Chapter 13 - The World of Atoms
The Exponential Law


Historical Foundations of Exponential Decay

L.J. Curtis, "Concept of the Exponential Decay Law Prior to 1900," Am.J.Phys. 46, 896 (1978).
Named among most memorable papers from Am.J.Phys., 1933-1990.

Ancient formulations

Introduction
Rhind papyrus
Problem 79
Solution to 7's problem
As I was going to St.Ives
Link to Euclid's formula
Application of Euclid's formula
Series, sum and difference
Louve cuneiform
Doubling time

Perceptive linearization of stimuli

Link to Weber-Fechner law
Sound
Keyboard
Response of the ear
Sound
Sound
Doppler
Doppler
Doppler
Pythagorean harmony
Link to musical intervals
Link to Tycho's supernova
Californium or iron?

Biological growth

Link to Malthus
Fibonacci series
Link to Fibonacci series
Phyllotaxis
Link to The Chambered Nautilus

The 17th century: Formulations

Napiers' logarithms
Quadrature of the hyperbola
Conic cuts
Ellipse and hyperbola
Huygens' exponential
Huygens' damped gravitational fall

The 18th century: Applications

Link to Newton's law of cooling
Bouguer's law
Link to Prony
Laplacian determinism/Social Sciences/Kinetic THeory

The 19th century: Departures from a pure exponential

Link to logistic curve
Blends
Cascades
Branching
Intermediate reactant

The 20th century: Radioactive decay

Radioactive chain
Rutherford's escutcheon

Exponential growth

The energy crisis
Energy supply estimates
Hubbert's candle
The end is near
Link to Hubbert's peak

Do particles decay or only pristinely disintegrate?

Summary

Theoretical rigor; experimental tests
Outline
(continued)
(continued)

Introduction

Aphorisms
Link to Buddha
Literary wisdom
Link to The Wonderful One-Hoss Shay
Link to A Picture of Dorian Gray
Link to Marcel Proust
Link to "Genuine" random numbers

Status of testing

Link to Published Article
Hypothesis testing
Parameter evaluation
Direct measurements of transition moment
Link to non-exponential quantum tunneling

Simulation study

Specific numerical computation
Models
Simulations
Fits
Results

AMS

Accelerator Mass Spectroscopy (AMS)
Link to AMS
Experimental setup
Comparison of precision
Bristle cone pine; survivors
Suitable isotopes

Cascading

Introduction

Cascades and blends
Cataract
Halflife of dice
Multisided coins
Supported decay
Cascade simulation

Diagrammatic mnemonic

Population equation
Example
Iterate
Diagrams
Cascade order
Application
Single cascade
Indirect cascading
Two hump cascade
Cascade & primary with similar lifetime