The COVID-19 pandemic continues to present enormous challenges for colleges and universities and strategies for save reopening remain a topic of ongoing debate. Many institutions that reopened cautiously in the fall experienced a massive wave of infections and colleges were soon declared as the new hotspots of the pandemic. However, the precise effects of college outbreaks on their immediate neighborhood remain largely unknown. Here we show that the first two weeks of instruction present a high-risk period for campus outbreaks and that these outbreaks tend to spread into the neighboring communities. By integrating a classical mathematical epidemiology model and Bayesian learning, we learned the dynamic reproduction number for 30 colleges from their daily case reports. Of these 30 institutions, 14 displayed a spike of infections within the first two weeks of class, with peak seven-day incidences well above 1,000 per 100,000, an order of magnitude larger than the nationwide peaks of 70 and 150 during the first and second waves of the pandemic. While most colleges were able to rapidly reduce the number of new infections, many failed to control the spread of the virus beyond their own campus: Within only two weeks, 17 campus outbreaks translated directly into peaks of infection within their home counties. These findings suggests that college campuses are at risk to develop an extreme incidence of COVID-19 and become superspreaders for neighboring communities. We anticipate that tight test-trace-quarantine strategies, flexible transition to online instruction, and-most importantly-compliance with local regulations will be critical to ensure a safe campus reopening after the winter break.

Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing equations. While the Lagrangian framework for ROM construction resolves the translational issue, it is valid only before a shock forms. Once that occurs, characteristic lines cross each other and projection from a high-fidelity model space onto a ROM space distorts a moving grid, resulting in numerical instabilities. We address this grid distortion issue by developing a physics-aware dynamic mode decomposition (DMD) method based on hodograph transformation. The latter provides a map between the original nonlinear system and its linear counterpart, which coincides with the Koopman operator. This strategy is consistent with the spirit of physics-aware DMDs in that it retains information about shock dynamics. Several numerical examples are presented to validate the proposed physics-aware DMD approach to constructing accurate ROMs.

No abstract

The COVID-19 pandemic continues to present enormous challenges for colleges and universities and strategies for save reopening remain a topic of ongoing debate. Many institutions that reopened cautiously in the fall experienced a massive wave of infections and colleges were soon declared as the new hotspots of the pandemic. However, the precise effects of college outbreaks on their immediate neighborhood remain largely unknown. Here we show that the first two weeks of instruction present a high-risk period for campus outbreaks and that these outbreaks tend to spread into the neighboring communities. By integrating a classical mathematical epidemiology model and Bayesian learning, we learned the dynamic reproduction number for 30 colleges from their daily case reports. Of these 30 institutions, 14 displayed a spike of infections within the first two weeks of class, with peak seven-day incidences well above 1,000 per 100,000, an order of magnitude larger than the nation-wide peaks of 70 and 150 during the first and second waves of the pandemic. While most colleges were able to rapidly reduce the number of new infections, many failed to control the spread of the virus beyond their own campus: Within only two weeks, 17 campus outbreaks translated directly into peaks of infection within their home counties. These findings suggests that college campuses are at risk to develop an extreme incidence of COVID-19 and become superspreaders for neighboring communities. We anticipate that tight test-trace-quarantine strategies, flexible transition to online instruction, and–most importantly–compliance with local regulations will be critical to ensure a safe campus reopening after the winter break.

The bentonite buffer long-term integrity is of significant interest in the performance assessment (PA) of nuclear waste disposal. This study aims at understanding how the initial geochemical parameters affect long-term chemical properties within the buffer, which will subsequently affect the transport. Using coupled thermal-hydrological-chemical (THC) models for migration of U(VI) in a generic repository, we performed a global sensitivity analysis (GSA) to identify the influence of each parameter on the temporal evolution of a spatially averaged distribution coefficient for the entire buffer. Such an analysis can be used in a repository-scale PA. In this work, we used the TOUGHREACT software to model coupled THC processes in a generic clay repository with bentonite buffer. In this model, U(VI) is released from a canister via schoepite dissolution, which is assumed to occur 1000 years after closure. U(VI) migrates through the bentonite buffer affected by two-site protolysis non-electrostatic surface complexation and cation exchange. GSA results showed that adsorption density on smectite, pH, volume fractions of smectite, calcite, Ca2+ aqueous concentration all play a significant role in U(VI) transport, since roughly 80% of adsorbed U(VI) is absorbed by smectite, and Ca2+ affects the aqueous complexation with U(VI). This work demonstrates the complex process models potential usefulness that can be transferred to the PA model. It also provides information needed to proceed with the development of a reduced-order model, which has the potential to optimize repository designs, site characterization, performance confirmation.