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Equation 2 · Part 4 · Einstein's Random Walk and the Mathematics of Genetic Drift

Symbol D

∂f(x,t)∂t=D ∂2f(x,t)∂x2\frac{\partial f(x,t)}{\partial t} = D\,\frac{\partial^{2} f(x,t)}{\partial x^{2}}
DD

What this part means

D is an input to the expression that computes the quantity on the left.

Its job in the formula

D is an input to the expression that computes the quantity on the left.

The passage around this formula

Working through the statistical mechanics of a wall permeable to solvent but not to suspended particles, Einstein arrived at a differential equation for how the concentration f(x,t) of particles along one axis changes over time: ∂f(x,t)∂t=D ∂2f(x,t)∂x2\frac{\partial f(x,t)}{\partial t} = D\,\frac{\partial^{2} f(x,t)}{\partial x^{2}}. the diffusion equation, in a form still written the same way today [ 1 ] . Solving it for particles released from a point gives a spreading distribution whose variance grows linearly, not with the square root of time as a naive guess might suggest but as

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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