A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical phenomenon, collected temperature data along the rod, then referenced the demonstration for purposes in and out of the classroom. Here, we discuss the experimental setup, how the demonstration informed practices in the classroom and a project based on the collected data, including analytical and computational components

Fluorescein Redirects a Ruthenium−Octaarginine Conjugate to the Nucleus

The cellular uptake and localization of a Ru−octaarginine conjugate with and without an appended fluorescein are compared. The inherent luminescence of the Ru(II) dipyridophenazine complex allows observation of its uptake without the addition of a fluorophore. Ru−octaarginine−fluorescein stains the cytosol, nuclei, and nucleoli of HeLa cells under conditions where the Ru−octaarginine conjugate without fluorescein shows only punctate cytoplasmic labeling. At higher concentrations, however, Ru−octaarginine without the fluorescein tag does exhibit cytoplasmic, nuclear, and nucleolar staining. Attaching fluorescein to Ru−octaarginine lowers the threshold concentration required for diffuse cytoplasmic labeling and nuclear entry. Hence, the localization of the fluorophore-bound peptide cannot serve as a proxy for that of the free peptide

Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $\mu$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Vorono\"i tessellation, we find the variance of the local volume fraction $\phi$ monotonically decreases as the system becomes more dense, independent of boundary condition and $\mu$. We examine the universality and origins of this trend using experiments and the recent granocentric model \cite{Clusel-2009-GMR,Corwin-2010-MRP}, modified to draw particle locations from an arbitrary distribution ${\cal P}(s)$ of neighbor distances $s$. The mean and variance of the observed ${\cal P}(s)$ are described by a single length scale controlled by $\bar \phi$. Through the granocentric model, we observe that diverse functional forms of ${\cal P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally-observed ${\cal P}(s)$ provides quantitative agreement with the measured $\phi$ fluctuations. Thus, we find that both ${\cal P}(s)$ and ${\cal P}(\phi)$ encode similar information about the ensemble of observed packings, and are connected to each other by the local granocentric model

Covid-19\u27s Effect on Education

The purpose for this paper is to inform the reader of what the effect of the Covid-19 pandemic has on students and teachers along with finding solutions. The biggest concern during this time is if students are meeting the required materials while in school. Many students are falling behind and there needs to be a solution on how to solve this problem. Covid has caused many problems in everyone’s life but, especially in the lives of students. Teachers are struggling to find solutions due to limitations of Nontraditional Instruction and virtual classrooms. Parents and teachers can team up to help one another out and to achieve the goals of their student(s)

Time-Frequency Analysis Reveals Pairwise Interactions in Insect Swarms

The macroscopic emergent behavior of social animal groups is a classic example of dynamical self-organization, and is thought to arise from the local interactions between individuals. Determining these interactions from empirical data sets of real animal groups, however, is challenging. Using multicamera imaging and tracking, we studied the motion of individual flying midges in laboratory mating swarms. By performing a time-frequency analysis of the midge trajectories, we show that the midge behavior can be segmented into two distinct modes: one that is independent and composed of low-frequency maneuvers, and one that consists of higher-frequency nearly harmonic oscillations conducted in synchrony with another midge. We characterize these pairwise interactions, and make a hypothesis as to their biological function