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Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics.

cubic-quartic Schrödinger equation --- cubic-quartic resonant Schrödinger equation --- parabolic law --- wave field transformation --- finite difference method --- Cole–Cole model --- Monte Carlo simulations --- percolation --- conductivity --- carbon nanotubes composite --- optical parametric amplification --- non-linear wave mixing --- micro-resonator --- optimization --- MRI system --- birdcage coil --- birdcage configurations --- coil capacitance --- analytical solution --- equivalent circuit modelling --- T-matrix theory --- 3D-EM simulation --- small volume RF coil --- method of auxiliary sources (MAS) --- electromagnetic scattering --- wedge --- numerical methods --- accuracy --- coil gun --- reluctance --- electromagnetic launcher --- mechatronics --- electronics --- mechanics --- simulation --- RoboCup --- magnetic field strength --- magnetic flux density --- magnetic potential --- current density --- power transmission line --- electromagnetic modelling --- integral formulation --- skin effect --- thin shell approach --- mutual inductance --- finite element method --- partial element equivalent circuit method --- magnetite nanoparticles --- Mie scattering theory --- near infrared laser --- photothermal therapy --- bioheat transfer --- diffusion approximation --- Arrhenius integral --- breast cancer --- air-core pulsed alternator --- electromagnetic rail launcher --- coupled analysis --- computational electromagnetics --- integral formulations --- n/a --- cubic-quartic Schrödinger equation --- cubic-quartic resonant Schrödinger equation --- Cole-Cole model

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Precipitation is a well-recognized pillar in global water and energy balances. An accurate and timely understanding of its characteristics at the global, regional, and local scales is indispensable for a clearer understanding of the mechanisms underlying the Earth’s atmosphere–ocean complex system. Precipitation is one of the elements that is documented to be greatly affected by climate change. In its various forms, precipitation comprises a primary source of freshwater, which is vital for the sustainability of almost all human activities. Its socio-economic significance is fundamental in managing this natural resource effectively, in applications ranging from irrigation to industrial and household usage. Remote sensing of precipitation is pursued through a broad spectrum of continuously enriched and upgraded instrumentation, embracing sensors which can be ground-based (e.g., weather radars), satellite-borne (e.g., passive or active space-borne sensors), underwater (e.g., hydrophones), aerial, or ship-borne.

satellite radiance --- WRF-Hydro --- meteorological radar --- QPE --- microstructure of rain --- TMPA --- evaluation --- precipitation --- volume matching --- CFSR --- GMI --- terminal velocity --- TRMM-TMPA --- surface rain intensity --- retrieval algorithm --- rain gauges --- tropical cyclone --- CMORPH --- T-Matrix --- Global Precipitation Measurement (GPM) --- statistical evaluation --- vertical air velocity --- heavy rainfall prediction --- GPM IMERG v5 --- Tianshan Mountains --- Red River Basin --- precipitation retrieval --- satellite precipitation --- PERSIANN-CCS --- validation network --- PEMW --- satellite rainfall estimate --- high latitude --- Cyprus --- GPM --- wet deposition --- CloudSat --- thundercloud --- GPS --- satellite remote sensing --- assessment --- numerical weather prediction --- mineral dust --- complex terrain --- mesoscale precipitation patterns --- GNSS meteorology --- lumped models --- satellites --- Southern China --- error analysis --- topography --- cloud scavenging --- radar reflectivity–rain rate relationship --- CHAOS --- RADOLAN --- hydrometeor classification --- TRMM --- thunderstorm --- CHIRPS --- satellite precipitation retrieval --- GPM/IMERG --- GSMaP --- bias correction --- Precise Point Positioning --- Mainland China --- supercooled droplets detection --- SEID --- Saharan dust transportation --- Huaihe River basin --- GPM Microwave Imager --- satellite --- TMPA 3B42RT --- forecast model --- quality indexes --- SEVIRI --- radiometer --- triple collocation --- satellite precipitation product --- Mandra --- synoptic weather types --- drop size distribution (DSD) --- Amazon Basin --- weather radar --- X-band radar --- downscaling --- precipitation rate --- neural networks --- rain rate --- CMIP --- GPM-era IMERG --- GR models --- weather --- typhoon --- satellite rainfall retrievals --- TRMM 3B42 v7 --- validation --- low-cost receivers --- rainfall retrieval techniques --- snowfall detection --- GPM satellite --- Zenith Tropospheric Delay --- 3B42 --- hurricane Harvey --- PERSIANN_CDR --- TRMM 3B42 V7 --- snow water path retrieval --- DPR --- satellite precipitation adjustment --- Peninsular Spain --- RMAPS --- daily rainfall estimations --- streamflow simulation --- regional climate models --- Red–Thai Binh River Basin --- Ensemble Precipitation (EP) algorithm --- cloud radar --- disdrometer --- TRMM-era TMPA --- hydrometeorology --- MSG --- radar data assimilation --- dust washout process --- runoff simulations --- geostationary microwave sensors --- radar --- topographical and seasonal evaluation --- goGPS --- XPOL radar --- TMPA 3B42V7 --- telemetric rain gauge --- harmonie model --- tropical storm rainfall --- linear-scaling approach --- Milešovka observatory --- precipitable water vapor --- heavy precipitation --- hydrological simulation --- reflectivity --- Ka-band --- Tibetan Plateau --- satellite rainfall estimates --- regional rainfall regimes --- Lai Nullah --- microwave scattering --- remote sensing --- pre-processing --- rainfall rate --- MSWEP --- climatology --- VIC model --- CMORPH_CRT --- IMERG --- single frequency GNSS --- PERSIANN --- flood-inducing storm --- climate models --- Pakistan --- precipitating hydrometeor --- data assimilation --- rainfall --- kriging with external drift --- dual-polarization --- quantitative precipitation estimates --- flash flood --- Satellite Precipitation Estimates --- gridded radar precipitation --- regional rainfall sub-regimes --- polar systems --- Environmental engineering. --- Environmental monitoring. --- Biomonitoring (Ecology) --- Ecological monitoring --- Environmental quality --- Monitoring, Environmental --- Applied ecology --- Environmental engineering --- Pollution --- Environmental control --- Environmental effects --- Environmental stresses --- Engineering --- Environmental health --- Environmental protection --- Sustainable engineering --- Measurement --- Monitoring