On a problem of Čech

Assuming CH (but we have stronger results) we partially solve a problem posed by E. ?ech. Kuratowski gave the axioms which a topological closure operator, ?, must satisfy. If we do not ask that ? be idempotent (i.e. that for all $\text{X,(?(X))=?(X)}$, then ? is known as a closure operator. E. ?ech asked if there is a nontrivial closure operator which is onto, that is, for which in some sense every subset of our ‘space’ is ‘closed’. We build such functions. The problem is also well motivated when presented in purely set theoretic terms.     

Investigation of cavitation noise using Eulerian-Lagrangian multiscale modeling

We have employed the large eddy simulation (LES) approach to investigate the cavitation noise characteristics of an unsteady cavitating flow around a NACA66 (National Advisory Committee for Aeronautics) hydrofoil by employing an Eulerian-Lagrangian based multiscale cavitation model. A volume of fluid (VOF) method simulates the large cavity, whereas a Lagrangian discrete bubble model (DBM) tracks the small bubbles. Meanwhile, noise is determined using the Ffowcs Williams-Hawkings equation (FW-H). Eulerian-Lagrangian analysis has shown that, in comparison to VOF, it is more effective in revealing microscopic characteristics of unsteady cavitating flows, including microscale bubbles, that are unresolvable around the cloud cavity, and their impact on the flow field. It is also evident that its evolution of cavitation features on the hydrofoil is more consistent with the experimental observations. The frequency of the maximum sound pressure level corresponds to the frequency of the main cavity shedding for the noise characteristics. Using the Eulerian-Lagrangian method to predict the noise signal, results show that the cavitation noise, generated by discrete bubbles due to their collapse, is mainly composed of high-frequency signals. In addition, the frequency of cavitation noise induced by discrete microbubbles is around 10 kHz. A typical characteristic of cavitation noise, including two intense pulses during the collapsing of the cloud cavity, is described, as well as the mechanisms that underlie these phenomena. The findings of this work provide for a fundamental understanding of cavitation and serve as a valuable reference for the design and intensification of hydrodynamic cavitation reactors.     

Do social media campaigns foster vaccination adherence? A systematic review of prior intervention-based campaigns on social media

The COVID-19 pandemic has demonstrated the importance of large-scale campaigns to facilitate vaccination adherence. Social media presents unique opportunities to reach broader audiences and reduces the costs of conducting national or global campaigns aimed at achieving herd immunity. Nonetheless, few studies have reviewed the effectiveness of prior social media campaigns for vaccination adherence, and several prior studies have shown that social media campaigns do not increase uptake rates. Hence, our objective is to conduct a systematic review to examine the effectiveness of social media campaigns and to identify the reasons for the mixed results of prior studies. Our methodology began with a search of seven databases, which resulted in the identification of 92 interventions conducted over digital media. Out of these 92 studies, only 15 adopted social media campaigns for immunization. We analyzed these 15 studies, along with a coding scheme we developed based on reviews of both health interventions and social media campaigns. Multiple coders, who were knowledgeable about social media campaigns and healthcare, analyzed the 15 cases and obtained an acceptable level of inter-coder reliability (> .80). The results from our systematic review show that only a few social media campaigns have succeeded in enhancing vaccination adherence. In addition, few campaigns have utilized known critical success factors of social media to induce vaccination adherence. Based on these findings, we discuss a set of research questions that informatics scholars should consider when identifying opportunities for using social media to resolve one of the most resilient challenges in public health. Finally, we conclude by discussing how the insights drawn from our systematic reviews contribute to advancing theories, such as social influence and the health belief model, into the realm of social media–based health interventions.