Equation 8 · The Valley of Stability Is a Fitness Landscape
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol B
B is part of the quantity the equation computes from the expression on the right.
Symbol A
A is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol a_V
is one of the signed contributions combined to compute the quantity on the left.
Symbol a_S
is one of the signed contributions combined to compute the quantity on the left.
Symbol A^2/3
/3 is one of the signed contributions combined to compute the quantity on the left.
Symbol a_C
is one of the signed contributions combined to compute the quantity on the left.
Symbol A^1/3
/3 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol a_A
is one of the signed contributions combined to compute the quantity on the left.
Symbol delta
delta is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
The quantity that plays fitness’s role has a name in nuclear physics already: binding energy per nucleon, B(A,Z)/A , where A = N + Z is the mass number. It is the energy that would have to be supplied to disassemble a nucleus into Z free protons and N free neutrons, divided by the number of nucleons, and a higher value means a more tightly bound, lower-energy configuration — precisely the sense in which a fitness function assigns a scalar payoff to a state. The theoretical account of how that payoff varies across the chart is the semi-empirical mass formula, first written down by Carl Friedrich von Weizsäcker in 1935 as a liquid-drop model of the nucleus [ 11 ] . In one common form, the…
Read the full surrounding passage
The quantity that plays fitness’s role has a name in nuclear physics already: binding energy per nucleon, B(A,Z)/A , where A = N + Z is the mass number. It is the energy that would have to be supplied to disassemble a nucleus into Z free protons and N free neutrons, divided by the number of nucleons, and a higher value means a more tightly bound, lower-energy configuration — precisely the sense in which a fitness function assigns a scalar payoff to a state. The theoretical account of how that payoff varies across the chart is the semi-empirical mass formula, first written down by Carl Friedrich von Weizsäcker in 1935 as a liquid-drop model of the nucleus [ 11 ] . In one common form, the binding energy is . with a pairing term commonly written
Sources cited in the surrounding passage
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