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The phrase "increases proportionally with" is correct and usable in written English.
It can be used when describing a relationship where one quantity grows in direct relation to another.
Example: "The cost of production increases proportionally with the number of units produced."
Alternatives: "grows in direct relation to" or "rises in accordance with".
Exact(60)
The rate increases proportionally with the step atom density.
It is found that ablation increases proportionally with the pulse number and applied energy.
The fraction of hydrogen atoms in HAC increases proportionally with the laser's power.
The time accuracy can be controlled under ±0.5 μs The peak discharge current increases proportionally with the anode voltage.
Interestingly, control authority increases proportionally with increasing mass ratio and also with decreasing the magnitude of the static margin.
Experimental results showed that the mean solute travel time, μt, increases proportionally with the depth (travel distance) and decreases with flow rate.
This secular trend probably either reflects the earlier existence of geochemical settings that were more favourable to dolomitization or is the logical result of the fact that the likelihood for a limestone to undergo dolomitization increases proportionally with its age.
The architecture of the MRN is effective at diffusing the global traffic on the network to all global rings, and the bandwidth of the network increases proportionally with increases in the system size.
When the repetition rate is varied, the deposition rate increases proportionally with the repetition rate less than 400 Hz, while the deposition rate at 1500 Hz is a factor of 1.3 times greater than that expected by the proportional relationship.
The overwhelming consideration for timing sensitivity is collecting area: contrary to most applications, the signal-to-noise ratio for the aperiodic timing phenomena produced by accretion flows increases proportionally with count rate rather than as the square root of it.
The width of stripes increases proportionally with the anodizing voltage.
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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