Diffusive Scaling - How does it work

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Diffusive scaling in one dimension indicates that when the size of a cell increases by a factor of 20, the average diffusion time increases by a factor of 400. This relationship arises from the mathematical theory of diffusion, where particle movement follows a normal distribution and the variance is time-dependent. The distance particles spread is proportional to the square root of time, leading to the conclusion that time is proportional to the square of the distance. For further understanding, researching "Brownian motion" or "diffusion" can provide additional insights. The discussion highlights the fundamental principles underlying diffusion processes.
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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?

Thanks
 
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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?

Thanks
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).

You can google "Brownian motion" or "diffusion" to get more details.
 
Thanks for your excellent reply mathman.
 

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