1) STATISTICAL MECHANICS
Definition of ensemble: micro-canonical, canonical and gran-canonical ensemble. Ensemble equivalence. The equipartition theorem. Chemical potentials. The Maximum Entropy Method.
2) CLASSICAL MOLECULAR DYNAMICS
Discretization of the Hamilton-Jacobi equations. The Liouville time evolution operator. Molecular dynamics as a canonical transformation. Multiple-Time-Step. Systolic and list methods.
3) STOCASTIC METHODS FOR THE EVALUATION OF THE PARTITION FUNCTION
The Monte Carlo method. Markov chains, the detailed balance principle, the Markov theorem, the Metropolis algorithm. Hybrid Monte Carlo. Brownian motion and the Langevin equation. The Fokker-Planck equation and its asymptotic solution.
4) FERMNIC SYSTEMS IN CONDENSED MATTER
Born-Oppenheimer approximation. The Thomas-Fermi model. Hartree-Fock approximation. Ab initio simulations: the density functional theory. The Car-Parrinello method.
5) APPLICATION TO BIOMOLECULES
Introduction to biomolecules modelling. Empirical force-fields: all atoms and coarse grained (Martini). Velocity-Verlet and leap-frog algorithms. Time reversibility. Algorithms to minimize energy. Simulations in the NVT and NPT ensembles. Ewald summation. Correlation functions and their computation in molecular dynamics. The diffusion coefficient.
6) PARALLEL PLATFORM PROGRAMMING TOOLS
Code structure for the molecular dynamics OF biomolecules. Agent-oriented programing.
The course aims at providing advanced preparation in the computational techniques used for the study of Biomolecules.
KNOWLEDGE AND UNDERSTANDING:
The student should know the main computational techniques and be able to choose which one to use for each specific system being investigated.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The student should be able to identify the important variables and develop a model of the biophysical problem under study.
The student should be able to carry out numerical simulations and data analysis of numerical simulations with the different techniques learned in the course and to understand which is the best technique to use for the problem he/she has to face.
The student should be able to collaborate with her/his colleagues in order to solve a problem. The student should be able explain the results obtained.
The student should be able to use the knowledge learned in the course to study topics related to those covered by the course and to expand her/his knowledge independently.