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The phrase "are found moving" is correct and usable in written English.
It can be used to describe the observation of something or someone in motion, often in a scientific or descriptive context.
Example: "In the study, various species of birds are found moving swiftly through the trees during migration."
Alternatives: "are seen moving" or "are observed moving".
Exact(1)
By examining the results for the vertical emissions obtained by the three different functionals under investigation, decreasing wavelengths are found moving from B3LYP to PBE0 to M06-2X, whish isimilarar to the trend reported in ref. 20.
Similar(59)
(2) Once a seed window (i.e., it meets the criteria) is found, move the window 150 bases forward and then evaluate the new window again.
When voids are found, move left or right about 1/4" or less and probe again.
These extrema are found by moving the probe back and forth along the line and the level at that point can then be measured on the meter.
Black widows are found to move around and go to dark areas such as underneath the mattress, in the basement, or in the attic.
When laminated sheets composed of PE with MWCNTs and PC are annealed in the molten state of both polymers, MWCNTs are found to move from PE to PC.
For Experiment 3, a main effect was found for moving item [ F 1, 15) = 8.57, p <.05, ηp =.36]: Participants made more errors when the moving item was a target.
It is found that moving the valve further upstream can reduce the noise by several decibels.
They say that in the 21st century, efficiency can be found by moving information rather than people.
Sydney Carton's self-sacrifice was found deeply moving by Dickens and by many readers; Dr. Manette now seems a more impressive achievement in serious characterization.
As Tom indicated that morning in a hospital hallway filled with grief, life is found by moving toward it, not in surrendering to the depredations that accompany it.
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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