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In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties also persists in the case of such wavepackets.

Objective-prism surveys which select galaxies on the basis of line-emission are extremely effective at detecting low-luminosity galaxies and constitute some of the deepest available samples of dwarfs. In this study, we confirm that emission-line galaxies (ELGs) in the University of Michigan (UM) objective-prism survey (MacAlpine et al. 1977-1981) are reliable tracers of large-scale structure, and utilize the depth of the samples to examine the spatial distribution of low-luminosity (M$_{B} > $ -18.0) dwarfs relative to higher luminosity giant galaxies (M$_{B} \leq$ -18.0) in the Updated Zwicky Catalogue (Falco et al. 1999). New spectroscopic data are presented for 26 UM survey objects. We analyze the relative clustering properties of the overall starbursting ELG and normal galaxy populations, using nearest neighbor and correlation function statistics. This allows us to determine whether the activity in ELGs is primarily caused by gravitational interactions. We conclude that galaxy-galaxy encounters are not the sole cause of activity in ELGs since ELGs tend to be more isolated and are more often found in the voids when compared to their normal galaxy counterparts. Furthermore, statistical analyses performed on low-luminosity dwarf ELGs show that the dwarfs are less clustered when compared to their non-active giant neighbors. The UM dwarf samples have greater percentages of nearest neighbor separations at large values and lower correlation function amplitudes relative to the UZC giant galaxy samples. These results are consistent with the expectations of galaxy biasing., Comment: 17 pages, 4 tables, 10 figures. Accepted for publication in the ApJ