10 Sextillion Atoms
Ellad Tadmor
Aerospace Engineering, University of Minnesota
ABSTRACT: In most engineering applications the material is a continuum “black box” represented by a constitutive model (like Hooke’s law) fitted to experimental observations. In reality a material is a complex dynamical system consisting of atoms (nuclei and electrons). There are about 10 sextillion (1022) atoms in a gram of copper. The typical separation between atoms is of the order of 1 angstrom (10-10 meters) and the characteristic time scale of atom vibration is 1 femtosecond (10-15 seconds). The challenge is to construct predictive constitutive relations for a material from the atoms up. This leads to many questions. How can we reliably predict the interactions between the atoms when there are too many for quantum mechanics to be used? How do we deal with the exponential complexity of the atomic energy landscape? How do we address the huge spatial and temporal scale disparities from the atomic to the macroscopic? How do we relate macroscopic concepts like stress and heat flux to the microscopic processes in a solid? How can non-equilibrium processes be modeled? These are the basic questions being explored today in the emerging field of multiscale science and engineering. In this talk, we will discuss the theoretical and computational methods being developed to address some of these issues.
