Dynamical Systems and Random Billiards

Resources

• Knudsen’s cosine law and random billiards - by Renato Feres and Gregory Yablonsky
• Probing surface structure via time-of-escape analysis of gas in Knudsen regime - by Renato Feres and Gregory Yablonsky
• Billiard and flat surface - by Diana Davis

Code

• Simulation with mode (solve next collision analytically) (fences, triangle, circle)
• With Mode

Solving each nextCollision using rootSolve (fences, triangle, circle, x^4) , Escape Tube

• Using rootSolve

Write Up

• Law of Large Numbers
• Reflection on Periodic Boundaries
• Simulation with R and Escape Tube

Data

• Expected Escape time Fixed tube length=100+width=2, vary circle radius from 0.5 to 8 with stepSize=0.05

• Cover Picture from Knudsen’s cosine law and random billiards - by Renato Feres and Gregory Yablonsky