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   https://doi.org/10.1029/2022JA030406  

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3. Crack Free Cr Coatings from Cr 3+ Electrolyte

   https://doi.org/10.1149/1945-7111/ac4bfa  

   Ahmadi, K. ; Dole, N. ; Karadavut, O. ; Hernandez, F. C. Robles ; Hall, T. D. ; Taylor, E. J. ; Brankovic, S. R. ( January 2022 , Journal of The Electrochemical Society)

   In this paper, we present the design of an effective pulse current deposition process for low stress, crack-free Cr coatings deposited from standard Cr³⁺electrolyte commonly used by industry. Parameters for pulse current deposition process such as$t_{on},$$t_{off},$and duty cycle are based on detailed analysis and modeling of in situ stress transients during Cr deposition and relaxation. A general procedure and criterion are derived for pulse current function design which should be of broader significance for the synthesis of functional Cr coatings. Comparative characterization of pulse and direct current deposited Cr films is presented. These data illustrate superior properties and stress-state of the Cr films deposited using our newly developed approach to pulse current function design.

    

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5. Obstruction flat rigidity of the CR 3-sphere

   https://doi.org/10.1515/crelle-2021-0051  

   Curry, Sean N. ; Ebenfelt, Peter ( October 2021 , Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We consider the obstruction flatness problem for small deformations of the standard CR 3-sphere. That rigidity holds for the CR sphere was previously known (in all dimensions) for the case of embeddable CR structures, where it also holds at the infinitesimal level. In the 3-dimensional case, however, a CR structure need not be embeddable.Unlike in the embeddable case, it turns out that in the nonembeddable case there is an infinite-dimensional space of solutions to the linearized obstruction flatness equation on the standard CR 3-sphere and this space defines a natural complement to the tangent space of the embeddable deformations. In spite of this, we show that the CR 3-sphere does not admit nontrivial obstruction flat deformations, embeddable or nonembeddable. 

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