Applications of momentum-space similarity

Summary Momentum-space similarity indices were used in studies linking chemical structure to observed activity. These included (a) the biological activity of various molecules that are of interest due to their capacity for HIV inhibition; and (b) the hyperpolarisabilities of series of conjugated molecules. Study (a) included comparisons of the total valence densities of different molecules or the densities associated with particular molecular fragments. Study (b) involved, for each molecule, a comparison of the momentum-space densities of the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals. The momentum-space approach, which is most sensitive to features of the long-range valence electron density, turned out to be particularly useful for cases such as these, in which the physical property or biological activity has no obvious dependence on the bonding topology of the molecules.     

The momentum of an electromagnetic wave inside a dielectric derived from the Snell refraction law

Author of the paper [M. Testa, Ann. Physics 336 (2013) 1] has derived a conclusion that there is a connection between the Snell refraction law and the Abraham form of the momentum of light in matter. In other words, author derived the Snell law on assumption that the momentum of light in matter decreases by n$n$ times as compared with that in free space. The conclusion is derived under assumption that the forces exerted on an optical medium by an electromagnetic field do not distinguish between polarization and free charges. We show that, on the contrary, the Minkowski form of the momentum of light in matter directly follows from the Snell law. No previous assumption is required for this purpose.     

The effects of flow structure and particle mass loading on particle dispersion in particle-laden swirling jets

A direct numerical simulation of particle dispersion in particle-laden swirling jets issued into a rectangular container through a round nozzle is carried out. The swirl number is S=1.42 when the bubble vortex breakdown takes place. Two cases are simulated for comparison, i.e. five types of particles with Stokes numbers St=0.01, 0.1, 1, 10 and 100 respectively under the same flow rate, and four types of particles with St=0.5, 1, 5 and 10 respectively under the same mass loading. After simulation, it is found that the rectangular flow domain induces an important modification to the flow structure. It influences the dispersion characteristics in the peripheral cross area, forming a centrosymmetric dispersion of particles in the cross-sectional area. A quantitative analysis of the non-uniform particle dispersion is carried out. Moreover, the effect of mass loading on particle dispersion is explored and explained. It indicates the correlation between the inter-phase moment coupling and particle mass loading via the change of probability density function of the inter-phase velocity difference. Heavy mass loading causes an insufficient inter-phase momentum transport and the worse dispersion of large particles than that of small mass loading.