Stochastic processes in natural sciences

basics of probability theory, basics of thermodynamics and statistical mechanics, elementary calculus

The course will familiarise students with applications of probability theory and stochastic processes in physics and natural sciences. Based on relevant problems in physics, chemistry, and biology, we will outline a range of methods used for the description of randomness and fluctuations in natural phenomena. We will show how the mathematical framework can be used for computer modelling of random processes on various scales.

Description:

- simple examples of random processes

- Markov processes

- Brownian motion

- M-equation

- Fokker-Planck equation

- The Langevin approach

- Fluctuation-dissipation theorem

- Numerical modelling of stochastic processes

A. Amir: Thinking Probabilistically

C. W. Gardiner: Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences

K. Jacobs: Stochastic Processes for Physicists

D. S. Lemons: An Introduction to Stochastic Processes in Physics

N.G. Van Kampen: Stochastic Processes in Physics and Chemistry

Student can identify a physical problem to which a probabilistic or stochastic approach is suitable. Student knows how model such phenomena using the standard techniques of M-equation, Fokker-Planck or Langevin equation. Student knows how to extract physically important informations of solutions to these equations. For special cases can find exact solutions or propose suitable a numerical technique.

mid-term exam, final exam (written and oral)