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Polylactic acid (PLA) and bioplastics alike have a designed degradability to avoid the environmental buildup that petroplastics have created. Yet, this designed biotic-degradation has typically been characterized in ideal conditions. This study seeks to relate the abiotic to the biotic degradation of PLA to accurately represent the degradation pathways bioplastics will encounter, supposing their improper disposal in the environment. Enzymatic hydrolysis was used to study the biodegradation of PLA with varying stages of photoaging. Utilizing a fluorescent tag to follow enzyme hydrolysis, it was determined that increasing the amount of irradiation yielded greater amounts of total enzymatic hydrolysis by proteinase K after 8 h of enzyme incubation. While photoaging of the polymers causes minimal changes in chemistry and increasing amounts of crystallinity, the trends in biotic degradation appear to primarily be driven by photoinduced reduction in molecular weight. The relationship between photoaging and enzyme hydrolysis appears to be independent of enzyme type, though commercial product degradation may be impacted by the presence of additives. Overall, this work reveals the importance of characterizing biodegradation with relevant samples that ultimately can inform optimization of production and disposal. 

We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function is unbounded. We also assume there are no cusps. Such billiard tables are called type D in the monograph of Chernov and Markarian [9]. For a class of non-degenerate type D dispersing billiards, we prove exponential decay of correlation and several other statistical properties. 

We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model and establish the local and global stabilities of its equilibria that characterize the threshold dynamics of cholera. We then perform an optimal control study on the general model with time-dependent controls and explore effective approaches to implement the education programs and water sanitation while balancing their costs. Our analysis and simulation highlight the complex interaction among the direct and indirect transmission pathways of the disease, the intrinsic growth of the environmental pathogen and the impact of multiple control measures, and their roles in collectively shaping the transmission dynamics of cholera.