Aerospace and Mechanical Engineering
Adjust Font Size: Normal Large X-Large

General Syllabus AEM 8551

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



Format of Course:

Lecture 3 hours a week.

Computer Usage:


Course Objectives:

Information not availabe

Course Outcomes:

Information not availabe

Course Outline

  Nonlinear thermoelasticity
  • 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.
  Heat conducting viscous fluids
  • 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.

Outcome Measurement:

Information not availabe

Last Modified: 2007-07-24 at 10:04:44 -- this is in International Standard Date and Time Notation