Biologically Motivated Problems in Statistical Physics

 

Ayþe Erzan

Department of Physics

Tel: 3277

erzan@itu.edu.tr

 

Prequisite (s)

Thermodynamics and Statistical Physics I or consent of the instructor

Topics                                                                                                                              Homework

1 Review of probability concepts, stochastic process and distributions.  The Random Walk. The Gaussian distribution.  The Central Limit Theorem.  Scaling relations.

2 Equilibrium statistical ensembles and thermodynamic functions.

Isolated systems : The microcanonical ensemble. Energy, entropy and temperature. Applications to noninteracting polymeric chains. 

3 Equilibrium statistical ensembles and thermodynamic functions, ctd.

Thermal equilibrium and the canonical ensemble. Application to the hydrophobic effect.

4 Ergodicity breaking and phase transitions. Order parameters, response functions and correlation functions. Applications to interacting polymeric chains, protein and RNA folds.

5 Fractals, Levy distributions, scale invariance, homogeneous functions.  Percolation. Applications.

6 Problems with rugged free energy landscapes I -  The protein folding problem.

 

7 Problems with rugged free energy landscapes II -  The spin glass problem. Associative memory models.

8 Far from equilibrium systems. Self Organized Criticality in systems with conserved currents. I - The sandpile model for the emergence of complex spatio-temporal behaviour.

9 SOC models II - Invasion percolation and simple evolutionary models.

10 SOC models III -  Laplacian growth as a model for the growth of bacterial colonies, neurons and pulmonary systems.

11 Non-equilibrium distributions, detailed balance and convergence to equilibrium The Master Equation.

12 Fat tailed distributions, slow dynamics. Anomalous relaxation. Applications to evolutionary dynamics and protein folding.

13 Genetic algorithms as adaptive systems. Bit string (Boolean) models of evolution. The Fokker-Planck equation. Relationship to the Ornstein-Uhlenbeck problem.

14 Biological  networks -  The characterisation and growth of networks.

 

Sources:

K. Huang, Statistical Mechanics (J Wiley and Sons, NY, 1963)

F. Reif, Fundamentals of statistical and thermal phsyics ( Mc Graw Hill, Boston, 1976)

J. Hertz, A.Krogh. R.G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley Publishing Co., Redwood City, Ca., 1991)

H. Risken,The Fokker-Planck equation : methods of solution and applications,  (Springer-Verlag, Berlin, c1996).

J. Maynard Smith, Evolutionary Genetics (Oxford UniversityPress, NY, 1998)

H. Flyvberg et al. (Ed.), Physics of Biological Systems (Springer Verlag, 1997).

M.V. Volkenstein, Physical Approaches to Biological Evolution (Springer Verlag 1994).

And journal articles to be assigned during the course.

 

 Homework 1,2,3,4,5, 6, 7,8,9,10,11,12

 

 

2 Midterm exams (20%), 12 Quizzes (12%) 12 Homework papers (24%) and Final Exam (44%)