INTRODUCTION
A cloud chamber is an interesting device that allows a user to see charged particles. it consists of supersaturated alcohol and water vapor which is ionized by the charged particle and begins to precipitate. Alcohol is used because its low freezing point allows for us to quickly reach the critical temperature at which ionization will cause precipitation. In this blogpost I will outline the mathematics required for the system, the mathematics for a program to automate detection, and the mathematics of the particles themselves. In an upcoming blogpost I will demonstrate an implementation of the Cloud Chamber and the software.
OVERVIEW
We begin with a brief overview of the particles themselves, as computations from this section will allow for proper design of the chamber, as well as proper mathematics and design of the subsequent program.
Suppose a particle P was launched at a velocity V towards Earth. It will be attracted to two plates mounted to the outside of the box following the coulomb equation. Also the degree of ionization is a function of the energy and ionization ability of the particle which adjusts the width of the ionized trail, therefore an algorithm can determine a particle type simply by analyzing trail width.
Program NOTATION
Custom Operator: $x$ returns the length of x
Turing Machine: <Machine|Function*|Tape>
Boolean Algebraic Program
The A* function applies the Y filter transform onto c
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