Unified treatment of momentum, energy, and chemical species transport including conservation laws, flux relations, and boundary conditions. Topics include convective and diffusive transport, transport with homogeneous and heterogeneous chemical reactions and/or phase change, and interfacial transport phenomena. Emphasis on problem analysis and mathematical modeling, including problem formulation, scaling arguments, analytical methods, approximation techniques, and numerical solutions. Undergraduate credit. Spring.
Teaching
Application of continuum mechanics approach to the understanding and prediction of fluid flow systems that may be chemically reactive, turbulent, or multiphase. Topics include tensor analysis, conservation equations, dimensional analysis, approximations, perturbation theory, Stokes flow, inviscid flow, Creeping flow, fluid mechanics, boundary layer theory, etc. Graduate Credit. Fall.
This is an elective course for graduate students in engineering and sciences that familiarizes them with basics of molecular modeling. The course commences with a brief overview of classical thermodynamics and statistical mechanics. Subsequently, the theoretical foundations and the algorithmic implementation aspects of the following techniques are covered: Monte Carlo simulations, molecular dynamics simulations, thermostats and barostats, estimation of static and dynamic properties, long-ranged interactions and Ewald-based methods, free energy calculations, constrained MD, biased simulations (Landau free energies, umbrella sampling, metadynamics), and rare events and rate calculations.
Students are expected to be proficient in calculus, probability theory, thermodynamics and statistical mechanics. They should also have basic familiarity with computer programming (preferably in C or C++).