Differential equations are fundamental for the modeling in Science and Engineering. As the computational power increase, it becomes feasible to use more accurate differential equation models and solve more demanding problems: for instance to determine input data from fundamental principles and to optimally reconstruct input data using measurements.The course includes lectures, computer exercises and student presentations on models, analysis and computational methods from nuclei-electron micro-systems to Euler and Navier-Stokes macro-systems for continuum fluids, using a unified mathematical method to derive and explain the coupling between the models on the different scales.
- Relation between Schrödinger-molecular dynamics-continuum partial differential equations
- Ehrenfest dynamics and surface-hopping
- the Born-Oppenheimer approximation
- electron structure calculation methods
- bridging ab initio and empirical molecular dynamics
- molecular dynamics: thermodynamics and statistical mechanics
- molecular dynamics: ensembles and simulations
- stochastic Langevin and Smolchuwski molecular dynamics
- molecular dynamics reaction paths and rates
- Euler and Navier-Stokes macroscopic equation derived from microscopic molecular dynamics
- project presentations on applications.