Airy Functions

 

The functions and are called “Airy functions” of the first and second kind respectively. Their plots are shown below.

 

 

For negative both functions oscillate and approach 0 as . For positive the function monotonically decays towards zero and the function approaches .

The values of where  (all at ) can’t be expressed in a simple form, so we label them , where is the first one, is the second one, and so on. Similarly, the zeroes of are , , and so on.

 

The derivatives of the Airy functions look similar.

 

 

We can label the zeroes of the derivatives in the same way: , , and so on.

Periodic Table

 

Hysteresis loop

 

M (internally generated field) vs H (externally applied field)

The green curve represents the initial change starting from the origin (no field of any kind). Thereafter the curve never returns to the origin, because when the external field is zero, the aligned domains still create a non-zero internal field.

Binding energy per nucleon

 

 

 

Curve of stability

 

Photograph of a pion decaying into a kaon and a lambda, and the lambda then decaying into a proton and a pion