Diffusive scaling in one dimension indicates that increasing the size of a cell by a factor of 20 results in an increase in average diffusion time by a factor of 400. This relationship is derived from the mathematical theory of diffusion, specifically Brownian motion, where the variance of particle distribution is proportional to time. Consequently, the distance spread is proportional to the square root of time, establishing that time is proportional to the square of the distance spread.
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The mathematical theory of diffusion (Brownian motion) has particles spreading out randomly with a normal distribution, where the variance is proportional to time. This means the distance spreading (square root of variance) is proportional to the square root of time, or time is proportional to the square of the distance spread. In your example 400 (time) is proportional to to the square of distance (20).jbunten said:I am reading that diffusive scaling in one dimension means that "increasing the size of a cell by a factor of 20 increases average diffusion time by a factor of 400". I can't find anything on diffusive scaling. Can anyone give me an explanation of this?
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