We have studied the impact of incoming preparation and demographic variables on student performance on the final exam in the standard introductory calculus-based mechanics course at three different institutions. Multivariable regression analysis was used to examine the extent to which exam scores can be predicted by a variety of variables that are available to most faculty and departments. The results are surprisingly consistent across the institutions, with only math SAT or ACT scores and concept inventory prescores having predictive power. They explain 20%-30% of the variation in student exam performance in all three cases. In all cases, although there appear to be gaps in exam performance if one considers only demographic variables (gender, underrepresented minority, first generation), once these two proxies of incoming preparation are controlled for, there is no longer a demographic gap. There is only a preparation gap that applies equally across the entire student population. This work shows that to properly understand differences in student performance, it is important to do statistical analyses that take multiple variables into account, covering both subject-specific and general preparation. Course designs and teaching better matched to the incoming student preparation will likely eliminate performance gaps across demographic groups, while also improving the success of all students.

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U 0 , reorientation time τ R , and mechanical energy k s T s = ζ a U 2 0 τ R /6, where ζ a is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D P = k B T /ζ P , where k B T is the thermal energy of the solvent and ζ P is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe s = U 0 a/D P . The active contribution to the diffusivity scales as Pe 2 s for weak swimming and Pe s for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ R , the active diffusivity scales as k s T s /ζ P : the probe moves as if it were immersed in a solvent with energy k s T s rather than k B T .

In a colloidal suspension at equilibrium, the diffusive motion of a tracer particle due to random thermal fluctuations from the solvent is related to the particle's response to an applied external force, provided this force is weak compared to the thermal restoring forces in the solvent. This is known as the fluctuation-dissipation theorem (FDT) and is expressed via the Stokes-Einstein-Sutherland (SES) relation D = kBT/ζ, where D is the particle's self-diffusivity (fluctuation), ζ is the drag on the particle (dissipation), and kBT is the thermal Boltzmann energy. Active suspensions are widely studied precisely because they are far from equilibrium-they can generate significant nonthermal internal stresses, which can break the detailed balance and time-reversal symmetry-and thus cannot be assumed to obey the FDT a priori. We derive a general relationship between diffusivity and mobility in generic colloidal suspensions (not restricted to near equilibrium) using generalized Taylor dispersion theory and derive specific conditions on particle motion required for the FDT to hold. Even in the simplest system of active Brownian particles (ABPs), these conditions may not be satisfied. Nevertheless, it is still possible to quantify deviations from the FDT and express them in terms of an effective SES relation that accounts for the ABPs conversion of chemical into kinetic energy.

A study of the problem-solving process used by skilled practitioners across science, engineering, and medicine revealed that their process can be characterized by a set of 29 specific decisions. They select and use frameworks of disciplinary knowledge to make those decisions. This work will enable better assessment and teaching of problem-solving skills.

In this study, we extend imaging and modeling work that was done in Part I of this report for a pure cellulose substrate (filter paper) to more industrially relevant substrates (untreated and pretreated hardwood and switchgrass). Using confocal fluorescence microscopy, we are able to track both the structure of the biomass particle via its autofluorescence, and bound enzyme from a commercial cellulase cocktail supplemented with a small fraction of fluorescently labeled Trichoderma reseii Cel7A. Imaging was performed throughout hydrolysis at temperatures relevant to industrial processing (50°C). Enzyme bound predominantly to areas with low autofluorescence, where structure loss and lignin removal had occurred during pretreatment; this confirms the importance of these processes for successful hydrolysis. The overall shape of both untreated and pretreated hardwood and switchgrass particles showed little change during enzymatic hydrolysis beyond a drop in autofluorescence intensity. The permanence of shape along with a relatively constant bound enzyme signal throughout hydrolysis was similar to observations previously made for filter paper, and was consistent with a modeling geometry of a hollowing out cylinder with widening pores represented as infinite slits. Modeling estimates of available surface areas for pretreated biomass were consistent with previously reported experimental results.