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Timoshenko Lecture: Prof. Michael Ortiz

Michael Ortiz
March 20, 2015 -
5:00pm to 6:00pm
ME Admin. Building 02-530, 440 Escondido Mall, Room 127
3:30-4:00pm Reception, Building 530, Lobby
4:00-5:00pm Lecture, Building 530, Room 127

Long-term simulation of atomistic systems including heat and mass transport

Professor Michael Ortiz
Frank and Ora-Lee Marble Professor of Aeronautics and Mechanical Engineering
California Institute of Technology

In a number of areas of application, the behavior of systems depends sensitively on properties that pertain to the atomistic scale, i.e., the angstrom and femtosecond scales. However, the properties and behaviors of interest are often macroscopic and take place on the scale of centimeters to meters, and are characterized by slow evolution on the scale of minutes to years. Molecular Dynamics (MD) and Monte Carlo (MC) methods are powerful techniques to study deformation and diffusion mechanisms in systems of particles, but they are limited to relatively small material samples and to time windows of microseconds at best. Considerable effort has been devoted to accelerating MD and MC methods and notable successes have been recorded in that direction. However, no generally applicable, computationally-tractable, atomistically-based, predictive models appear to be as yet available to study slow phenomena, over time scales of the order of minutes to years, while maintaining a strictly atomistic description of the material.

We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules that effectively plugs this long-standing chronic gap in computational material science. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, we formulate discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the mesoscopic evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires, hydrogen desorption from palladium thin films and cavitation of nanovoids in metals that demonstrate the range and scope of the approach and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomic-level properties while simultaneously spanning time scales much longer than those accessible to direct MD. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable.