mechanicsComputational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely...
- MultiphysicsMultiphysicsMultiphysics treats simulations that involve multiple physical models or multiple simultaneous physical phenomena. For example, combining chemical kinetics and fluid mechanics or combining finite elements with molecular dynamics...
- Integrated computational materials engineeringIntegrated computational materials engineeringIntegrated Computational Materials Engineering is an approach to design products, the materials that comprise them, and their associated materials processing methods by linking materials models at multiple length scales. Key words are "Integrated", involving integrating models at multiple length...