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The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-wave analysis of electromagnetic fields in complex media and for detailed geometries. Applications of the FDTD method cover a range of time and spatial scales, extending from subatomic to galactic lengths and from classical to quantum physics. Technology areas that benefit from the FDTD method include biomedicine — bioimaging, biophotonics, bioelectronics and biosensors; geophysics — remote sensing, communications, space weather hazards and geolocation; metamaterials — sub-wavelength focusing lenses, electromagnetic cloaks and continuously scanning leaky-wave antennas; optics — diffractive optical elements, photonic bandgap structures, photonic crystal waveguides and ring-resonator devices; plasmonics — plasmonic waveguides and antennas; and quantum applications — quantum devices and quantum radar. This Primer summarizes the main features of the FDTD method, along with key extensions that enable accurate solutions to be obtained for different research questions. Additionally, hardware considerations are discussed, plus examples of how to extract magnitude and phase data, Brillouin diagrams and scattering parameters from the output of an FDTD model. The Primer ends with a discussion of ongoing challenges and opportunities to further enhance the FDTD method for current and future applications. 

Space weather can affect the Earth over time spans of hours and days. However, time-stepping increments for FDTD models are typically on the order of a fraction of a second. This paper introduces a means of increasing the time stepping increment’s upper limit by artificially slowing down the speed of light. Numerically slowing down the speed of light is achieved by appropriately modifying the permittivity, permeability, and conductivity values in the model. Proof-of-concept results are provided to show that the method works well for homogeneous media. 

We present images obtained with LABOCA on the APEX telescope of a sample of 22 galaxies selected via their red Herschel SPIRE 250-, 350- and $500\textrm{-}\mu\textrm{m}$ colors. We aim to see if these luminous, rare and distant galaxies are signposting dense regions in the early Universe. Our $870\textrm{-}\mu\textrm{m}$ survey covers an area of $\approx0.8\,\textrm{deg}^2$ down to an average r.m.s. of $3.9\,\textrm{mJy beam}^{-1}$, with our five deepest maps going $\approx2\times$ deeper still. We catalog 86 DSFGs around our 'signposts', detected above a significance of $3.5\sigma$. This implies a $100\pm30\%$ over-density of $S_{870}>8.5\,\textrm{mJy}$ DSFGs, excluding our signposts, when comparing our number counts to those in 'blank fields'. Thus, we are $99.93\%$ confident that our signposts are pinpointing over-dense regions in the Universe, and $\approx95\%$ confident that these regions are over-dense by a factor of at least $\ge1.5\times$. Using template SEDs and SPIRE/LABOCA photometry we derive a median photometric redshift of $z=3.2\pm0.2$ for our signposts, with an interquartile range of $z=2.8\textrm{-}3.6$. We constrain the DSFGs likely responsible for this over-density to within $|\Delta z|\le0.65$ of their respective signposts. These 'associated' DSFGs are radially distributed within $1.6\pm0.5\,\textrm{Mpc}$ of their signposts, have median SFRs of $\approx(1.0\pm0.2)\times10^3\,M_{\odot}\,\textrm{yr}^{-1}$ (for a Salpeter stellar IMF) and median gas reservoirs of $\sim1.7\times10^{11}\,M_{\odot}$. These candidate proto-clusters have average total SFRs of at least $\approx (2.3\pm0.5)\times10^3\,M_{\odot}\,\textrm{yr}^{-1}$ and space densities of $\sim9\times10^{-7}\,\textrm{Mpc}^{-3}$, consistent with the idea that their constituents may evolve to become massive ETGs in the centers of the rich galaxy clusters we see today.