Impact of a New Introductory Mathematical Modeling Course on Student Confidence in Mathematical Ability and Skills

Interdisciplinary mathematics and science courses are increasing in popularity. Faculty teaching these courses are given the opportunity to show how mathematics plays an important role in science and how it can be used to improve our understanding of mathematics and science. This paper discusses a new course in mathematical modeling that focuses on environmental issues. Course content and format are presented, as well as the results of a study on the changes in students’ perceptions of their mathematical abilities as a result of taking this new course

Adventures in Invariant Theory

We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics.Comment: 12 pp, includes supplementary discussion of example

Development of improved-durability plasma sprayed ceramic coatings for gas turbine engines

As part of a NASA program to reduce fuel consumption of current commercial aircraft engines, methods were investigated for improving the durability of plasma sprayed ceramic coatings for use on vane platforms in the JT9D turbofan engine. Increased durability concepts under evaluation include use of improved strain tolerant microstructures and control of the substrate temperature during coating application. Initial burner rig tests conducted at temperatures of 1010 C (1850 F) indicate that improvements in cyclic life greater than 20:1 over previous ceramic coating systems were achieved. Three plasma sprayed coating systems applied to first stage vane platforms in the high pressure turbine were subjected to a 100-cycle JT9D engine endurance test with only minor damage occurring to the coatings

Impact vesiculation – a new trigger for volcanic bubble growth and degassing

We highlight a potentially important trigger for bubble growth and degassing in volcanic bombs. We have successfully triggered bubble growth in previously unvesiculated samples of silicate melt during experiments to simulate volcanic bomb impact, by firing pellets at, and dropping weights onto, melt samples. We call this phenomenon "impact vesiculation". Further work is required on real volcanic bombs to establish the extent to which impact vesiculation occurs in nature. However, our experiments are sufficient to demonstrate that impact vesiculation is a viable processes and should be borne in mind in analysis of bubble populations and degassing histories of bombs and spatter-fed lava flows. Degassing caused by impact vesiculation can occur only at ground-level, so any attempt to calculate the amount of erupted gas available for transport high into the atmosphere by convection above the source of a fountain-fed lava flow that is based on subtracting the volatile content of fluid inclusions from the volatile content of the resulting lava flow would be an overestimate if significant impact vesiculation has occurred

Partly melted DNA conformations obtained with a probability peak finding method

Peaks in the probabilities of loops or bubbles, helical segments, and unzipping ends in melting DNA are found in this article using a peak finding method that maps the hierarchical structure of certain energy landscapes. The peaks indicate the alternative conformations that coexist in equilibrium and the range of their fluctuations. This yields a representation of the conformational ensemble at a given temperature, which is illustrated in a single diagram called a stitch profile. This article describes the methodology and discusses stitch profiles vs. the ordinary probability profiles using the phage lambda genome as an example.Comment: 11 pages, 9 figures; v3: major changes; v4: applications sectio