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1. The concentration-dependent behaviour of nanoparticles

   https://doi.org/10.1071/EN15142  

   Baalousha, Mohammed; Sikder, Mithun; Prasad, Ashwini; Lead, Jamie; Merrifield, Ruth; Chandler, G. Thomas (January 2016, Environmental Chemistry)

   Environmental contextStudies of manufactured nanoparticles (NPs) in the environment have been performed almost exclusively at high NP concentrations. These data lead to misunderstandings related to NP fate and effects at relevant environmental concentrations, which are expected to be low. A better understanding of the concentration-dependent behaviour of NPs will improve our understanding of their fate and effects under environmentally realistic conditions.AbstractThis rapid communication highlights the importance of nanoparticle concentration in determining their environmental fate and behaviour. Notably, two fate processes have been considered: dissolution and aggregation. The decrease in nanoparticle concentration results in increased dissolution and decreased aggregate sizes, inferring higher potential for environmental transport of nanoparticles. 

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2. 100 Years of Rising Corporate Concentration

   https://doi.org/10.1257/aer.20220621  

   Kwon, Spencer Y; Ma, Yueran; Zimmermann, Kaspar (July 2024, American Economic Review)

   We collect data on the size distribution of US businesses for 100 years, and use these data to estimate the concentration of production (e.g., asset share or sales share of top businesses). The data show that concentration has increased persistently over the past century. Rising concentration was stronger in manufacturing and mining before the 1970s, and stronger in services, retail, and wholesale after the 1970s. The results are robust to different measurement methods and consistent across different historical sources. Our findings suggest that large firms have become more important in the US economy for a long period of time. (JEL D22, E24, L11, L25, N12) 

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3. On concentration properties of disordered Hamiltonians

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   Auffinger, Antonio; Chen, Wei-Kuo (April 2018, Proceedings of the American Mathematical Society)
4. Matrix Concentration for Products

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   Huang, De; Niles-Weed, Jonathan; Tropp, Joel A.; Ward, Rachel (August 2021, Foundations of Computational Mathematics)
5. Higher Temperature Enhances Spatiotemporal Concentration of Rainfall

   https://doi.org/10.1175/JHM-D-21-0034.1  

   Long, K.; Wang, D.; Wang, G.; Zhu, J.; Wang, S.; Xie, S. (December 2021, Journal of Hydrometeorology)

   Abstract The relationship between extreme precipitation intensity and temperature has been comprehensively studied over different regions worldwide. However, the effect of temperature on the spatiotemporal organization of precipitation, which can have a significant impact on precipitation intensity, has not been adequately studied or understood. In this study, we propose a novel approach to quantifying the spatial and temporal concentration of precipitation at the event level and study how the concentration varies with temperature. The results based on rain gauge data from 843 stations in the Ganzhou county, a humid region in south China, show that rain events tend to be more concentrated both temporally and spatially at higher temperature, and this increase in concentration qualitatively holds for events of different precipitation amounts and durations. The effects of temperature on precipitation organization in space and in time differ at high temperatures. The temporal concentration increases with temperature up to a threshold (approximately 24°C) beyond which it plateaus, whereas the spatial concentration keeps rising with temperature. More concentrated precipitation, in addition to a projected increase of extreme precipitation, would intensify flooding in a warming world, causing more detrimental effects. 

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