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Each individual beta decay, then, is a single step along this fixed- A parabola: a discrete jump from one (N,Z) point to its immediate neighbor at (N-1,Z+1) or (N+1,Z-1) , taken because it lowers the mass and therefore raises binding energy per nucleon, with the released energy carried off by the emitted lepton and antineutrino or neutrino. A decay chain is a sequence of such steps, sometimes purely beta, more often threaded with alpha emissions that jump A downward by four and Z downward by two in a single move. Uranium-238’s decay chain to stable lead-206 is the standard worked example, and it takes fourteen recorded steps to complete: an alpha emission to thorium-234, a beta decay to…
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Equation 38 · Evolutionary Nuclear Physics
The Valley of Stability Is a Fitness Landscape
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Each individual beta decay, then, is a single step along this fixed- A parabola: a discrete jump from one (N,Z) point to its immediate neighbor at (N-1,Z+1) or (N+1,Z-1) , taken because it lowers the mass and therefore raises binding energy per nucleon, with the released energy carried off by the emitted lepton and antineutrino or neutrino. A decay chain is a sequence of such steps, sometimes purely beta, more often threaded with alpha emissions that jump A downward by four and Z downward by two in a single move. Uranium-238’s decay chain to stable lead-206 is the standard worked example, and it takes fourteen recorded steps to complete: an alpha emission to thorium-234, a beta decay to…
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Equation guide → · Article →Equation 50 · Evolutionary Nuclear Physics
The Valley of Stability Is a Fitness Landscape
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Stated most narrowly, the part of evolutionary theory’s formal apparatus that maps onto the chart of nuclides without qualification is this: a scalar objective function defined over a discrete state space, together with a rule for what counts as a local move, together with the observation that a system occupying a given state will, given the opportunity, take a move that increases the objective. Binding energy per nucleon is the objective; the (N,Z) lattice is the state space; single beta decay, or the small number of other elementary transitions available at a given point, is the local move. An adaptive walk under strong selection and weak mutation — a population that reliably takes the…
Equation guide → · Article →Equation 51 · Evolutionary Nuclear Physics
The Valley of Stability Is a Fitness Landscape
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
There is a further reason the borrowed vocabulary fits with unusual precision here, and it runs backward through the history of the metaphor itself. Sewall Wright introduced the image of a landscape of gene combinations, graded by adaptive value and read by its topography of peaks and valleys, in a 1932 paper to the Sixth International Congress of Genetics. Wright’s own diagram is worth reading in his own words: having reduced an intractably high-dimensional “field of gene combinations” to a two-dimensional contour plot for the sake of illustration, he wrote that “there may be innumerable other peaks which are higher but which are separated by ‘valleys,’” and that “the problem of evolution…
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