COMPLEX SYSTEMS ANALYSIS - SOFT MATTER AND COMPUTATIONAL BIOLOGY

This course is divided into two parts. The first part (15 h) dealing with the general topic and
the techniques, the second part (15 h) discussing a set of case studies with practical
sessions. At the end of the course, students are expected to be able to read the current
literature in this area, identify the optimal technique (experimental, theoretical or
computational), and tackle a specific problem, knowing the pros and cons of each of them.

Any student with a scientific general background (e.g. Chemistry, Physics, Material Science
etc) at the Master level is expected to be able to find this course useful. Some previous
knowledge of computer programming could be useful but not necessary.

Part I: Statistical Thermodynamics (3 hours)
Review of Thermodynamic potentials and Legendre transformation; Gibbs ensembles (NVE,
NVT, NPT, μVT); Universality and Scaling.
Part II: Liquid Theory (3 hours)
Virial expansion; Perturbation theory; Mean Field theory; Exact solutions; Phase transitions;
Maxwell construction and van der Waals gas; Integral equation theory; Electrostatic theory,
Debye Huckel theory; Polar and non-polar solvents.
Part III: Colloidal systems (2 hours)

2

Energy and length scales; Packing problems; Entropically driven transitions, Glasses and
gels; Depletion interactions; Patchy particles; Janus fluids.
Part IV: Liquid Crystals (2 hours)
Historical perspectives; Liquid crystals phases; Technological applications; Theoretical
approaches (Onsager theory, Density Functional Theory).
Part V: Non-equilibrium systems (2 hours)
Euler equation for fluids; Viscosity; Navier-Stokes equation; Stokes Law; Brownian motion;
Langevin equation; White noise; Diffusion equation; Stokes-Einstein relation; Fokker-Planck
equation; Arrhenius law.
Part VI: Polymers: Equilibrium properties (2 hours)
Linear polymers; Connection with Diffusion Equation; Phase diagram; Flory Theory; Solvent
effects; Polymer solutions; Flory-Huggins for solutions; Experimental probes.
Part VII: Polymers: Dynamical properties (2 hours)
The Rouse model; Comparison with experiments; The Oseen tensor; The Zimm model.
Practical Cases Studies (14 hours)
Theoretical basis for Numerical Simulations; Monte Carlo Methods and Metropolis algorithm;
Molecular Dynamics; GROMACS and LAMMPS software packages; Numerical simulations
illustrated for generic polymer chains, lipid membranes, DNA and proteins.

General part: Fluids and Colloidal Systems
• 530.13 KARDM M. Kardar, Statistical Physics of Particles (Cambridge Univ. Press 2007)
• 547.7 HAMLI Hampley, Introduction of Soft Matter (Wiley 2002)
• 541.3 FUNIC1 Lyklema, Fundamental of interfaces and colloidal science Vol 1-5 (Academic
1991)
• 530.413 FOFTM Gompper, Schick, Soft Matter Vol 1-3 (Wiley 2006)
• 530.4 HANSJP Hansen, McDonald, Theory of Simple Liquids (Academic 2006)
• 530.42 BARRJ Barrat, Hansen, Basic Concepts for Simple and Complex Liquids
(Cambridge 2003)
Numerical and Computational Techniques
• 532.01 ALLENMP Allen, Tildesley, Computer Simulations of Liquids (Clarendon 1987)
• 539.6 FREND Frenkel, Smit, Molecular Simulations (Academic 2002)
Polymers

3

• LT547.7 DOIM Doi, Edwards, Theory of Polymer Dynamics (Oxford, 1986)
• 530.41 RUBIC Rubinstein, Colby, Polymer Physics (Oxford 2003)
Liquid Crystals
• 530.429 GENNPF de Gennes, Prost, The Physics of Liquid Crystals (Oxford 1993
• 530.41 CHAIPM Chaikin, Lubensky, Principles of Condensed Matter Physics (Cambridge
1995)
Proteins and DNA
• 574.19 FINKAV Finkelstein, Ptitsyn, Protein Physics (Academic Press 2002)
• 574.1 CANTC Cantor, Schimmel, Biophysical Chemistry (Vol 1,2,3) (Freeman 1980)
• LT574.19.LEHNA.4 Nelson, Cox, I Principi di Biochemica di Lehninger (Zanichelli 2004)

Traditional interacting methods, on-line teaching, or a combination of the two will be used,
depending on students logistic and situations.

English

The final exam will be based on a report and a presentation by the students on a specific
topic/case study agreed with the instructor.