PVD · Particle transport
The same marginals. A different arrival pattern.
Reveal the angular dependence hidden by separate directional summaries.
Bottom first-contact fraction
Values & comparison details
Difference = comparison − reference. Rounded for display; original data retained.
- Diagonal distribution
- 53.333333333333336 %
- Anti-diagonal distribution
- 93.33333333333333 %
Same rotated feature. Fraction of the opening-conditioned incident population; not deposited thickness.
Open full figure THE QUESTION
Can two angular distributions share both axis marginals yet deliver different first contacts to a rotated feature?
THE APPROACH
Three prescribed probability distributions on nine directions are passed through fixed first-contact geometry. Aligned and rotated feature responses are compared, then observation rows are added to an exact finite-basis rank analysis.
WHAT THE COMPARISON SHOWS
Three things to take away.
- 01
The diagonal and anti-diagonal distributions share the full axis marginals. In the aligned aspect-1 feature, both give a 66.67% bottom first-contact fraction.
- 02
Rotating that feature separates the two responses to 53.33% and 93.33%. The denominator is the opening-conditioned incident population.
- 03
The cumulative observation ranks are 1, 5, 6, 7, 7, 8, 8 and 9. Two added signals are redundant; more observations do not always add independent information.
Evidence, assumptions & the next question
What was numerically checked
Exact geometry and rank witnesses independently check the stored finite model. The sealed unit records 895 deterministic checks and 15 damaged-evidence refusals in each Python mode.
How far the result goes
A prescribed nine-direction model with fixed geometry. First contact is not deposited thickness. Finite-basis rank does not establish continuous angular uniqueness, measured chamber calibration or material-specific growth.
What a physical study would need next
Connect detector response, angular resolution and paired physical measurements before using this idea to infer a real process distribution.
SA-PROC-DEP-PVD-012 · Angular observability, unit 008 · 2026-10-02
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