Solitary Waves in Discrete Media with Four Wave Mixing

In this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear inter-component coupling and four wave mixing. The relevant four branches of solutions consist of two single mode branches (transverse electric and transverse magnetic) and two mixed mode branches, involving both components (linearly polarized and elliptically polarized). These solutions are obtained explicitly and their stability is analyzed completely in the anti-continuum limit (where the nodes of the lattice are uncoupled), illustrating the supercritical pitchfork nature of the bifurcations that give rise to the latter two, respectively, from the former two. Then the branches are continued for finite coupling constructing a full two-parameter numerical bifurcation diagram of their existence. Relevant stability ranges and instability regimes are highlighted and, whenever unstable, the solutions are dynamically evolved through direct computations to monitor the development of the corresponding instabilities. Direct connections to the earlier experimental work of Meier et al. [Phys. Rev. Lett. {\bf 91}, 143907 (2003)] that motivated the present work are given.Comment: 13 pages, 10 figure

The effect of pictorial depth information on projected size judgments.

When full depth cues are available, size judgments are dominated by physical size. However, with reduced depth cues, size judgments are influenced less by physical size and more by projected size. By manipulating monocularly presented pictorial depth cues only, in this study we reduced depth cues further than had previous size judgment studies. Participants were presented monocularly with two shapes against a background of zero (control), one, two, or three pictorial depth cues. Each cue was added progressively in the following order: height in the visual field, linear perspective, and texture gradient. Participants made a same/different judgment regarding the projected size of the two shapes (i.e., ignoring any depth cues). As was expected, accuracy increased and response times decreased as the ratio between the projected size of the two shapes increased (range of projected size ratios, 1:1-1:5). In addition, with the exception of the larger size ratios (1:4 and 1:5), detection of projected size difference grew poorer as depth cues were added. One- and two-cue conditions had the most weighting in this performance decrement, with little weighting from the three-cue condition. We conclude that even minimal depth information is difficult to inhibit, which indicates that depth perception requires little focused attention

Vortex Structures Formed by the Interference of Sliced Condensates

We study the formation of vortices, vortex necklaces and vortex ring structures as a result of the interference of higher-dimensional Bose-Einstein condensates (BECs). This study is motivated by earlier theoretical results pertaining to the formation of dark solitons by interfering quasi one-dimensional BECs, as well as recent experiments demonstrating the formation of vortices by interfering higher-dimensional BECs. Here, we demonstrate the genericity of the relevant scenario, but also highlight a number of additional possibilities emerging in higher-dimensional settings. A relevant example is, e.g., the formation of a "cage" of vortex rings surrounding the three-dimensional bulk of the condensed atoms. The effects of the relative phases of the different BEC fragments and the role of damping due to coupling with the thermal cloud are also discussed. Our predictions should be immediately tractable in currently existing experimental BEC setups.Comment: 8 pages, 6 figures (low res). To appear in Phys. Rev. A. Full resolution preprint available at: http://www-rohan.sdsu.edu/~rcarrete/publications

Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

Introduction to the special issue on reproducibility in neuroimaging

The last decade has seen increasing attention to the problem of scientific reproducibility, across a broad range of scientific fields (Camerer et al., 2016;Morrison, 2014;Open Science Collaboration, 2015). Within the field of neuroimaging, there has been a particular focus on issues of analytic variability (Bowring et al., 2019;Carp, 2012) statistical power (Button et al., 2013;Poldrack et al., 2017), and test-retest reliability (Bennett and Miller, 2013), all of which have raised alarms regarding the potential for irreproducible results. In addition, failed replications (Boekel et al., 2015;Dinga et al., 2019) and meta-analytic null results (Müller et al., 2017) have raised particular concern about studies of group and individual differences. This special issue was developed in light of these emerging concerns, with the goal of highlighting and encouraging work that aims to both quantify and improve the reproducibility of neuroimaging research. Here we provide a brief overview of the papers within this special issue