Neural field simulator: two-dimensional spatio-temporal dynamics involving finite transmission speed.

Neural Field models (NFM) play an important role in the understanding of neural population dynamics on a mesoscopic spatial and temporal scale. Their numerical simulation is an essential element in the analysis of their spatio-temporal dynamics. The simulation tool described in this work considers scalar spatially homogeneous neural fields taking into account a finite axonal transmission speed and synaptic temporal derivatives of first and second order. A text-based interface offers complete control of field parameters and several approaches are used to accelerate simulations. A graphical output utilizes video hardware acceleration to display running output with reduced computational hindrance compared to simulators that are exclusively software-based. Diverse applications of the tool demonstrate breather oscillations, static and dynamic Turing patterns and activity spreading with finite propagation speed. The simulator is open source to allow tailoring of code and this is presented with an extension use case.

Buckling the equatorial anion plane: octahedral anion distortions in ferroic perovskites and related systems resolved via neutron diffraction.

A framework for describing anion displacements from perfect octahedra in perovskites has been developed for use with neutron diffraction data sets. We describe the distortions as noncoplanar arrangements, or buckling, of oxygen ions in any central plane of the octahedron, ignoring the central cation. Nonplanar distortions of octahedra have been calculated for perovskite structures contained within the Inorganic Crystal Structure Database. We find that antiferroelectric materials have buckling angles larger than ~2° and ferroelectric materials have buckling angles between 0° and 1°. The trend is found as a function of solid solution composition and temperature for common antiferroelectrics. For example, the described method resolves a structural difference between the end members PbTiO(3) and PbZrO(3), which exhibit ferroelectric and antiferroelectric responses, respectively. This technique is applicable to other structures containing anion octahedra, e.g., pyrochlores, spinels, and tungsten bronzes.