Nonlinear semigroups for nonlocal conservation laws

We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux functions and initial data via semigroup theory in Banach spaces and, in particular, via the celebrated Crandall–Liggett Theorem. We also show that the unique mild solution satisfies a Kružkov-type nonlocal entropy inequality. Similarly to the local case, we demonstrate an efficient way of proving various desirable qualitative properties of the unique solution

Leverage of Environmental Pollutant Crump Rubber on the Dry Sliding Wear Response of Epoxy Composites.

The effect of crump rubber on the dry sliding wear behavior of epoxy composites is investigated in the present study. Wear tests are carried out for three levels of crump rubber (10, 20, and 30 vol.%), normal applied load (30, 40, and 50 N), and sliding distance (1, 3, and 5 km). The wear behavior of crump rubber-epoxy composites is investigated against EN31 steel discs. The hybrid mathematical approach of Taguchi-coupled Grey Relational Analysis (GRA)-Principal Component Analysis (PCA) is used to examine the influence of crump rubber on the tribological response of composites. Mathematical and experimental results reveal that increasing crump rubber content reduces the wear rate of composites. Composites also show a significant decrease in specific wear values at higher applied loads. Furthermore, the coefficient of friction also shows a decreasing trend with an increase in crump rubber content, indicating the effectiveness of reinforcing crump rubber in a widely used epoxy matrix. Analysis of Variance (ANOVA) results also reveal that the crump rubber content in the composite is a significant parameter to influence the wear characteristic. The post-test temperature of discs increases with an increase in the applied load, while decreasing with an increase in filler loading. Worn surfaces are analyzed using scanning electron microscopy to understand structure-property correlations. Finally, existing studies available in the literature are compared with the wear data of the present study in the form of a property map

<i>Escherichia coli</i> B2 strains prevalent in inflammatory bowel disease patients have distinct metabolic capabilities that enable colonization of intestinal mucosa

Abstract Background Escherichia coli is considered a leading bacterial trigger of inflammatory bowel disease (IBD). E. coli isolates from IBD patients primarily belong to phylogroup B2. Previous studies have focused on broad comparative genomic analysis of E. coli B2 isolates, and identified virulence factors that allow B2 strains to reside within human intestinal mucosa. Metabolic capabilities of E. coli strains have been shown to be related to their colonization site, but remain unexplored in IBD-associated strains. Results In this study, we utilized pan-genome analysis and genome-scale models (GEMs) of metabolism to study metabolic capabilities of IBD-associated E. coli B2 strains. The study yielded three results: i) Pan-genome analysis of 110 E. coli strains (including 53 isolates from IBD studies) revealed discriminating metabolic genes between B2 strains and other strains; ii) Both comparative genomic analysis and GEMs suggested that B2 strains have an advantage in degrading and utilizing sugars derived from mucus glycan, and iii) GEMs revealed distinct metabolic features in B2 strains that potentially allow them to utilize energy more efficiently. For example, B2 strains lack the enzymes to degrade amadori products, but instead rely on neighboring bacteria to convert these substrates into a more readily usable and potentially less sought after product. Conclusions Taken together, these results suggest that the metabolic capabilities of B2 strains vary significantly from those of other strains, enabling B2 strains to colonize intestinal mucosa.The results from this study motivate a broad experimental assessment of the nutritional effects on E. coli B2 pathophysiology in IBD patients

A Multiwell Platform for Studying Stiffness-Dependent Cell Biology

Adherent cells are typically cultured on rigid substrates that are orders of magnitude stiffer than their tissue of origin. Here, we describe a method to rapidly fabricate 96 and 384 well platforms for routine screening of cells in tissue-relevant stiffness contexts. Briefly, polyacrylamide (PA) hydrogels are cast in glass-bottom plates, functionalized with collagen, and sterilized for cell culture. The Young's modulus of each substrate can be specified from 0.3 to 55 kPa, with collagen surface density held constant over the stiffness range. Using automated fluorescence microscopy, we captured the morphological variations of 7 cell types cultured across a physiological range of stiffness within a 384 well plate. We performed assays of cell number, proliferation, and apoptosis in 96 wells and resolved distinct profiles of cell growth as a function of stiffness among primary and immortalized cell lines. We found that the stiffness-dependent growth of normal human lung fibroblasts is largely invariant with collagen density, and that differences in their accumulation are amplified by increasing serum concentration. Further, we performed a screen of 18 bioactive small molecules and identified compounds with enhanced or reduced effects on soft versus rigid substrates, including blebbistatin, which abolished the suppression of lung fibroblast growth at 1 kPa. The ability to deploy PA gels in multiwell plates for high throughput analysis of cells in tissue-relevant environments opens new opportunities for the discovery of cellular responses that operate in specific stiffness regimes