The coronavirus disease 2019 pandemic has led to a major shortage of N95 respirators, which are essential for protecting healthcare professionals and the general public who may come into contact with the virus. Thus, it is essential to determine how we can reuse respirators and other personal protective equipment in these urgent times. We investigated multiple commonly used disinfection schemes on media with particle filtration efficiency of 95%. Heating was recently found to inactivate the virus in solution within 5 min at 70°C and is among the most scalable, user-friendly methods for viral disinfection. We found that heat (≤85°C) under various humidities (≤100% relative humidity, RH) was the most promising, nondestructive method for the preservation of filtration properties in meltblown fabrics as well as N95-grade respirators. At 85°C, 30% RH, we were able to perform 50 cycles of heat treatment without significant changes in the filtration efficiency. At low humidity or dry conditions, temperatures up to 100°C were not found to alter the filtration efficiency significantly within 20 cycles of treatment. Ultraviolet (UV) irradiation was a secondary choice, which was able to withstand 10 cycles of treatment and showed small degradation by 20 cycles. However, UV can potentially impact the material strength and subsequent sealing of respirators. Finally, treatments involving liquids and vapors require caution, as steam, alcohol, and household bleach all may lead to degradation of the filtration efficiency, leaving the user vulnerable to the viral aerosols.

Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace-i.e., the active subspace-of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction.

The COVID-19 pandemic is currently causing a severe disruption and shortage in the global supply chain of necessary personal protective equipment (e.g., N95 respirators). The U.S. CDC has recommended use of household cloth by the general public to make cloth face coverings as a method of source control. We evaluated the filtration properties of natural and synthetic materials using a modified procedure for N95 respirator approval. Common fabrics of cotton, polyester, nylon, and silk had filtration efficiency of 5–25%, polypropylene spunbond had filtration efficiency 6–10%, and paper-based products had filtration efficiency of 10–20%. An advantage of polypropylene spunbond is that it can be simply triboelectrically charged to enhance the filtration efficiency (from 6 to >10%) without any increase in pressure (stable overnight and in humid environments). Using the filtration quality factor, fabric microstructure, and charging ability, we are able to provide an assessment of suggested fabric materials for homemade facial coverings.

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned "least squares shadowing (LSS) problem". The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged "statistical" quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.