Modeling, state estimation, and optimal control for the US COVID-19 outbreak.

The novel coronavirus SARS-CoV-2 and resulting COVID-19 disease have had an unprecedented spread and continue to cause an increasing number of fatalities worldwide. While vaccines are still under development, social distancing, extensive testing, and quarantining of confirmed infected subjects remain the most effective measures to contain the pandemic. These measures carry a significant socioeconomic cost.

Characterization of Aqueous 1-Ethyl-3-Methylimidazolium Ionic Liquids for Calculation of Ion Dissociation.

We employ precise measuring techniques to determine the densities, viscosities, and ionic conductivities of three aqueous 1-ethyl-3-methylimidazolium [emim] ionic liquid (IL) systems with minimal experimental uncertainty. We simultaneously present a novel method for estimating ion dissociation relying only on these three measurements and the estimated Stokes radii of the ions based on the Stokes-Einstein and Nernst-Einstein equations. Ion dissociation values are estimated across a range of IL concentrations, emphasizing dilute IL regions, using ionic radii calculated from widely used UNIQUAC and UNIFAC values.

Probability bounds analysis for nonlinear population ecology models.

Mathematical models in population ecology often involve parameters that are empirically determined and inherently uncertain, with probability distributions for the uncertainties not known precisely. Propagating such imprecise uncertainties rigorously through a model to determine their effect on model outputs can be a challenging problem. We illustrate here a method for the direct propagation of uncertainties represented by probability bounds though nonlinear, continuous-time, dynamic models in population ecology.

Deterministic global optimization of molecular structures using interval analysis.

The search for the global minimum of a molecular potential energy surface is a challenging problem. The molecular structure corresponding to the global minimum is of particular importance because it usually dictates both the physical and chemical properties of the molecule. The existence of an extremely large number of local minima, the number of which may increase exponentially with the size of the molecule, makes this global minimization problem extremely difficult.