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In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the socalled generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.
wave equation  spherically symmetric spacetimes  lie symmetries  roots  optimal systems  invariant solutions  n/a  Noether symmetry approach  FLRW spacetime  action integral  variational principle  first integral  modified theories of gravity  GaussBonnet cosmology  Noether’s theorem  action integral  generalized symmetry  first integral  invariant  nonlocal transformation  boundary term  conservation laws  analytic mechanics  Noether’s theorem  generalized symmetry  energymomentum tensor  Lagrange anchor  viscoelasticity  KelvinVoigt equation  Lie symmetries  optimal system  groupinvariant solutions  conservation laws  multiplier method  continuous symmetry  symmetry reduction  integrable nonlocal partial differential equations  symmetries  conservation laws  Noether operator identity  quasiNoether systems  quasiLagrangians  Lie symmetry  conservation law  double dispersion equation  Boussinesq equation  systems of ODEs  Noether operators  Noether symmetries  first integrals  partial differential equations  approximate symmetry and solutions
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This Special Issue covers a wide range of topics from fundamental studies to applications of ionized gases. It is dedicated to four topics of interest: 1. ATOMIC COLLISION PROCESSES (electron and photon interactions with atomic particles, heavy particle collisions, swarms, and transport phenomena); 2. PARTICLE AND LASER BEAM INTERACTION WITH SOLIDS (atomic collisions in solids, sputtering and deposition, and laser and plasma interactions with surfaces); 3. LOW TEMPERATURE PLASMAS (plasma spectroscopy and other diagnostic methods, gas discharges, and plasma applications and devices); 4. GENERAL PLASMAS (fusion plasmas, astrophysical plasmas, and collective phenomena). This Special Issue of Atoms will highlight the need for continued research on ionized gas physics in different topics ranging from fundamental studies to applications, and will review current investigations.
strongfield physics  attoscience  bicircular field  highorder harmonic generation  abovethreshold ionization  spinpolarized electrons  capacitivelycoupled discharge  oxygen  particleincell/Monte Carlo collision  electron heating  secondary electron emission  Large Helical Device (LHD)  deuterium experiment  ion temperature of 10 keV  plasma research  spectroscopic study  dispersion interferometer  modified theories of gravity  methods: analytical  methods: numerical  galaxies: elliptical  galaxies: fundamental parameters  nonequilibrium  collisions  radiation  planetary atmospheric entry  laser matter interaction  laserinduced breakdown  plasma  spectroscopy  streak camera  plasma  spectral lines  Stark broadening  oxygen  silicon  spectroscopy  gas discharges  plasma applications  databases  virtual observatory  cross sections  rate coefficients  runway electron  plasma current  fusion plasma  tokamak  glow discharge  argon  nitrogen admixture  discharge voltage  diffuse discharge  constricted discharge  electrical theory of DBDs  QVplot  instantaneous power  rainbow scattering  positron channeling effect  timedependent Schrödinger equation  chiral single wall carbon nanotubes  black hole physics  cosmology  quasar spectroscopy  cosmological parameters  ionized gas  broad line region  Rydberg atoms  dynamic instability  control of atomic states  Förster resonance  plasma spectroscopy  Stark broadening  plasma diagnostics  line shape modeling  ZeemanDoppler broadening  Balmer line series  radiative recombination  photoacoustic  photothermal  inverse problem  thermal memory  minimum volume cell  neural networks  thermal diffusivity  conductivity  linear coefficient of thermal extension  AGN  black holes  gravitational waves  binary black holes  quasars  photodetachment  magnetically confined fusion  neutral beam injection  plasma heating  optical cavity amplification  lowenergy electrons  electron–molecule interactions  astrochemistry  laboratory plasma  astrophysical plasma  fusion plasma  lasers  stars  extragalactic objects  spectra  spectroscopy  scaling laws
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