Effect of Bilayer Thickness on Membrane Bending Rigidity

The bending rigidity $k_c$ of bilayer vesicles self-assembled from amphiphilic diblock copolymers has been measured using single and dual-micropipet techniques. These copolymers are nearly a factor of 5 greater in hydrophobic membrane thickness $d$ than their lipid counterparts, and an order of magnitude larger in molecular weight $\bar{M}_n$. The macromolecular structure of these amphiphiles lends insight into and extends relationships for traditional surfactant behavior. We find the scaling of $k_c$ with thickness to be nearly quadratic, in agreement with existing theories for bilayer membranes. The results here are key to understanding and designing soft interfaces such as biomembrane mimetics

The role of sign in students' modeling of scalar equations

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.Comment: 5 pages, 1 figure, to be published in The Physics Teache

Moller operators and Lippmann-Schwinger equations for step-like potentials

The Moller operators and the asociated Lippman-Schwinger equations obtained from different partitionings of the Hamiltonian for a step-like potential barrier are worked out, compared and related.Comment: 15 pages, 1 inlined figure, iopart.cl

Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work

Reinventing College Physics for Biologists: Explicating an epistemological curriculum

The University of Maryland Physics Education Research Group (UMd-PERG) carried out a five-year research project to rethink, observe, and reform introductory algebra-based (college) physics. This class is one of the Maryland Physics Department's large service courses, serving primarily life-science majors. After consultation with biologists, we re-focused the class on helping the students learn to think scientifically -- to build coherence, think in terms of mechanism, and to follow the implications of assumptions. We designed the course to tap into students' productive conceptual and epistemological resources, based on a theoretical framework from research on learning. The reformed class retains its traditional structure in terms of time and instructional personnel, but we modified existing best-practices curricular materials, including Peer Instruction, Interactive Lecture Demonstrations, and Tutorials. We provided class-controlled spaces for student collaboration, which allowed us to observe and record students learning directly. We also scanned all written homework and examinations, and we administered pre-post conceptual and epistemological surveys. The reformed class enhanced the strong gains on pre-post conceptual tests produced by the best-practices materials while obtaining unprecedented pre-post gains on epistemological surveys instead of the traditional losses.Comment: 35 pages including a 15 page appendix of supplementary material

A study of commuter airplane design optimization

Problems of commuter airplane configuration design were studied to affect a minimization of direct operating costs. Factors considered were the minimization of fuselage drag, methods of wing design, and the estimated drag of an airplane submerged in a propellor slipstream; all design criteria were studied under a set of fixed performance, mission, and stability constraints. Configuration design data were assembled for application by a computerized design methodology program similar to the NASA-Ames General Aviation Synthesis Program

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Potential Energy Surface for H_2 Dissociation over Pd(100)

The potential energy surface (PES) of dissociative adsorption of H_2 on Pd(100) is investigated using density functional theory and the full-potential linear augmented plane wave (FP-LAPW) method. Several dissociation pathways are identified which have a vanishing energy barrier. A pronounced dependence of the potential energy on ``cartwheel'' rotations of the molecular axis is found. The calculated PES shows no indication of the presence of a precursor state in front of the surface. Both results indicate that steering effects determine the observed decrease of the sticking coefficient at low energies of the H_2 molecules. We show that the topology of the PES is related to the dependence of the covalent H(s)-Pd(d) interactions on the orientation of the H_2 molecule.Comment: RevTeX, 8 pages, 5 figures in uufiles forma