Daniel Barker | Searcharxiv

arXiv2021

Stability of bakeable capacitance diaphragm gauges

Here, we study the stability of capacitance diaphragm gauges. We focus on their stability before and after a controlled series of bakes. We find that baking results in appreciable shifts of the zero offset, but note that these can easily be corrected at time of use. Linearity however cannor be corrected at time of use, so it is essential to understand its effect if one wished to use similar gauges in a system that requires baking. For the gauges in this study, we find that baking introduces a minimal additional uncertainty, and that the total uncertainty can be kept to below about 0.3% at the k=2 confidence level (95%).

physics.ins-det↗

arXiv2015

Upper bounds on pairs of dot products

Given a large finite point set, $P\subset \mathbb R^2$, we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, $(α, β)$, we bound the size of the set $$\left\{(p,q,r)\in P \times P \times P : p \cdot q = α, p \cdot r = β\right\}.$$

math.CO↗