Appendix
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
Pythagorean harmony
Link to musical intervals
Link to Tycho's
supernova
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 (4/6/98)
Population equation
Example
Iterate
Diagrams
Cascade order
Application
Single cascade
Indirect cascading
Two hump cascade
Cascade & primary with similar lifetime
Driven excitation
Formulation
Parts integration
Iteration formulation
Impulsive, stepwise & rectangularly pulsed excitation
Gaussian excitation
Phase shift measurements
Compared with pulsed excitation
Modulated excitation
Reduction of mnemonic
Uncascaded and single cascade
Cascade joint analysis
Blend and two direct cascades
Indirect cascade
General expression
Strength of cascading
Integrated and differentiated
Criteria for heavy cascading
Replenishment ratio
R(0) from curve fits and intensity ratios
Window convolution
ANDC analysis
Isoelectronic trends
Simulations for Na sequence
Simulations for Kr VIII
Simulations for Cu XIX
Si IV and P V on isoelectronic plot
Kr VIII Grotrian diagram
Relative lifetime trends
ANDC plot
ANDC Grotrian for 6p
Advantages of cascade analysis
ANDC Grotrian for 3s3p
ANDC Grotrian for Y III
Si IV decay curves
ANDC method
Multiexponential decay curve
ANDC Grotrian for 5p
ANDC plots for Kr VIII
Schematic
Advantage of heavy cascading
Chapter 11
Chapter 12
Chapter 13
Chapter 7
Chapter 8
Chapter 9
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