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We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid variables are defined on the nodes, and we leverage this framework to design novel spatial and temporal discretizations for the two-phase problem. The benefits of the nodal collocation framework are best exemplified through our novel discretizations, which employ a hybrid finite difference-finite volume methodology to treat the boundary and interfacial jump conditions in an entirely sharp manner. We demonstrate the capabilities of our novel approach using a variety of canonical two- and three-dimensional examples and outline how our framework can be extended to address more complicated physics. The overall algorithm achieves high accuracy with simplified data structures, making this solver ideal for scientific and engineering applications. 

Abstract We investigate nuclear reactions and feedback in hyperaccreting neutron star environments, considering accretion rates in the range 0.3–3 × 10⁴M_⊙yr⁻¹, typical of short-period compact-object binaries in common envelopes. Our models account for weak reactions, neutrino energy loss, nuclear energy release, pair production, degenerate equations of state, and general relativistic hydrodynamics. Depending on the accretion rates, these systems can develop both proton- and neutron-rich atmospheres with strong convective instabilities linking the neutrino sphere to the outgoing accretion shock inside the radiation trapping zone. Convection drives nucleons through multiple heating and cooling cycles, with photodisintegration dominating during the heating phase and heavy element synthesis during the cooling phase, ejecting material with abundances that depend on the accretion rate and depth of the final decompression trajectory. The turbulent nature of convective currents is conducive to creating a wide range of nuclear products through a variety of effects, including nuclear statistical equilibrium freeze-out and ther-,p-, andγ-processes. We also observe a novel multistep process in reheated trajectories, consisting of proton-capture and photodissociation reactions operating onr-process seeds, producing overall neutron-deficient isotopes. A significant amount of infalling gas experiences high entropy and short (millisecond) freeze-out timescales capable of makingr-process elements with high overabundances through a disequilibrium effect between neutrons andα-particles that does not require an excess of neutrons. 

This study explores how Learning by Evaluating (LbE) can be integrated into the 5E instructional model to support Technology and Engineering Education. LbE, influenced by comparative judgment, engages students in analyzing peer work to foster reflection, design reasoning, and iterative thinking. Using qualitative content analysis of teacher interviews, this research investigates how LbE can contribute to each phase of the 5E model: Engage, Explore, Explain, Elaborate, and Evaluate. Findings suggest that LbE enhances engagement during the Engage phase by leveraging real-world examples and peer comparisons to activate interest and prior knowledge. In the Explore phase, it aids design ideation and constraint recognition, though students often need structure to express their insights. During the Explain phase, LbE supports analytical thinking by helping students distinguish strong and weak designs, yet misconceptions may persist without debriefing. In the Elaborate phase, LbE reinforces the value of feedback and supports refinement of criteria and constraints, serving as a primer for redesign. In the Evaluate phase, it promotes reflection and group communication, though many students struggle to articulate evaluative reasoning without scaffolding. Overall, LbE offers a flexible and impactful way to deepen learning when intentionally embedded across the 5E framework. However, its success depends on thoughtful implementation and alignment with broader design thinking goals. The study recommends future research to explore how LbE supports long-term learning outcomes and how it may be adapted for diverse classroom settings. 

Despite their ecological significance and unique endosymbiotic capabilities, diatoms in the genusRhopalodiaremain poorly represented in genomic databases, particularly with respect to the availability of complete genomes from multiple organellar compartments. This study addresses that gap by presenting, for the first time, the complete chloroplast (133,086 bp), mitochondrial (36,786 bp), and spheroid body (3,024,495 bp) genomes ofRhopalodia sterrenburgii, a nitrogen-fixing diatom with a cyanobacterial endosymbiont. Phylogenetic reconstruction based on five genes from different cellular compartments (18S,28S,rbcL,psbC,cob) placedR. sterrenburgiias a basal lineage relative toR. gibba(Rhopalodia sensu lato) and theEpithemia sensu strictospeciesE. argus,E. turgida, andE. sorex, providing new insights into evolutionary relationships within Rhopalodiales. Additionally, pathway analysis revealed the progressive loss of genes involved in vitamin B₁₂and chlorophyllabiosynthesis in more recently divergedRhopalodiaandEpithemialineages. Our findings support a pattern of genome reduction in symbiotic diazotrophic diatoms, potentially driven by coevolution with their endosymbionts, and an increasing reliance on integrated metabolic functions between the host and the endosymbiont.