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"distributed uniformly" is correct and can be used in written English.
It is usually used in a mathematical or scientific context to describe how something or some things are situated or allocated evenly or evenly distributed. Example: The seeds were distributed uniformly in the field.
Exact(59)
These 724 genotypes are distributed uniformly across the flowering time distribution within each family.
These reserves are not distributed uniformly in all individuals.
Mineral deposits are not distributed uniformly through Earth's crust.
But air pollution, except for ozone, is not distributed uniformly across an urban environment.
This requires that barriers to slip be distributed uniformly throughout the crystalline grains.
Inspired air and blood flow normally are distributed uniformly, and each alveolus receives approximately equal quantities of both.
All PAN nanofibers were distributed uniformly.
Nodes are distributed uniformly and independently.
The packet losses are distributed uniformly.
This soluble food is assumed to be distributed uniformly.
Internal heat generation is distributed uniformly throughout the solid body.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com