This content will become publicly available on May 1, 2023

Erratum: “Flux-based modeling of heat and mass transfer in multicomponent systems” [Phys. Fluids 34 , 033113 (2022)]
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10335627
Journal Name:
Physics of Fluids
Volume:
34
Issue:
5
Page Range or eLocation-ID:
059905
ISSN:
1070-6631
1. Abstract We show that for some even $k\leqslant 3570$ and all  $k$ with $442720643463713815200|k$, the equation $\phi (n)=\phi (n+k)$ has infinitely many solutions $n$, where $\phi$ is Euler’s totient function. We also show that for a positive proportion of all $k$, the equation $\sigma (n)=\sigma (n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao, and PolyMath.
2. A bstract We report the first measurement of the exclusive cross sections e + e − → $$B\overline{B}$$ B B ¯ , e + e − → $$B{\overline{B}}^{\ast }$$ B B ¯ ∗ , and e + e − → $${B}^{\ast }{\overline{B}}^{\ast }$$ B ∗ B ¯ ∗ in the energy range from 10 . 63 GeV to 11 . 02 GeV. The B mesons are fully reconstructed in a large number of hadronic final states and the three channels are identified using a beam-constrained-mass variable. The shapes of the exclusive cross sections showmore »