Using an exactly soluble one-dimensional atomic model we explore the idea
that the recently observed high-order nonlinearity in optical filaments is due
to virtual transitions involving the continuum states. We show that the model's
behavior is qualitatively comparable with the experimentally observed
cross-over from self-focusing to de-focusing at high intensities, and only
occurs at intensities which result in significant ionization. Based on these
observations, we conjecture that this continuum electron nonlinear refraction
exhibits strong memory effects, and most importantly, the change of its sign is
effectively masked by the de-focusing due to free electrons.Comment: 4 pages, 2 figure
Exact analytic expressions are derived for the dipole moment and nonlinear current of a one-dimensional quantum particle subject to a short-range attractive potential and an arbitrary time-dependent electric field. An efficient algorithm for the current evaluation is described and a robust implementation suitable for numerical simulations is demonstrated.
Knowledge growth models, based on primary principles, play a fundamental role in the cognitive sciences. The authors submit an extension of their model (ENKI) from 2005, with the results of the practical testing, which was performed using the method developed for the purpose of model ENKI of solving tasks with immediate feedback. This was applied to the curriculum of parallel configuration of resistors in electrical circuits. There were 73 pupils from six elementary schools in attendance for testing. Analysis based on ENKI indicates that three autonomous units (scopes) were evaluated simultaneously during the assessment. Results showed that 25% of pupils knew the curriculum, 9% of pupils showed no improvement, while 66% of pupils showed an increased success in accordance with the ENKI model (significance level = 0.05). Solving 7.2 typical tasks on average, by a method of immediate feedback resulted in 90% of the pupils mastering the curriculum.
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