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We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint subdomains. We prove well-posedness and present an a priori error analysis of the discretization. Numerical examples verify our analysis. 

Punishment regulates selfish behaviors and maintains cooperation. However, because punishment imposes costs on another person, it could also harm relationships. The current work asked how punishment shapes 5- to 10-year-olds' (Study 1; n=128) and adults' (Study 2; n=159) attitudes toward punishers and those who receive punishment as well as their inferences about relationships between punishers and targets. We reasoned that the motives underlying punishment might shape evaluations; punishments motivated by prosocial desires may elicit more positive responses than punishments motivated by antisocial desires. We tested both motives that were external to the punisher (the behavior that elicited the punishment) as well as internal motives (the desire to harm versus rehabilitate transgressors). The main result is that we found negative social relationships among punishers, targets, and observers. Both children and adults preferred punishers who inflicted punishment for behaviors that violated (versus did not violate) norms, preferred targets of punishment who had not (versus had) violated norms, and expected punishers and targets to dislike each other. External motives, but not internal motives, consistently influenced participants’ own social preferences. In contrast, neither external nor internal motives consistently shaped participants' inferences about social relationships between punishers and their targets. Our work contributes to social cognitive development by clarifying how motives shape children's and adults' understanding of social relationships. 

Abstract Planar magnetic microswimmers offer substantial potential for in vivo biomedical applications, owing to their efficient mass production via photolithography. In this study, we demonstrate the effective control of these microswimmers using an open-loop approach in environments with minimal external disturbances. We investigate their surface motion characteristics through both theoretical modeling and experimental testing under varying magnetic field strengths and rotation frequencies, identifying regions of stable and unstable motion. Additionally, we analyze how field frequency and strength influence surface motion speed and identify the frequencies that promote stability. Open-loop control of surface motion in fluid environments and swimming in channels is also demonstrated, highlighting the operational flexibility of these microswimmers. We further demonstrate swarm motion for both swimming and surface operations, exhibiting larger-scale coordination. Our findings emphasize their potential for future applications in biomedical engineering and microrobotics, marking a step forward in the development of microscale robotic systems.