Catalog Description:

AEM 8551. Multiscale Methods for Bridging Length and Time Scales. (3.0 cr; prereq Basic knowledge of [continuum mechanics, atomic forces], familiarity with partial differential equations, grad student in [engineering or mathematics or physics]; A-F only) Classical/emerging techniques for bridging length/time scales. Nonlinear thermoelasticity, viscous fluids, and micromagnetics from macro/atomic viewpoints. Statistical mechanics, kinetic theory of gases, weak convergence methods, quasicontinuum, effective Hamiltonians, MD, new methods for bridging time scales. Effective: Fall 2003

• Constitutive theory, thermodynamics, stability and energy minimization.
• Atomic theory of elasticity for crystals; stress in a crystal lattice.
• Central forces and Cauchy relations.
• Realistic descriptions of atomic forces: a summary of descriptions of atomic forces from full quantum mechanics to atomic potentials.
• Theory of effective Hamiltonians.
• Statistical mechanics of crystal elasticity.
• Quasicontinuum methods; degree-of-freedom thinning.
• Curvature elasticity and interfacial energy.
• Remarks on weak convergence and homogenization methods for atomic to continuum.

• Constitutive theory, thermodynamics, Stokes' relation.
• Basic definitions of the kinetic theory of gases.
• Dynamics of molecular encounters.
• Maxwell-Boltzmann equatino.
• Deductino of the balance laws of continuum mechanics.
• H-theorem.
• Why do we lack nonequilibrium statistical mechanics for other materials?
• Methods for speeding up molecular dynamics.

• Electromagnetic forces.
• Exchange, anisotropy and field energy.
• B=H microscopically, but B=H + M macroscopically: Lorentz's calculation of the field and energy of a lattice of dipoles.
• Origins of exchange and anisotropy energy.
• Towards the use of multiscale methods in the search for new materials.