Equation 2 · Part 5 · Einstein's Random Walk and the Mathematics of Genetic Drift
Symbol x^2
What this part means
The square of x: multiply x by itself.
Its job in the formula
occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Symbol x^2→Article meaning
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: . 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
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the surrounding passage
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