# MathMods :: Erasmus Mundus Joint MSc

## Classical simulations with particles

• ECTS credits: 6
• Semester: 3
• University: Gdansk University of Technology
• Objectives:

During this course the basic principles of classical equilibrium and non-equilibrium molecular dynamics simulations will be presented, with stress posed on applications to materials' properties modelling. The students will learn how to use the molecular dynamics method, will be familiar with the method's limitations, will be able to evaluate critically the numerical results and carefully compare them with experimental data.

• Topics:

1. Things to be simulated
a. Structure of crystals and glasses. Quasiperiodic structures. Crystallization and glass formation.
b. Elements of crystallography. Bravais lattices, crystal symmetry, reciprocal lattice, diffraction.
c. Bonding in solids. Binding energies.
d. Lattice vibrations. Dispersion relations, normal modes, phonons. Specific heat of crystals, classical, Einstein and Debye models.
e. Lattice defects: point defects, dislocations, plane defects.
f. Free electron gas. Drude model. Electric and thermal conductivities of solids.
g. Optical properties of metals and dielectrics.
h. Magnetism of solids. Superconductivity.

2. Simulations with classical particles – molecular dynamics methods
a. Simulation box and periodic boundary conditions
b. Basic Molecular Dynamics algorithm
c. Numerical integration methods for equations of motion: basic Verlet algorithm and
velocity Verlet algorithm
d. Methods for describing interactions: interatomic potentials
e. Identification of nearest neighbors: Verlet list and linked-list cell algorithm
f. Starting simulation: choosing initial positions and initial velocities, system equilibration and velocity
rescaling
g. Calculating thermodynamic parameters: temperature and pressure
h. Simulations in various thermodynamic ensembles: thermostatic and barostating

### Connect with us

#### University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

#### Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

#### Gdansk University of Technology, Poland (GUT)

Department of Solid State Physics, G. Narutowicza 11/12, 80-952 Gdansk, Poland

#### University of Hamburg, Germany (UHH)

Department of Mathematics
Bundesstr. 55 20146 Hamburg - Germany

#### University of Nice - Sophia Antipolis, France (UNS)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2

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