Summary Background: The majority of complex and advanced materials contain nanoparticles. The properties of these materials depend crucially on the size and shape of these nanoparticles. Wulff construction offers a simple method of predicting the equilibrium shape of nanoparticles given the surface energies of the material. Results: We review the mathematical formulation and the main applications of Wulff construction during the last two decades. We then focus to three recent extensions: active sites of metal nanoparticles for heterogeneous catalysis, ligand-protected nanoparticles generated as colloidal suspensions and nanoparticles of complex metal hydrides for hydrogen storage. Conclusion: Wulff construction, in particular when linked to first-principles calculations, is a powerful tool for the analysis and prediction of the shapes of nanoparticles and tailor the properties of shape-inducing species.

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The COVID-19 pandemic has affected all countries of the world producing a substantial number of fatalities accompanied by a major disruption in their social, financial and educational organization [1]. The strict disciplinary measures implemented by China were very effective and thus were subsequently adopted by most world countries to various degrees. The infection duration and number of infected persons are of critical importance for the battle against the pandemic [2,3]. We use the quantitative landscape of the disease spreading in China as a benchmark and utilize infection data from eight countries to estimate the complete evolution of the infection in each of these countries. This analysis predicts both the expected number of daily infections per country and, perhaps more importantly, the duration of the epidemic in each country. Our predicted data show that Italy, Spain and the Netherlands have passed the highest point of infection while Greece, France and Germany are close to it.