arXiv subjects

Peter Hugo Nelson

Publications and source records attributed to Peter Hugo Nelson.

4 recordsLinked to original sources

arXiv2021

Introductory models of COVID-19 in the United States

Students develop and test simple models of the spread of COVID-19. Microsoft Excel is used as the modeling platform because it's non-threatening to students and because it's widely available. Students develop finite difference models and implement them in the cells of preformatted spreadsheets following a guided-inquiry pedagogy that introduces new model parameters in a scaffolded step-by-step manner. That approach allows students to investigate the implications of new model parameters in a systematic way. Students fit the resulting models to reported cases-per-day data for the United States using least-squares techniques with Excel's Solver. Using their own spreadsheets, students discover for themselves that the initial exponential growth of COVID-19 can be explained by a simplified unlimited growth model and by the SIR model. They also discover that the effects of social distancing can be modeled using a Gaussian transition function for the infection rate coefficient and that the summer surge was caused by prematurely relaxing social distancing and then reimposing stricter social distancing. Students then model the effect of vaccinations and validate the resulting SIRV model by showing that it successfully predicts the reported cases-per-day data from Thanksgiving through February 14, 2021. The same SIRV model is then extended and successfully fits the fourth peak up to June 1, 2021, caused by further relaxation of social distancing measures. Finally, students extend the model up to the present day and successfully account for the appearance of the delta variant of SARS-CoV-2. The fitted model also predicts that the delta-variant peak will be comparatively short, and the cases-per-day data should begin to fall off in early September 2021 - counter to current expectations. This case study would make an excellent capstone experience for students interested in scientific modeling.

physics.ed-ph↗

arXiv2016

Osmosis and thermodynamics explained by solute blocking

A solute-blocking model is presented that provides a kinetic explanation of osmosis and ideal solution thermodynamics. It validates a diffusive model of osmosis that is distinct from the traditional convective flow model of osmosis. Osmotic equilibrium occurs when the fraction of water molecules in solution matches the fraction of pure water molecules that have enough energy to overcome the pressure difference. Solute-blocking also provides a kinetic explanation for why Raoult's law and the other colligative properties depend on the mole fraction (but not the size) of the solute particles, resulting in a novel kinetic explanation for the entropy of mixing and chemical potential of ideal solutions. Some of its novel predictions have been confirmed, others can be tested experimentally or by simulation.

physics.bio-ph↗

arXiv2014

Osmosis, colligative properties, entropy, free energy and the chemical potential

A diffusive model of osmosis is presented that explains currently available experimental data. It makes predictions that distinguish it from the traditional convective flow model of osmosis, some of which have already been confirmed experimentally and others have yet to be tested. It also provides a simple kinetic explanation of Raoult's law and the colligative properties of dilute aqueous solutions. The diffusive model explains that when a water molecule jumps from low to high osmolarity at equilibrium, the free energy change is zero because the work done pressurizing the water molecule is balanced by the entropy of mixing. It also explains that equal chemical potentials are required for particle exchange equilibrium in analogy with the familiar requirement of equal temperatures at thermal equilibrium.

cond-mat.soft↗

arXiv2012

Teaching introductory STEM with the Marble Game

Recently there have been multiple calls for curricular reforms to develop new pathways to the science, technology, engineering and math (STEM) disciplines. The Marble Game answers these calls by providing a conceptual framework for quantitative scientific modeling skills useful across all the STEM disciplines. The approach actively engages students in a process of directed scientific discovery. In a "Student Assessment of their Learning Gains" (SALG) survey, students identified this approach as producing "great gains" in their understanding of real world problems and scientific research. Using the marble game, students build a conceptual framework that applies directly to random molecular-level processes in biology such as diffusion and interfacial transport. It is also isomorphic with a reversible first-order chemical reaction providing conceptual preparation for chemical kinetics. The computational and mathematical framework can also be applied to investigate the predictions of quantitative physics models ranging from Newtonian mechanics through RLC circuits. To test this approach, students were asked to derive a novel theory of osmosis. The test results confirm that they were able to successfully apply the conceptual framework to a new situation under final exam conditions. The marble game thus provides a pathway to the STEM disciplines that includes quantitative biology concepts in the undergraduate curriculum - from the very first class.

physics.ed-ph↗