Many-body system with a four-parameter family of point interactions in one dimension

We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual $\delta$-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the $\delta$-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is not satisfied except when the four-parameter family is essentially reduced to the $\delta$-function potential.Comment: 8 pages, 4 figure

Emotion-Antecedent Appraisal Checks: EEG and EMG datasets for Goal Conduciveness, Control and Power

This document describes the full details of the second data set (Study 2) used in Coutinho et al., to appear. The Electroencephalography (EEG) and facial Electromyography (EMG) signals included in this data set, and now made public, were collected in the context of a previous study by Gentsch, Grandjean, and Scherer, 2013 that addressed three fundamental questions regarding the mechanisms underlying the appraisal process: Whether appraisal criteria are processed (1) in a fixed sequence, (2) independent of each other, and (3) by different neural structures or circuits. In this study, a gambling task was applied in which feedback stimuli manipulated simultaneously the information about goal conduciveness, control, and power appraisals. EEG was recorded during task performance, together with facial EMG, to measure, respectively, cognitive processing and efferent responses stemming from the appraisal manipulations

Fronts and interfaces in bistable extended mappings

We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the convolution with a function of bounded variation. We prove the existence of travelling wave interfaces, namely fronts, and the uniqueness of the corresponding selected velocity and shape. This selected velocity is shown to be the propagating velocity for any interface, to depend continuously on the couplings and to increase with the symmetry parameter of the local nonlinearity. We apply the results to several examples including discrete and continuous couplings, and the planar fronts' dynamics in multi-dimensional Coupled Map Lattices. We eventually emphasize on the extension to other kinds of fronts and to a more general class of bistable extended mappings for which the couplings are allowed to be nonlinear and the local map to be smooth.Comment: 27 pages, 3 figures, submitted to Nonlinearit