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LIGHT ANALOGY. “The conclusion from this merely is that it likely is possible to fashion a structure within flat space-time and endow particle interactions with overall properties in relation to it, with an end result in rough agreement with light diffraction.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

STRIKING ANALOGIES. “It is remarkable that the structural levels found for biopolymers such as proteins or polysaccharides have similar features as the structural levels found in a mesocrystal. Both structures rely on self organization/structuration processes in a solvent and it is useful to consider analogies.” https://lnkd.in/eNACsghr View in LinkedIn

BUCKMINSTER. “The upshot of the above is that through the symmetry, it is possible to identify a flat geometry where hyperbolae are geodesics.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

SCALAR ASSUMPTION. “However, we will assume a decent separation of scales between the various effects, so that the different structures can be considered to be nested within each other and dealt with separately.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

NESTED PROPERTIES. “The full symmetry picture is quite intricate, since the configuration of the obstacles have nested geometrical qualities. For a double-slit, there are single slits at the foci, and for a single slit, there are edges at the foci. In addition, an elliptic transformation does not give a diffeomorphism for the line between the foci.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

THE JOINT. “A large part of the appropriate geometry hence is elliptic, and we will illustrate that the elliptic geometry is compatible with a flat space-time metric that seamlessly connects to the vacuum flat metric far away from the apertures.” https://link.springer.com/content/pdf/10.1007/JHEP07(2019)140.pdf View in LinkedIn

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