Volume I

1
Irrelevant Topics in Physics

• Volume I

2
An Introduction
By way of a rant
3
Three topics

• Dissipative Lagrangians
• Forbidden couplings in phase space
• Supershapes
• Ellipses are for sissies with only 2 parameters
• Markov process in 2D and 3D
• The art of drunks

4
Dissipative Lagrangians

• Normally we work with nice potentials
• There are some systems whose potentials depend on
  the path taken. The simplest is the damped
  harmonic oscillator.

5
The forbidden coupling

• One way to formalize this system was done by
  Morse and Feshbach
• When applying Euler equations of motion

Ernie says they wrote a really good Math Phys
book!
6
The forbidden coupling

• This gives the following differential equations
• The system conserves energy! For every bit lost
  by the original damped harmonic oscillator, it is
  gained by its mirror.

7
But wait! Theres more.

• Lest we think that dissipative Lagrangian can
  only be stated by constructing a dual, one can
  also use
• The exponential multiplier does not induce any
  extraneous solutions. Eulers equations of motion
  would produce the original differential equation

8
(not so) Supershapes Circles Ellipies


.
9
Supershapes Superellipses
I cant even make this stuff up
The squircle
10
Supershapes!!!1!
11
Markov chains 1D
Thus random walk is recurrent
12
Markov Chains 2D
Xn and Xn- are simple symmetric
independent random walks .
Thus random walk is recurrent
Since
13
Markov Chains 3D
Thus random walk NOT recurrent
14
Moral?

• Do not get drunk in 3D!
• If you lose your keys, odds are you will never
  find them again
• Thankfully, Earth has a 2D periodic surface!
• Fun physics is good physics.

15
Fin.