Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

We present a preliminary analysis of the cool pulsating white dwarf GD1212, enabled by more than 11.5 days of space-based photometry obtained during an engineering test of a two-reaction wheel controlled _Kepler_ spacecraft. We detect at least 21 independent pulsation modes, ranging from 369.8 − 1220.8s, and at least 17 nonlinear combination frequencies of those independent pulsations. Our longest uninterrupted light curve, 9.0 days in length, evidences coherent difference frequencies at periods inaccessible from the ground, up to 14.5hr, the longest-period signals ever detected in a pulsating white dwarf. These results mark some of the first science to come from a two-wheel controlled _Kepler spacecraft_, proving the capability for unprecedented discoveries afforded by extending _Kepler_ observations to the ecliptic.