On some singularities of the correlation functions that determine neutrino opacities

Certain perturbation graphs in the calculation of the effects of the medium on neutrino scattering in supernova matter have a nonintegrable singularity in a physical region. A number of papers have addressed the apparent pathology through an ansatz that invokes higher order (rescattering) effects. Taking the Gamow-Teller terms as an example, we display an expression for the spin-spin correlation function that determines the cross-sections. It is clear from the form that there are no pathologies in the order by order perturbation expansion. Explicit formulae are given for a simple case, leading to an answer that is very different from one given by other authors.Comment: 8 page

Absence of resonant enhancements in some inclusive rates

A toy model is defined and solved perturbatively with the aim of examining some claimed "resonant" enhancements of certain reaction rates that enter popular models of leptogenesis. We find: a) that such enhancements are absent; and b) that the perturbative solution, as done correctly using finite- temperature field theory, is well defined without the "resumming" procedures found in the literature. The pathologies that led to the perceived need for these procedures are an artifact of uncritical use of weighted vacuum cross- sections in the determination of rates, without adequate attention to the effects of the medium upon the single particle states within it.Comment: 11 pages, no figures. Some typos corrected. More typos correcte

Numerical Toy-Model Calculation of the Nucleon Spin Autocorrelation Function in a Supernova Core

We develop a simple model for the evolution of a nucleon spin in a hot and dense nuclear medium. A given nucleon is limited to one-dimensional motion in a distribution of external, spin-dependent scattering potentials. We calculate the nucleon spin autocorrelation function numerically for a variety of potential densities and distributions which are meant to bracket realistic conditions in a supernova core. For all plausible configurations the width of the spin-density structure function is found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates the width and thus suggests a large suppression of the neutrino opacities by nucleon spin fluctuations. Our results suggest that it may be justified to neglect the collisional broadening of the spin-density structure function for the purpose of estimating the neutrino opacities in the deep inner core of a supernova. On the other hand, we find no indication that processes such as axion or neutrino pair emission, which depend on nucleon spin fluctuations, are substantially suppressed beyond the multiple-scattering effect already discussed in the literature. Aside from these practical conclusions, our model reveals a number of interesting and unexpected insights. For example, the spin-relaxation rate saturates with increasing potential strength only if bound states are not allowed to form by including a repulsive core. There is no saturation with increasing density of scattering potentials until localized eigenstates of energy begin to form.Comment: 14 latex pages in two-column format, 15 postscript figures included, uses revtex.sty and epsf.sty. Submitted to Physical Review

Artificial Intelligence Chatbot as a Mathematics Curriculum Developer: Discovering Preservice Teachers’ Overconfidence in ChatGPT

Instructors in many colleges and universities are responsible for supporting their preservice teachers’ understanding of mathematics curriculum to best serve elementary students’ needs. As such, preservice teachers are taught how to critically analyze curriculum materials. However, with the advent of technologies like ChatGPT, preservice teachers are utilizing artificial intelligence (AI) tools in new ways to collate and construct mathematical curricula. As of now, little is known about how to adapt these new resources for the classroom. ChatGPT, an AI chatbot, can create a mathematics curriculum based on user questions, which teachers can then adapt to their classrooms. Although this AI chatbot can produce a quick response, researchers have identified that ChatGPT can produce biased responses and inaccurate mathematical data. This study evaluates the quality of the mathematics curriculum created by ChatGPT’s responses, how preservice teachers adapted those resources, and their perceptions of using ChatGPT. Overall, ChatGPT’s responses tended to construct high levels of cognitive demand with age-inappropriate text for elementary students. Despite formally teaching how to be critical of resources, the majority of preservice teachers’ adaptations merely changed visual appeal alone, demonstrating how some preservice teachers have overconfidence in the abilities of AI tools. This implies that preservice teachers should be cautious of ChatGPT and be taught specific mathematical prompt engineering techniques to create innovative tasks

Fringe Science: Defringing CCD Images with Neon Lamp Flat Fields

Fringing in CCD images is troublesome from the aspect of photometric quality and image flatness in the final reduced product. Additionally, defringing during calibration requires the inefficient use of time during the night to collect and produce a "supersky" fringe frame. The fringe pattern observed in a CCD image for a given near-IR filter is dominated by small thickness variations across the detector with a second order effect caused by the wavelength extent of the emission lines within the bandpass which produce the interference pattern. We show that essentially any set of emission lines which generally match the wavelength coverage of the night sky emission lines within a bandpass will produce an identical fringe pattern. We present an easy, inexpensive, and efficient method which uses a neon lamp as a flat field source and produces high S/N fringe frames to use for defringing an image during the calibration process.Comment: accepted to PAS

Completely modular Thermionic Reactor Ion Propulsion System (TRIPS)

The nuclear reactor powered ion propulsion system described is an advanced completely modularized system which lends itself to development of prototype and/or flight type components without the need for complete system tests until late in the development program. This modularity is achieved in all of the subsystems and components of the electric propulsion system including (1) the thermionic fuel elements, (2) the heat rejection subsystem (heat pipes), (3) the power conditioning modules, and (4) the ion thrusters. Both flashlight and external fuel type in-core thermionic reactors are considered as the power source. The thermionic fuel elements would be useful over a range of reactor power levels. Electrical heated acceptance testing in their flight configuration is possible for the external fuel case. Nuclear heated testing by sampling methods could be used for acceptance testing of flashlight fuel elements. The use of heat pipes for cooling the collectors and as a means of heat transport to the radiator allows early prototype or flight configuration testing of a small module of the heat rejection subsystem as opposed to full scale liquid metal pumps and radiators in a large vacuum chamber. The power conditioner (p/c) is arranged in modules with passive cooling

Analyzing Machupo virus-receptor binding by molecular dynamics simulations

In many biological applications, we would like to be able to computationally predict mutational effects on affinity in protein-protein interactions. However, many commonly used methods to predict these effects perform poorly in important test cases. In particular, the effects of multiple mutations, non-alanine substitutions, and flexible loops are difficult to predict with available tools and protocols. We present here an existing method applied in a novel way to a new test case; we interrogate affinity differences resulting from mutations in a host-virus protein-protein interface. We use steered molecular dynamics (SMD) to computationally pull the machupo virus (MACV) spike glycoprotein (GP1) away from the human transferrin receptor (hTfR1). We then approximate affinity using the maximum applied force of separation and the area under the force-versus-distance curve. We find, even without the rigor and planning required for free energy calculations, that these quantities can provide novel biophysical insight into the GP1/hTfR1 interaction. First, with no prior knowledge of the system we can differentiate among wild type and mutant complexes. Moreover, we show that this simple SMD scheme correlates well with relative free energy differences computed via free energy perturbation. Second, although the static co-crystal structure shows two large hydrogen-bonding networks in the GP1/hTfR1 interface, our simulations indicate that one of them may not be important for tight binding. Third, one viral site known to be critical for infection may mark an important evolutionary suppressor site for infection-resistant hTfR1 mutants. Finally, our approach provides a framework to compare the effects of multiple mutations, individually and jointly, on protein-protein interactions.Comment: 33 pages, 8 figures, 5 table