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Equation 13 · Part 6 · Einstein's Random Walk and the Mathematics of Genetic Drift

Symbol D

∂p(x,t)∂t=−∂∂x[μ(x,t) p(x,t)]+∂2∂x2[D(x,t) p(x,t)],\frac{\partial p(x,t)}{\partial t} = -\frac{\partial}{\partial x}\big[\mu(x,t)\,p(x,t)\big] + \frac{\partial^{2}}{\partial x^{2}}\big[D(x,t)\,p(x,t)\big],
DD

What this part means

the governed by a single constant.

Its job in the formula

D is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

Einstein’s equation described one physical system: particles buffeted by a fluid held at a fixed temperature, governed by a single constant D .

The passage around this formula

Einstein’s equation described one physical system: particles buffeted by a fluid held at a fixed temperature, governed by a single constant D . Within a decade, physicists working on an unrelated problem — how the energy of a rotating electric dipole settles under both random radiative kicks and a systematic damping force in a radiation field — found they needed the same mathematical object with one addition: a drift term standing…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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