1-Introduction to Statistical Mechanics
-The postulate of classical statistical mechanics.
-Grand Canonical Ensemble.
2-Thermodynamics and Kinetic Theory
-The laws of Thermodynamics.
-The problem of Kinetic Theory.
3-The Boltzmann equation
-Derivation (Lanford Theorem). Existence of solutions (Diperna-Lions Theorem).
-The BBGKY Hierarchy.
-Elementary properties of the collision operator.
-Boundary conditions and the gas-surface interaction.
-The H-Theorem and the problem of irreversibility.
4-Methods of solution of the Boltzmann equation
-Transformation into Integral Equations.
-The method of Elementary Solutions.
5-Application of the Boltzmann equation to Microfluidics
-Analytical and numerical investigation of microchannel flows (Poiseuille, Couette and
Thermal-Creep problems; sound waves propagation).
-Slip boundary conditions for the Navier-Stokes equations.
-Kinetic modeling of gas mixtures.
6-Mathematical Models and Methods in Micro-Nano-Technologies
-Characterization of Micro-Electro-Mechanical Systems (MEMS) devices.
-Analysis of damping forces in low-frequency and radio-frequency MEMS devices.
7-Boltzmann-type equations in Socio-Economic applications