Course Identification

Statistical Physics I

1. Introduction to Complex Systems
2. Units and Scaling
   1. Dimensional analysis
   2. Nondimensionalization and scaling
3. Continuum mechanics
   1. Kinematics of Continua
   2. Equations of motion and equations of state
   3. Fluid dynamics
   4. Solid elasticity
   5. Membranes and surfaces
4. Dynamical systems
   1. Invariant points and manifolds
   2. Perturbations and stability
   3. Bifurcations
   4. Lyapunov exponents, irreversibility and chaos
5. Stochastic dynamics
   1. Markov processes
   2. Langevin and Fokker-Planck equations
   3. Characterizing noise, fluctuations and correlations
   4. Generalized central limit theorem and extreme value statistics

Upon successful completion of this course students will be able to:

Demonstrate understanding of the concepts and mechanisms underlying the behavior of complex systems, and identify their role in various natural phenomena.

Digest contemporary research papers, lectures and seminars in complex systems, statistical physics, soft condensed matter, biological physics and related fields.

Take more advanced courses in soft, biological, chemical and statistical physics.

• Barenblatt, GI, Flow, deformation and fracture (Cambridge, 2014)
• Ott, E, Chaos in Dynamical System (Cambridge University Press, 2002)
• Amir, A, Thinking Probabilistically: Stochastic Processes, Disordered System, and Their Applications, (Cambridge University Press, 2021)