Nonlinear dynamics and solitons in Debye bi-crystals

The nonlinear dynamics of longitudinal dust lattice waves propagating in a dusty plasma bi-crystal is investigated. A “diatomic”-like one-dimensional dust lattice configuration is considered, consisting of two distinct dust grain species with different charges and masses. Two different frequency dispersion modes are obtained in the linear limit, namely, an optical and an acoustic wave dispersion branch. Nonlinear solitary wave solutions are shown to exist in both branches, by considering the continuum limit for lattice excitations in different nonlinear potential regimes. For this purpose, a generalized Boussinesq and an extended Korteweg de Vries equation is derived, for the acoustic mode excitations, and their exact soliton solutions are provided and compared. For the optic mode, a nonlinear Schrödinger-type equation is obtained, which is shown to possess bright- (dark-) type envelope soliton solutions in the long (short, respectively) wavelength range. Optic-type longitudinal wavepackets are shown to be generally unstable in the continuum limit, though this is shown not to be the rule in the general (discrete) case.

Tact training versus bi-directional intraverbal training in teaching a foreign language

The current study involved an evaluation of the emergence of untrained verbal relations as a function of between three different foreign-language teaching strategies. Two Spanish-speaking adults received foreign-language (English) tact-training as well as native-to-foreign and foreign-to-native intraverbal training. The results indicated that tact training and native-to-foreign intraverbal training are more likely to result in the emergence of untrained relations, and may thus be more efficient compared to foreign-to-native intraverbal training.