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Compact Cylindrical Green Function (CCGF)

Preface by Tohline

Cohl & Tohline (1999) present an expression for the Newtonian gravitational potential in terms of a Compact Cylindrical Green's Function expansion. Over a professional career that dates back to 1976, this has turned out to be one of my most oft-cited research publications and certainly has proven to be the publication with the most citations from research groups outside of the astrophysics community. A sample of citations from outside the field of astronomy is presented, below. Howard Cohl deserves full credit for the important discovery presented in this paper; I simply tagged along as his physics doctoral dissertation advisor and harshest skeptic.

Whitworth's (1981) Isothermal Free-Energy Surface
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Sample Citations from Fields Outside of Astronomy

Journal of Quantitative Spectroscopy and Radiative Transfer

Journal of Computational Physics

Journal of Physics A:   Mathematical and Theoretical

Physical Review B

  • [2014] Spin and impurity effects on flux-periodic oscillations in core-shell nanowires, by T. O. Rosdahl, A. Manolescu, & V. Gudmundsson, Phys. Rev. B 90, 035421 — The key reference to CCGF appears in the paragraph associated with their equation (30); the authors state that numerical evaluation of the relevant set of Legendre functions was carried out using a code provided in J. Segura & A. Gil, Comput. Phys. Commun. 124, 104, (2000)
  • [2011] Transverse domain wall propagation in modulated cylindrical nanostructure and possible geometric control, by S. Allende, & R. Arias, Phys. Rev. B 83, 174452
  • [2005] Ground-state densities and pair correlation functions in parabolic quantum dots, by M. Gattobigio, P. Capuzzi, M. Polini, R. Asgari, & M. P. Tosi, Phys. Rev. B 72, 045306

Physical Review C

  • [2010] Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase approximation, by C. Losa, A. Pastore, T. Døssing, E. Vigezzi, & R. A. Broglia, Phys. Rev. C 81, 064307

Physical Review D

Journal of the Mechanics and Physics of Solids

Journal of Applied Physics

IEEE Transactions on Microwave Theory and Techniques

IEEE Transactions on Magnetics

  • [2015] Field distribution around surface cracks in metallic cylindrical structures excited by high-frequency current-carrying coils of arbitrary shape, by A. Akbari-Khezri, S. H. H. Sadeghi, & R. Moini, IEEE Transactions on Magnetics, Volume 51, Issue 2
  • [2013] Optimal Configuration for Electromagnets and Coils in Magnetic Actuators, by S. Afshar, M. B. Khamesee, & A. Khajepour, IEEE Transactions on Magnetics, Volume 49, Issue 4 — Relevant to "… the development of medical instrumentation …"
  • [2007] Computation of the three-dimensional magnetic field from solid permanent-magnet bipolar cylinders by employing toroidal harmonics, by J. P. Selvaggi, S. Salon, & O.-Mun Kwon, IEEE Transactions on Magnetics, Volume 43, Issue 10 — Relevant to "… the development of medical instrumentation …"

IEEE Transactions on Antennas and Propagation

New Journal of Physics

  • [2008] Calculation of electrostatic fields using quasi-Green's functions: application to the hybrid Penning trap, by J. Veruú, S. Kreim, K. Blaum, H. Kracke, W. Quint, S. Ulmer, & J. Walz, New Journal of Physics, Volume 10, October

Journal of Molecular Physics

Plasma Physics …

Physics of Plasmas

Plasma Physics and Controlled Fusion

Plasma Physics Reports

Selected Citations from Astrophysicists

  1. (2019) A Fast Poisson Solver of Second-order Accuracy for Isolated Systems in Three-dimensional Cartesian and Cylindrical Coordinates, by S. Moon, W.-T. Kim & E. C. Ostriker, ApJS, Volume 241, Issue 2, 24
  2. (2019) AGAMA: action-based galaxy modelling architecture, by E. Vasiliev, MNRAS, Volume 482, Issue 2, p. 1525 - 1544
  3. (2016) Equilibrium sequences and gravitational instability of rotating isothermal rings, by W.-T. Kim & S. Moon, ApJ, Volume 829, Number 1
  4. (2016) Zonal toroidal harmonic expansions of external gravitational fields for ring-like objects, by T. Fukushima, The Astronomical Journal, Volume 152, Number 2
  5. (2016) Vector potentials for the gravitational interaction of extended bodies and laminas with analytical solutions for two disks, by J. T. Conway, Celestial Mechanics and Dynamical Astronomy, Volume 125, Issue 2, pp. 161-194
  6. (2015) Applying Schwarzschild's orbit superposition method to barred or non-barred disc galaxies, by E. Vasiliev & E. Athanassoula, MNRAS, Volume 450, Issue 3
  7. (2012) A substitute for the singular Green kernel in the Newtonian potential of celestial bodies, by J.-M. Ouré & A. Dieckmann, Astronomy & Astrophysics, Volume 541, A130
  8. (2007) The Newtonian force experienced by a point mass near a finite cylindrical source, by J. P. Selvaggi, Sheppard Salon & M. V. K. Chari, Classical and Quantum Gravity, Volume 25, Number 1
  9. (2006) Self-consistent response of a galactic disc to vertical perturbations, by K. Saha & C. J. Jog, MNRAS, Volume 367, Issue 3
  10. (2005) Accurate numerical potential and field in razor-thin, axisymmetric disks, by J.-M. Ouré, ApJ, Volume 624, Number 1
  11. (2004) Evolution of self-gravitating magnetized disks. I. Axisymmetric simulations, by S. Forming, S. A. Balbus, & J.-P. De Villers, ApJ, Volume 616, Number 1

See Also

  • John Thomas Conway has authored many articles — appearing in journals covering a wide range of disciplines — whose research topics overlap, if not incorporate, the Cohl & Tohline (1999) work.

Whitworth's (1981) Isothermal Free-Energy Surface

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