IDEAL QUANTUM GAS DYNAMICS
Instructor: Prof. Dr. J. Y. Yang
The carriers of microscale and nanoscale transport phenomena in modern engineering and nanotechnology including atoms, molecules, electrons, photons and phonons. The equilibrium flows of these carriers provide important foundations for further non-equilibrium transport. A unified approach to treat all these carriers is warranted. This course aims first to provide the unified microscopic description of various transport carriers based on statistical mechanics and second to explore the mathematical and theoretical properties of these ideal equilibrium gas dynamics and its numerical computations. The contents of this course consist of:
1. Introduction and Basic Concepts
2. Elements of Equilibrium Statistical Mechanics
3.Elements of Classical Kinetic Theory of Gas
4.Elements of Quantum Kinetic Theory
7.Equilibrium Quantum Gas Flows
8.Hyperbolicity and Wave Propagation
9.Kinetic Numerical Methods
10.Kinetic Beam Scheme
11.Kinetic Flux Vector Splitting Scheme
12.High Resolution Shock-Capturing Schemes.
Some knowledge on gas dynamics, kinetic theory, statistical thermodynamics, quantum mechanics and numerical methods for hyperbolic conservation laws are helpful but not essential. Computing project to work on a specific problem will be assigned.
Textbook: Lecture Notes (handout given at the class)
References: 1. Kerson Huang (1987), Statistical Mechanics, Second Edition, Wiley.
2. Gang Chen (2005), Nanoscale Energy Transport and Conversion, Oxford University Press.
3. E. F. Toro (1999) Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer.
Grading Policy: Homework (40 %); Term Project (30 %); and Final Exam. (30 %).