Multiscale modeling information

The discussion above focused on onion-type hybrid multiscale simulation. Finally, even though there are a limited number of examples published, I expect that the multigrid-type hybrid simulations share the same problems with onion-type hybrid multiscale models. In addition, appropriate boundary conditions for the microscopic grid model need to be developed to increase the accuracy and robustness of the hybrid scheme. Furthermore, the inverse problem of mapping coarse-grid information into a microscopic grid is ill posed. Thus, it is... 

I expect that SA of stochastic and multiscale models will be important in traditional tasks such as the identification of rate-determining steps and parameter estimation. I propose that SA will also be a key tool in controlling errors in information passing between scales. For example, within a multiscale framework, one could identify what features of a coarse-level model are affected from a finer scale model and need higher-level theory to improve accuracy of the overall multiscale simulation. Next a brief overview of SA for deterministic systems is given followed by recent work on SA of stochastic and multiscale systems. 

Maroudas, D., Modeling of radical-surface interactions in the plasma-enhanced chemical vapor deposition of silicon thin films, in (A.K. Chakraborty, Ed.), Molecular Modeling and Theory in Chemical Engineering , vol. 28, p. 252. Academic Press, New York (2001). Maroudas, D. Multiscale modeling, Challenges for the chemical sciences in the 21st century Information and communications report , National Academies, Washington, DC. p. 133. 

In multiscale modeling approaches the microscopic behavior of a system is linked by a compression operator to the macroscopic state variable. The strategy is then to use the microscopic model to provide necessary information for extracting the macroscale behavior of the system. Such a combined macro-microscale technique is supposed to be much more efficient than solving the full microscopic... 

One of the key linkages between continuum and microscopic descriptions of interfaces is the notion of an interfacial energy. Though the use of such energies is by now entirely routine, nevertheless, this exemplifies the type of information passage that is one of the hallmarks of multiscale modeling. Note that from the perspective of the continuum mechanics of materials with interfaces, the total energy is often written in the form... 

I am grateful to Jane Kondev, Michael Ortiz, Ellad Tadmor, Ron Miller, Vijay Shenoy, Vivek Shenoy, David Rodney, Klaus Schulten, Darren Segall, and Laurent Dupuy for collaboration and conversation. All of them played a key role in the development of my understanding of multiscale modeling. Farid Abraham first illustrated the meaning of a terabyte to me by comparing it to the informational content of a library. 

Sprawling multiscale and multiphysics approaches promise to rapidly reproduce any kind of fuel cell response function if only sufficient input information is provided—the more complex the multiscale model, the more phenomena it can describe, finding answers without asking questions. The approaches that Michael and Andrei overview here follow a different guiding principle that drove our very first steps in Jiilich start with formulating a problem or question of scientific interest using appropriate scientific concepts, build a consistent model that then is developed and solved, and answer the relevant questions. While a number of new questions arise in the course of the study, select those which should be given priority to be solved and so forth. But the key rule is the simpler the model that provides consistent answers... 

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