Symbol f
f occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Published equation contexts
Why this formula appears here
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
Read the representative guide
Symbol x
x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol t
t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol D
D is an input to the expression that computes the quantity on the left.
Read this term in its guide →Denominator: partial t
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →Numerator: partial^2 f(x,t)
The complete quantity above the fraction bar.
Read this term in its guide →Denominator: partial x^2
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →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.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 2 · Einstein & Evolution
Einstein's Random Walk and the Mathematics of Genetic Drift
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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
Equation guide → · Article →