COMPLEX SYSTEMS ANALYSIS

The aim of the course is to provide the student with a general overview of Soft Matter systems and how they can be investigated and understood with numerical methods, within the unifying approach of Statistical Thermodynamics. The students will then be exposed to these topics at a PhD level, with a special emphasis on current on-going work.

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.

Fundamental tools of Mathematics and Physics

Part I Principle of Statistical Thermodynamics (5 hours)
Review of Thermodynamic potentials and Legendre transformation, Gibbs ensembles (NVE, NVT, NPT, μVT) ; Universality and Scaling, Virial expansion, Perturbation theory, Mean Field theory; Exact solutions, Phase transitions; Maxwell construction and van der Waals gas; Electrostatic theory, Debye Huckel theory; Polar and non-polar solvents.

Part II Self-assembly patchy colloids (2 hours)
Energy and length scales; Packing problems; Entropically driven transitions, Glasses and gels; Depletion interactions; Patchy particles; Janus fluids; Integral equation theory;

Part III Liquid Crystals (2 hours)
Historical perspectives; Liquid crystals phases; Technological applications; Theoretical approaches (Onsager theory, Density Functional Theory)

Part IV Polymers (2 hours)
Linear polymers; Connection with Diffusion Equation; Phase diagram; Flory Theory; Solvent effects; Polymer solutions; Flory-Huggins for solutions; Experimental probes

Part V Proteins (2 hours)
Hierarchical structure of proteins; Peptide bonds and amino acids; Secondary and Tertiary structures; How proteins fold; Funnel energy landscape theory; Protein misteries

Part VI DNA (2 hours)
DNA structure; Fundamental interactions; Coarse-grained models for DNA; DNA nanotechnologies

Part VII Introduction to Simulation Methods (4 hours)
Simulation Methods; Introduction to Molecular Dynamics and Monte Carlo Methods

Part VIII Monte Carlo (4 hours)
Practical Examples of Monte Carlo simulations in three different ensembles

Part IX Molecular Dynamics (2 hours)
Practical Examples of Molecular Dynamics simulations

Part X Enhanced Sampling Techniques (5 hours)
Umbrella Sampling, Metadynamics, Forward-flux sampling, Free-energy methods

General part, fluids, colloidal systems
530.13KARDM M. Kardar Statistical Physics of Particles (Cambridge Univ. Press 2007)
547.7HAMLI Hampley Introduction of Soft Matter (Wiley 2002)
541.3FUNIC1 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
532.01ALLENMP Allen, Tildesley Computer Simulations of Liquids (Clarendon 1987)
539.6FREND Frenkel, Smit Molecular Simulations (Academic 2002)

Polymers
LT547.7.DOIM Doi, Edwards, Theory of Polymer Dynamics (Oxford, 1986)
530.41RUBIC 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
574.19FINKAV 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)

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

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