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LINEAR PARTS OF HYPERBOLAE. “Since the wave pattern describes hyperbolae for single or double slits, the symmetry of the light diffraction is that of an elliptic cylindrical coordinate system. In that setting, the hyperbolae describe lines parameterized by one of the coordinate variables, providing an elementary example of straight lines.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

The winds causing the persistent eddy of winds on the Costa Brava. https://lnkd.in/e4_PbbuJ View in LinkedIn

STRANGE CIRCULAR WINDS. I observed that the Costa Brava weather often had conflicting wind conditions as seen by layered cloud movements. It turns out that the wind weather maps show that the winds tend to roar down undeterred through France to the southerly mountain gap between Marseille and Perpignan -- the powerful Mistral, and the Tramontana and then eddy in a large stationary gyre between Palafrugell and Barcelona. Between the funnel of the Pyrenees and the Alps mountains, the barrier of the African heat, and the coolness of the Mediterranean made this a persistent winter and spring pattern. https://lnkd.in/e4_PbbuJ View in LinkedIn

SO ENDS this section on mesocrystals in biomineral materials found in nature. The combination of proteins and minerals in a mesocrystal structure gives these biomineral materials considerable strength without brittleness. As is always the case, self assembly is key. Curiously, the chemistry points to magnetic and electric fields being important for the formation of mesocrystals but it is not yet described in living systems. https://lnkd.in/eNACsghr View in LinkedIn

SELF-ORGANIZATION. “Nonclassical crystallization has many facets, which so far may appear unrelated. However, the common underlying principle is controlled self organization. As this is a common principle in nature, we can further learn from natural organization schemes to take advantage of evolutionary optimization.” https://lnkd.in/eNACsghr View in LinkedIn

BIOLOGY IN CHEMISTRY. “Mesocrystal formation has a lot in common with known biological structuration processes and one can state that there is certainly a lot of "biology" involved in such nonclassical crystallization processes. This is also found in the related field of the so called biomorphs.” https://lnkd.in/eNACsghr View in LinkedIn

BIOMIMICRY. “In addition, the close similarity between the structural cascades from primary to quaternary structures can explain the "bio-Iike" appearance and morphologies of many crystals formed by a nonclassical crystallization pathway. The formation of biopolymer quaternary structures from several different molecules (e.g., the insulin tertiary structure is formed from chain A and B) implies that it should also be possible to form mesocrystals that consist of chemically different nanocrystals.” https://lnkd.in/eNACsghr View in LinkedIn

LEVELS OF STRUCTURE. “Finally, the interaction between several tertiary units of a biopolymer forms the quaternary structure, for instance the fibrils in the collagen example in Figure 15. The analogy in the nonclassical crystallization scenario is the mesocrystal. with an either self-determined morphology (this is the usual case) or a morphology determined by an external template, which is likely the case for some biominerals.” https://lnkd.in/eNACsghr View in LinkedIn

EXQUISITE REASONING. “The symmetry of a sharp edge is not obvious.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

LEGO BLOCKS. “In analogy, a number of unit cells build the nanocrystal with potentially unusual shape and interaction pattern, which is the primary building unit in a nonclassical crystallization process.” https://lnkd.in/eNACsghr View in LinkedIn