Homework 5

This homework looks at the dynamics of small objects with random forces and external potentials. These kinds of problems are found in an enormous variety of different systems for example, molecular motion, optical traps, bacterial chemotaxis. The motion at these scales is inherently noisy and we will start examining general properties of noise.

Do problems 1, 2, and 3, if doing a one week project. If instead your group wants to do a two week project (problem 4), in addition, do problem 3.

• 1 Correlation functions and power spectra
• 2 Brownian motion in an optical trap
• 3 Diffusion in double well potential

Two week project

• 4 Modeling bacterial chemotaxis

optional

• 5 Brownian motion of a free particle