Multiscale and multiphysics applications are now commonplace, and many researchers focus on combining existing models to construct combined multiscale models. Here we present a concise review of multiscale applications and their source communities. We investigate the prevalence of multiscale projects in the EU and the US, review a range of coupling toolkits they use to construct multiscale models and identify areas where collaboration between disciplines could be particularly beneficial. We conclude that multiscale computing has become increasingly popular in recent years, that different communities adopt very different approaches to constructing multiscale simulations, and that simulations on a length scale of a few metres and a time scale of a few hours can be found in many of the multiscale research domains. Communities may receive additional benefit from sharing methods that are geared towards these scales.
Aside from numerous publications, project websites and domain-specific reviews, we have identified a few sources which provide information on multiscale simulations in various scientific domains. One such source of information is the Journal of Multiscale Modeling and Simulation (epubs.siam.org mms), which defines itself as an interdisciplinary journal focusing on the fundamental modeling and computational principles underlying various multiscale methods. The Journal of Multiscale Modeling (www.worldscinet.com jmm ) is also targeted at multiscale modeling in general. There are also several books which present multiscale research in a range of domains @cite_17 @cite_12 , as well as dozens of multiscale modeling workshops such as the Multiscale Materials Meeting (www.mrs.org.sg mmm2012) or the Modelling and Computing Multiscale Systems workshop (www.computationalscience.nl MCMS2013). There are several articles which focus on the theoretical aspects of multiscale modelling across domains. @cite_3 present a thorough and systematic review of the computational and (especially) the conceptual toolkits for multiscale modelling. In addition, @cite_13 investigate the modeling aspects of multiscale simulations, emphasizing simulations using Cellular Automata.
@cite_3 @cite_13 @cite_12 @cite_17
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Abstract Analytical methods for studying tsunami run-up become untenable when the tsunami wave runs on beaches. In this study, we use a finite-element procedure that includes the interaction between solid and fluid based on the potential flow theory to simulate the dynamics of tsunami wave induced by a thrust fault earthquake in order to investigate the effect of different beach slopes on the tsunami run-up. The simulated run-up shows significantly differences from that predicted by the analytical solution. The maximum run-up shows a negative linear relationship with the square root of the cotangent of the beach slope, similar to the result of the analytical solution using a solitary wave as the incident wave, but with different slopes and amplitudes. Cellular Automata (CA) are generally acknowledged to be a powerful way to describe and model natural phenomena [1–3]. There are even tempting claims that nature itself is one big (quantum) information processing system, e.g. [4], and that CA may actually be nature’s way to do this processing [5–7]. We will not embark on this philosophical road, but ask ourselves a more mundane question. Can we use CA to model the inherently multi-scale processes in nature and use these models for efficient simulations on digital computers? Multiscale modeling is required for linking physiological processes operating at the organ and tissue levels to signal transduction networks and other subcellular processes. Several XML markup languages, including CellML, have been developed to encode models and to facilitate the building of model repositories and general purpose software tools. Progress in this area is described and illustrated with reference to the heart Physiome Project which aims to understand cardiac arrhythmias in terms of structure-function relations from proteins up to cells, tissues and organs. Small scale features and processes occurring at a nanometer and femtoseconds scales have a profound impact on what happens at a larger scale and over extensive period of time. The primary objective of this volume is to reflect the-state-of-the art in multiscale mathematics, modeling and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during the transfer of information? What are the optimal ways to achieve such transfer of information? How to quantify variability of physical parameters at multiple scales and how to account for it to ensure design robustness? Various multiscale approaches in space and time presented in this Volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches, various scales are simultaneously resolved, whereas in the information-passing methods, the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools is discussed in several, which focus on hierarchy of multiscale models and a posterior model error estimation including uncertainty quantification. Component software that can be effectively combined to address a wide range of multiscale simulations is described as well. Applications range from advanced materials, to nanoelectromechanical systems (NEMS), to biological systems, and nanoporous catalysts where physical phenomena operate across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales. A valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.