Rachel E. Pepper

Splashing on elastic membranes: The importance of early-time dynamics

We study systematically the effect of substrate compliance on the threshold for splashing of a liquid drop using an elastic membrane under variable tension. We find that the splashing behavior is strongly affected by the tension in the membrane and splashing can be suppressed by reducing this tension. The deflection of the membrane upon droplet impact is measured using a laser sheet, and the results allow us to estimate the energy absorbed by the film upon drop impact. Measurements of the velocity and acceleration of the spreading drop after impact indicate that the splashing behavior is set at very early times after, or possibly just before, impact, far before the actual splash occurs. We also provide a model for the tension dependence of the splashing threshold based on the pressure in the drop upon impact that takes into account the interplay between membrane tension and drop parameters.

Explosively launched spores of ascomycete fungi have drag-minimizing shapes.

The forcibly launched spores of ascomycete fungi must eject through several millimeters of nearly still air surrounding fruiting bodies to reach dispersive air flows. Because of their microscopic size, spores experience great fluid drag, and although this drag can aid transport by slowing sedimentation out of dispersive air flows, it also causes spores to decelerate rapidly after launch. We hypothesize that spores are shaped to maximize their range in the nearly still air surrounding fruiting bodies. To test this hypothesis we numerically calculate optimal spore shapes—shapes of minimum drag for prescribed volumes—and compare these shapes with real spore shapes taken from a phylogeny of >100 species. Our analysis shows that spores are constrained to remain within 1% of the minimum possible drag for their size. From the spore shapes we predict the speed of spore launch, and confirm this prediction through high-speed imaging of ejection in Neurospora tetrasperma. By reconstructing the evolutionary history of spore shapes within a single ascomycete family we measure the relative contributions of drag minimization and other shape determinants to spore shape evolution. Our study uses biomechanical optimization as an organizing principle for explaining shape in a mega-diverse group of species and provides a framework for future measurements of the forces of selection toward physical optima.

Nearby boundaries create eddies near microscopic filter feeders.

We show through calculations, simulations and experiments that the eddies often observed near sessile filter feeders are frequently due to the presence of nearby boundaries. We model the common filter feeder Vorticella, which is approximately 50 µm across and which feeds by removing bacteria from ocean or pond water that it draws towards itself. We use both an analytical stokeslet model and a Brinkman flow approximation that exploits the narrow-gap geometry to predict the size of the eddy caused by two parallel no-slip boundaries that represent the slides between which experimental observations are often made. We also use three-dimensional finite-element simulations to fully solve for the flow around a model Vorticella and analyse the influence of multiple nearby boundaries. Additionally, we track particles around live feeding Vorticella in order to determine the experimental flow field. Our models are in good agreement both with each other and with experiments. We also provide approximate equations to predict the experimental eddy sizes owing to boundaries both for the case of a filter feeder between two slides and for the case of a filter feeder attached to a perpendicular surface between two slides.

Thickness of the rim of an expanding lamella near the splash threshold

The evolution of the ejected liquid sheet, or lamella, created after impact of a liquid drop onto a solid surface is studied using high-speed video in order to observe the detailed time evolution of the thickness of the rim of the lamella. Since it has been suggested that splashing behavior is set at very early times after impact, we study early times up to D0/U0, where D0 and U0 are the diameter and speed of the impacting drop, respectively, for different liquid viscosities and impact speeds below the splashing threshold. Within the regime of our experiments, our results are not consistent with the idea that the lamella rim grows similar to the boundary layer thickness. Rather, we find that the rim thickness is always much larger than the boundary layer thickness, and that the rim thickness decreases with increasing impact speed. For lower impact speeds, the increase in the rim thickness is consistent with a t response over the limited time range available, but the dependence is not simply proportional t...

Thinking like a physicist: A multi-semester case study of junior-level electricity and magnetism

Physics faculty agree on many of the skills and habits of mind they expect physics students to acquire by the end of their degree, including mathematical sophistication, problem-solving expertise, and an ability to work independently and become expert learners. What is less clear is how these outcomes are best achieved within the context of upper-division courses. Focusing on one key course in the career of an undergraduate major—junior-level Electricity & Magnetism (E&M)—we have investigated this critical question over the course of 4 years and across multiple universities and instructors. With the aim of educating our majors based on a more complete understanding of the cognitive and conceptual challenges of upper-division courses, we transformed junior-level E&M using results and theory from education research. We present the process and content of the transformation and several measures of its success. Students and instructors enjoyed the new course materials. Students in courses using the new materia...

But does it last? Sustaining a research-based curriculum in upper-division electricity & magnetism

We report on the process and outcomes from a four-year, eight-semester project to develop, establish, and maintain a new course approach in junior-level electricity and magnetism (E&M). Almost all developed materials (i.e., clicker questions, tutorials, homework, and student difficulties) were used successfully by several subsequent instructors, indicating a high rate of sustainability over time and between instructors. We describe the factors related to successful transfer and to decisions not to adopt the materials, based on observations, instructor interviews, and student data.

Our best juniors still struggle with Gauss’s Law: Characterizing their difficulties

We discuss student conceptual difficulties with Gauss’s law observed in an upper‐division Electricity and Magnetism (EM we present further quantitative and qualitative evidence that upper‐division students still struggle with Gauss’s law. This evidence is drawn from analysis of upper‐division E&M conceptual post‐tests, traditional exams, and formal student interviews. Examples of student difficulties include difficulty with the inverse nature of the problem, difficulty articulating complete symmetry arguments, and trouble recognizing that in situations without sufficient symmetry it is impossible (rather than “difficult”) to calculate the electric field using Gauss’s law. One possible explanation for some of these conceptual difficulties is that even students at the upper level may struggle to connect mathematical expressions to physical meanings.

Facilitating faculty conversations: Development of consensus learning goals

Our upper-division course reform efforts at the University of Colorado start with expert input from non-PER faculty, and these conversations with faculty enrich and guide our course reforms. We have discovered additional benefits of these conversations, such as the fact that they serve as a forum for discussions of pedagogy and PER. However, it is not always obvious - to the faculty or to the PER researchers - what approach will lead to successful meetings. During the process of several course transformations we have met with diverse faculty to generate consensus learning goals and course assessments. We describe the general approach used to structure and facilitate these meetings, and include details on what these meetings entailed, how we achieved broad participation and productive conversations, as well as potential pitfalls to avoid.

Issues and progress in transforming a middle-division classical mechanics/math methods course

The physics department at the University of Colorado, Boulder has recently begun the transformation of its Classical Mechanics/Math Methods course, a middle-division course taken primarily by sophomore physics majors. We discuss the process of course transformation, including holding faculty meetings to create consensus learning goals and a conceptual diagnostic, and adopting, adapting and creating course materials and structures. We also report preliminary observations of student learning gains, student attitudes towards the transformation, and common student difficulties with the course material. We also discuss ongoing plans for the course transformation.

Multiple roles of assessment in upper-division physics course reforms

The University of Colorado at Boulder has been involved in a systematic program of upper-division undergraduate course transformations. The role of assessment has been critical at multiple, interconnected scales: (1) formative evaluation focused on the course itself in the design phase; (2) formative assessment focused on students in the instructional phase and (3) summative assessment to determine student performance and the success of course design. We summarize the role and nature of assessments at each of these levels. At the design scale, investigative measures include observations and surveys of students and student work. In the classroom, assessments to determine and address student difficulties include clicker questions and tutorials. At the summative scale, assessments include faculty interviews and course and tutorial-scale posttests. We discuss examples, affordances, outcomes, and challenges associated with these different layers of assessments at the upper-division level.