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.

Sample Citations from Fields Outside of Astronomy

Journal of Computational Physics

[2018] An integral equation-based numerical solver for Taylor states in toroidal geometries, by M. O'Neil & A. J. Cerfon, J. Comp. Phys., Volume 359, pp. 263-282
[2016] Determination of normalized electric eigenfields in microwave cavities with sharp edges, by J. Helsing & A. Karlsson, J. Comp. Phys., Volume 304, pp. 465-486
[2014] An explicit kernel-split panel-based Nyström scheme for integral equations on axially symmetric surfaces, by J. Helsing & A. Karlsson, J. Comp. Phys., Volume 272, pp. 686-703

Journal of Physics A: Mathematical and Theoretical

[2007] A method for studying electron-density-based dynamics of many-electron systems in scaled cylindrical coordinates, by A. Poddar & B. M. Deb, Journal of Physics A: Mathematical and Theoretical, Volume 40, pp. Number 22

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

Journal of the Mechanics and Physics of Solids

[2016] Cyclic density functional theory: A route to the first principles simulation of bending in nanostructures, by A. S. Banerjee & P. Suryanarayana, Journal of the Mechanics and Physics of Solids 96, pp. 605-631

Journal of Applied Physics

[2013] Reflectance modulation by free-carrier exciton screening in semiconducting nanotubes, by F. Pinto, Journal of Applied Physics, Volume 114, 024310
[2010] Magnetoexcitons in electron-hole bilayer nanotubes made of rolled-up type-II band aligned quantum wells, by M. Bagheri, Journal of Applied Physics, Volume 107, 114305

IEEE Transactions on Microwave Theory and Techniques

[2015] Determination of Normalized Magnetic Eigenfields in Microwave Cavities, by J. Helsing & A. Karlsson, IEEE Transactions on Microwave Theory and Techniques, Volume 63, Issue 5 — Relevant to "… the development of medical instrumentation …"

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

^†[2005] New exact solution procedure for the near fields of the general thin circular loop antenna, by J. T. Conway, IEEE Transactions on Antennas and Propagation, Volume 53, Issue 1

Physics of Plasmas

[2018] Reaction of the toroidal resistive wall on the magnetic field variations in tokamak-like systems, by V. D. Pustovitov, Physics of Plasmas, 25, 062510
[2008] General formulation of the resistive wall mode coupling equations, by V. D. Pustovitov, Physics of Plasmas, 15, 072501 — Relevant to "… toroidal plasmas …"

Plasmas Physics and Controlled Fusion

[2008] Decoupling in the problem of tokamak plasma response to asymmetric magnetic perturbations, by V. D. Pustovitov, Plasma Physics and Controlled Fusion, Volume 50, Number 10

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

[2005] Scaling in complex systems: analytical theory of charged pores, by A. Enriquez & L. Blum, J. Molecular Physics, Volume 103, pp. 3201-3208

Selected Citations from Astrophysicists

(2019) AGAMA: action-based galaxy modelling architecture, by E. Vasiliev, MNRAS, Volume 482, Issue 2, p. 1525 - 1544
(2016) Equilibrium sequences and gravitational instability of rotating isothermal rings, by W.-T. Kim & S. Moon, ApJ, Volume 829, Number 1
(2016) Zonal toroidal harmonic expansions of external gravitational fields for ring-like objects, by T. Fukushima, The Astronomical Journal, Volume 152, Number 2
^†(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
(2015) Applying Schwarzschild's orbit superposition method to barred or non-barred disc galaxies, by E. Vasiliev & E. Athanassoula, MNRAS, Volume 450, Issue 3
(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
(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
(2006) Self-consistent response of a galactic disc to vertical perturbations, by K. Saha & C. J. Jog, MNRAS, Volume 367, Issue 3
(2005) Accurate numerical potential and field in razor-thin, axisymmetric disks, by J.-M. Ouré, ApJ, Volume 624, Number 1
(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

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