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Scaling law: Difference between revisions
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* make educated guesses at local transport mechanisms | * make educated guesses at local transport mechanisms | ||
The typical scaling law expression for | The typical scaling law expression for a (dependent) variable ''y'' as a function of some (independent) system variables ''x<sub>1</sub>'', ''x<sub>2</sub>'',... is: | ||
:<math>y = \alpha_0 x_1^{\alpha_1} x_2^{\alpha_1} ...</math> | :<math>y = \alpha_0 x_1^{\alpha_1} x_2^{\alpha_1} ...</math> | ||
Here, the α<sub>i</sub> are the scaling parameters. | Here, the α<sub>i</sub> are the scaling parameters. | ||
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However, a proper analysis requires: | However, a proper analysis requires: | ||
* using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately) | * using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately) | ||
* | * guaranteeing the (linear) ''statistical independence'' of the independent variables (applying, e.g., Principal Component Analysis) | ||
== Confinement time scaling == | == Confinement time scaling == | ||