Note on the boundary layer on a rotating sphere

Zusammenfassung Die gleichmässige Strömung in der Grenzschicht bei einer gleichmässig rotierenden Kugel wird behandelt. Die Grenzschicht entsteht an den Polen und entwickelt sich in beiden Hemisphären nach dem Äquator zu. An den Polen verhält sich die Kugel wie eine rotierende Scheibe, und Flüssigkeit strömt hier ein. Am Äquator verhält sich die Kugel wie ein rotierender Zylinder, und die Flüssigkeit strömt in dessen Bereich aus.     

Surface effects on quantum dot-based energy transfer

CdSe quantum dot (QD)-phthalocyanine (Pc) conjugates were prepared as energy transfer donor-acceptor pairs, and the efficiency of the energy transfer process in this system was investigated as a function of QD size and under different surface chemistry conditions. The kinetics and efficiency of the energy transfer process were studied by femtosecond time-resolved laser spectroscopy. We observed that the energy transfer efficiency does not follow a linear dependence on spectral overlap integrals as predicted by the F?rster theory for molecules. This observation is found to be due to the involvement of QD surface states in the energy transfer process from the photoexcited QDs to the molecular energy acceptor.     

A new method of calculating the piezo-electric constants of α-quartz

A method of calculating the piezo-electric constants of α-quartz is described which consists in determining the electric moment developed by changes of bond-lengths and bond-angles on strain. Considering three atoms P, Q, R, of which P and R are silicon atoms and Q an oxygen atom orvice-versa, the electric moment developed on strain may be resolved into moments in the plane PQR and moments perpendicular to this plane. Resolving these moments along the axes of the crystal and summing up for all the forty-two planes in the unit cell, we get the piezoelectric equations and constants of the crystal. The electric moment in the plane is equivalent to the moment produced by the change of bondlength along the direction of the bonds before strain, while for the moment normal to the plane we take the average value,i.e., half the value of the moment normal to the plane when the displacements of the atoms are wholly normal to the plane. The method gives good agreement with the observed values.     

X-ray reflections of the second kind in metallic crystals

Proceedings - Mathematical Sciences -