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.     

Lattice dynamics of ND4I and NH4I crystals

The phonon dispersion curves and one phonon density of states for ND₄I and NH₄I crystals in the sodium chloride structure have been calculated by making use of the deformation dipole model of Hardy incorporating general short range forces out to second neighbours. Since the electronic configuration of both the compounds is identical, we have used the input data of NH₄I to calculate the model parameters for both the crystals. The results have been compared in the three principal symmetry directions with the neutron scattering measurements available only in case of ND₄I. The theoretical results show a reasonably good agreement with the experimental data.     

Dynamics of Hollow Nanofiber Formation During Solidification Subjected to Solvent Evaporation

Summary: To mimic the emergence of gradient morphology in polymer nanofibers, a new theoretical approach has been developed in the context of Cahn‐Hilliard time evolution equation, alternatively known as time‐dependent Ginzburg‐Landau equation (Model B) involving concentration order parameter. The effects of solvent evaporation on the morphology evolution of the nanofibers have been demonstrated. The numerical simulation showed that the formation of skin layers is governed by the competition between solvent evaporation rate and mutual diffusion rate. That is to say the skin layers are formed in the nanotube whenever the rate of evaporation exceeds a critical value; otherwise, a solid fiber is formed. In hollow nanofibers, the layer can grow to a substantial fraction of the fiber diameter, allowing it to remain intact, albeit often in a collapsed form.

The cross‐sectional concentration profile of the emerging fiber.     

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 -