Multiscale Modeling and Simulation
Computational materials science and engineering is emerging as a mainstream approach to tackling fundamental and practical problems in materials science and engineering. In computational science, although complementary, there is a clear distinction between theory, modeling and simulation. A theory consists of a set of axioms that provide a mathematical description of the natural world. A model is a physical description of a real-world system formulated within a theory and a simulation is a computational realization of a particular model. Rigorous computational science relies on the separability of Theory, Model and Simulation, that is, improvement in the reliability of a computation may result from the choice of a better theory (e.g. classical mechanics versus quantum mechanics), more refined model (e.g. fixed charge system versus variable charge system), more accurate computational methods (e.g. finite difference versus finite elements). However, the complexity of problems in materials science and engineering (and other fields) results from underlying physical phenomena that span time- and length- scales over several orders of magnitude, challenging the development of robust computational science frameworks. Consequently, multiscale modeling and simulation emerges as a computational approach that combines more than one theory (so-called multiscience or multiphysics), or more than one model. Multiscale modeling and simulation exploit significant length scales (time and space) of constitutive models in concurrent or serial methodologies. Even though multiscale modeling has advanced significantly over the past several years, computer limitations have not allowed complete linkage of nano- and micro- spatio-temporal phenomena to macro-ones thus hindering a quantum leap in the understanding of basic scientific problems. In this field, to date, progress has been made in a somewhat ad-hoc way. Here, we focus on the development of more robust methodologies and algorithm with quantification of the inherent limitation of the approaches. For this purpose a powerful tool is wavelet transformation and the so-called compound wavelet matrix (CWM) method and dynamic CWM (dCWM) method that enables the construction of a compounded multiscale model, union of several models more limited in their time and space resolution. Several fundamental problems benefit from this approach, namely (a) homogeneous failure of brittle materials (i.e. glass), (b) heterogeneous reactive-transport problems, (c) self-assembly, (d) water origin in planetary body formation.
Compound Wavelength Matrix (CWM) Method
Viscosity of Liquid Metals
Path Integral Molecular Dynamics
Assembly and Friction of Self-Assembled Monolayers
Brittle Fracture of Silica
Origin of Water in the Solar System