| Abstract |
Our world is full of systems where there is a strong relationship between a wide range of scales, as turbulence and reacting flows, biological processes, nanodevices… Classical approaches to these problems have been hindered by two different shortcomings: it was impossible to get experimental information of the nanoscale, and, due to the limited computer power, it was unfeasible to include a complete description of the finest scales in the simulation. The only way to introduce the effect of these scales was by means of a “closure”, that is to say, a very simplified model of the finest scale, obtained at best empirically, and in most cases ad hoc (e.g. turbulence models).
In the last twenty years new mathematical concepts as homogeneization theory, hybrid numerical methods and the variational multiscale method have improved the understanding of multiscale problems. Many of the current methods assume a large separation between scales and are usually focused on the assessment of one specific scale (usually, macroscale values). Furthermore, these techniques have been developed in different areas without a general approach leading to a landscape of disjoint, ad-hoc and extremely limited multiscale methods.
Scientific, technological and societal issues for carrying out further research
The simulation of multiscale systems presents one of the major challenges of the new millennium in applied mathematics and computational mechanics, and obviously, many fields of engineering where multiscale problems are present. As an example, recent progress in nanotechnology and biotechnology has extended the envelope of scales, starting the design process at the nanoscale. In order to facilitate further advances and translate them into practice, reliable multiscale simulation is required.
Even though in the last decades effective and fast numerical methods have been developed and we have profit from tremendous increase in computational power, simulation of whole systems only with the finest scales model will not be affordable during our research lives. Extrapolating the current trends in computational power increase, almost one century will be required until the computational facilities needed for one second simulation of crack propagation in cooper using molecular dynamics become available.
The demand of new methodologies for multiscale simulation has increased dramatically in the last ten years. In USA, research in multiscale simulation is considered a bottom line of the research to be funded by the department of energy (DOE): “… physical and mathematical complications that arise in multiscale systems currently presents one of the major obstacles to future progress in many fields of science and engineering.”
The application of the present proposal is focused on nanotechnology, due to the fact that this is one of the strategical research lines of the EU. Nanotechnology is an important new area in materials research. The syntesis of nanoscale materials promises lower energy usage, lower environmental pollution, structural perfection, small size, high stiffness, high strength and excellent electronic properties. Nanoscale materials may be used in material reinforcement, as sensors, and as medical diagnostic and delivery systems. Nanotechnology is expected to have a profound impact on the basic research being performed in medicine, electronics, and materials science in the coming years. Engineering software which incorporates multiscale simulation will be needed, the main objective of this proposal. Why? Consider materials constructed at the nanoscale. Such materials cannot be described with standard continuum models. Some of the critical phenomena need to be described at the atomistic and molecular level. However, nanoscale materials may interact with other components that are larger and have longer response times. Therefore, there is a need to simulate systems over an enormous range of time and length scales, spanning many orders of magnitude. This will necessitate a coupling of atomistic, molecular and continuum models. The mathematical and computational challenges will be to link these models together and to make the simulation of fully coupled systems feasible. To this end, the emerging field of multiscale analysis and multiscale methods promises great research opportunities.
However, applications reach a wider range of problems. Environmental science is an example. Climate modelling will become an increasingly important tool in order to predict and control the effect of human activities on Earth. For global climate simulation, many submodels are of interest: atmosphere, ocean, land surface, cryosphere and biosphere. The spatial resolution of these submodels will increase significantly in the future (down to about 10 km), and new submodels will be added (e.g., atmospheric chemistry). The incorporation of local effects will have to be accounted for using multiscale modelling. Climate models will provide individual nations and the international community with increasingly reliable predictive tools that can possibly also be used for educational purposes.
Systems biology is used as a general term for the systematic analysis of complex relationships in living organisms, in particular, at a macromolecular level. The current trend indicates that system biology will become very important in the years ahead. Computational demands will most likely come in the area of simulating cellular and (macro)molecular systems, and in particular in combined, multiscale simulations, where different levels of complexity are combined in a single, integrated system. In the future, the ability to better predict and understand complex biological systems is expected to lead to advances in drug design, disease diagnosis, biologically inspired computers, and environmental health .
The present project is a fully multidisciplinary process. Applied mathematics and computational mechanics will help to develop an abstract framework and analyze multiscale numerical methods. Physics are needed for the comprehension of the finest scales and the obtention of appropriate models. Engineering will help the identification of current applications of interest in technology and society that will need multiscale simulation, its application to real problems and validation of codes. Computer scientists must be considered due to the high requirement of computer power in the simulation, e.g. parallelization techniques. |
