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Step-based tutoring consists in breaking down complicated problem-solving procedures into individual steps whose inputs can be immediately evaluated to promote effective student learning. Here, recent progress on the extension of a step-based tutoring for linear circuit analysis to cover new topics requiring complex, multi-step solution procedures is described. These topics include first and second-order transient problems solved using classical differential equation approaches. Students use an interactive circuit editor to modify the circuit appropriately for each step of the analysis, followed by writing and solving equations using methods of their choice as appropriate. Initial work on Laplace transform-based circuit analysis is also discussed. Detailed feedback is supplied at each step along with fully worked examples, supporting introductory multiple-choice tutorials and YouTube videos, and a full record of the student's work is created in a PDF document for later study and review. Further, results of a comprehensive independent evaluation involving both quantitative and qualitative analysis and users across four participating institutions are discussed. Overall, students had very favorable experiences using the step-based system across Fall 2020 and Spring 2021. At least 48% of students in the Fall 2020 semester and 60% of students in the Spring 2021 semester agreed or strongly agreed with all survey questions about positive features of the system. Those who had used the step-based system and the commercial MasteringEngineering system preferred the former by 69% to 12% margins in surveys. Instructors were further surveyed and 86% would recommend the system to others. 

Step-based tutoring consists in breaking down complicated problem-solving procedures into individual steps whose inputs can be immediately evaluated to promote effective student learning. Here, recent progress on the extension of a step-based tutoring for linear circuit analysis to cover new topics requiring complex, multi-step solution procedures is described. These topics include first and second-order transient problems solved using classical differential equation approaches. Students use an interactive circuit editor to modify the circuit appropriately for each step of the analysis, followed by writing and solving equations using methods of their choice as appropriate. Initial work on Laplace transform-based circuit analysis is also discussed. Detailed feedback is supplied at each step along with fully worked examples, supporting introductory multiple-choice tutorials and YouTube videos, and a full record of the student's work is created in a PDF document for later study and review. Further, results of a comprehensive independent evaluation involving both quantitative and qualitative analysis and users across four participating institutions are discussed. Overall, students had very favorable experiences using the step-based system across Fall 2020 and Spring 2021. At least 48% of students in the Fall 2020 semester and 60% of students in the Spring 2021 semester agreed or strongly agreed with all survey questions about positive features of the system. Those who had used the step-based system and the commercial MasteringEngineering system preferred the former by 69% to 12% margins in surveys. Instructors were further surveyed and 86% would recommend the system to others. 

We report the effect of neutral macromolecular crowders poly(ethylene glycol) (PEG) (8 kDa) and Ficoll (70 kDa) on liquid–liquid phase separation in a polyuridylic acid (polyU)/spermine complex coacervate system. The addition of PEG decreased both the amount of spermine required for phase separation and the coacervation temperature ( T C ). We interpret these effects on phase behavior as arising due to excluded volume and preferential interactions on both the secondary structure/condensation of spermine-associated polyU molecules and on the association of soluble polyU/spermine polyelectrolyte complexes to form coacervate droplets. Examination of coacervates formed in the presence of fluorescently-labeled PEG or Ficoll crowders indicated that Ficoll is accumulated while PEG is excluded from the coacervate phase, which provides further insight into the differences in phase behavior. Crowding agents impact distribution of a biomolecular solute: partitioning of a fluorescently-labeled U15 RNA oligomer into the polyU/spermine coacervates was increased approximately two-fold by 20 wt% Ficoll 70 kDa and by more than two orders of magnitude by 20 wt% PEG 8 kDa. The volume of the coacervate phase decreased in the presence of crowder relative to a dilute buffer solution. These findings indicate that potential impacts of macromolecular crowding on phase behavior and solute partitioning should be considered in model systems for intracellular membraneless organelles. 

Abstract Despite the growing number of binary black hole coalescences confidently observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include the effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that have already been identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total source-frame massM> 70M_⊙) binaries covering eccentricities up to 0.3 at 15 Hz emitted gravitational-wave frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place a conservative upper limit for the merger rate density of high-mass binaries with eccentricities 0 <e≤ 0.3 at 16.9 Gpc⁻³yr⁻¹at the 90% confidence level.