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We report on a variety of innovative projects that are at different stages of development and implementation. We start by presenting a project still in development to help address Klein’s second discontinuity problem, that is, the perception of pre-college teachers that the advanced mathematics courses they took at the university are of little use in the practice of their profession. Then we briefly discuss the study and research paths (SRP). This is the proposal from the Anthropological Theory of the Didactic (ATD) to foment a move from the prevailing paradigm of visiting works to that of questioning the world. This is followed by the discussion of an online course for inservice teachers, designed to help them experience, adapt, and class-test a modeling intervention, as well as reflect on institutional issues that might constrain the future application of modeling in their teaching. We end with a discussion of a project based on the idea of guided reinvention, to design and study the implementation of inquiry-oriented linear algebra. 

We report on a variety of innovative projects that are at different stages of development and implementation. We start by presenting a project still in development to help address Klein’s second discontinuity problem, that is, the perception of pre-college teachers that the advanced mathematics courses they took at the university are of little use in the practice of their profession. Then we briefly discuss the study and research paths (SRP). This is the proposal from the Anthropological Theory of the Didactic (ATD) to foment a move from the prevailing paradigm of visiting works to that of questioning the world. This is followed by the discussion of an online course for in- service teachers, designed to help them experience, adapt, and class-test a modeling intervention, as well as reflect on institutional issues that might constrain the future application of modeling in their teaching. We end with a discussion of a project based on the idea of guided reinvention, to design and study the implementation of inquiry-oriented linear algebra. 

The McMurdo Dry Valleys, Antarctica, are a polar desert populated with numerous closed‐watershed, perennially ice‐covered lakes primarily fed by glacial melt. Lake levels have varied by as much as 8 m since 1972 and are currently rising after a decade of decreasing. Precipitation falls as snow, so lake hydrology is dominated by energy available to melt glacier ice and to sublimate lake ice. To understand the energy and hydrologic controls on lake level changes and to explain the variability between neighboring lakes, only a few kilometers apart, we model the hydrology for the three largest lakes in Taylor Valley. We apply a physically based hydrological model that includes a surface energy balance model to estimate glacial melt and lake sublimation to constrain mass fluxes to and from the lakes. Results show that lake levels are very sensitive to small changes in glacier albedo, air temperature, and wind speed. We were able to balance the hydrologic budget in two watersheds using meltwater inflow and sublimation loss from the ice‐covered lake alone. A third watershed, closest to the coast, required additional inflow beyond model uncertainties. We hypothesize a shallow groundwater system within the active layer, fed by dispersed snow patches, contributes 23% of the inflow to this watershed. The lakes are out of equilibrium with the current climate. If the climate of our study period (1996–2013) persists into the future, the lakes will reach equilibrium starting in 2300, with levels 2–17 m higher, depending on the lake, relative to the 2020 level.

 

Gasoline particulate filters (GPFs) are practically adoptable devices to mitigate particulate matter emissions from vehicles using gasoline direct ignition engines. This paper presents a newly developed control-oriented model to characterize the thermal and soot oxidation dynamics in a ceria-coated GPF. The model utilizes the GPF inlet exhaust gas temperature, exhaust gas mass flow rate, the initial GPF soot loading density, and air– fuel ratio to predict the internal GPF temperature and the amount of soot oxidized during regeneration events. The reaction kinetics incorporated in the model involve the rates of both oxygen- and ceria-initiated soot oxidation reactions. Volumetric model parameters are calculated from the geometric information of the coated GPF, while the air–fuel ratio is used to determine the volume fractions of the exhaust gas constituents. The exhaust gas properties are evaluated using the volume fractions and thermodynamic tables, while the cordierite specific heat capacity is identified using a clean experimental data set. The enthalpies of the regeneration reactions are calculated using thermochemical tables. Physical insights from the proposed model are thus enhanced by limiting the number of parameters obtained from fitting to only those which cannot be directly measured from experiments. The parameters of the model are identified using the particle swarm optimization algorithm and a cost function designed to simultaneously predict both thermal and soot oxidation dynamics. Parameter identification and model validation are performed using independent data sets from laboratory experiments conducted on a ceria-coated GPF. This work demonstrates that the proposed model can be successfully implemented to predict ceria-coated GPF dynamics under different soot loading and temperature conditions.