Publications

Publications Listed in Chronological Order

  1. "Viscous damping of nonlinear magnetoacoustic waves" (1975), Astrophysics and Space Science 36, 479-487.
  2. "Steady magnetogravity flow" (1975), Quarterly Journal of Mechanics and Applied Mathematics 28, 397-103.
  3. "Alfven wave reflection at a density transition region" (1976), Journal of Physics A: Mathematical and General 9, L193-L194.
  4. "Maximum growth rates of magnetoatmospheric instabilities" (1977), Astrophysics and Space Science 47, L5-L7.
  5. "On the occurrence of critical levels in solar magnetohydrodynamics" (1977), Solar Physics 52, 293-307.
  6. "Hydrodynamic instability of convectively unstable atmospheres in shear flow" (1977), Astrophysics and Space Science, 50, 493-514.
  7. "Solar magnetoatmospheric waves -a simplified mathematical treatment". (1977) Astronomy and Astrophysics 60, 171-179.
  8. "Solutions of the inhomogeneous acoustic-gravity wave equation". (1977), Journal of Physics A: Mathematical and General, 10, L169-L173.
  9. "Stability of aligned magnetoatmospheric flow" (1978), J. Plasma Phys. 19, 77-86.
  10. "Magnetohydrodynamic wave energy flux in a stratified compressible atmosphere with shear" (1978) Q.J. Mech. Appl. Math. 31 77-98.
  11. "Evolution in space and time of resonant wave triads I. the pump-wave approximation". (With A.D.D. Craik) (1978) Proc. R. Soc. Lond. . 363, 243-255.
  12. "Explosive resonant wave interactions in a three-layer fluid flow". (With A.D.D. Craik) (1979) J. Fluid Mech. 92, 15-33.
  13. "Maximum growth rate of magnetoatmospheric instabilities. II: Hilbert space approach". (1980 J. Phys. A. Math. & Gen. 13, 373-378.
  14. "Some wave reflection problems in solar physics". (1981) The Irish Astronomical Journal, 14, 133-137.
  15. "Eigenvalue bounds in magnetoatmospheric shear flow". (1980) J. Phys. A. Math. & Gen. 13, 3325-3338.
  16. "Some thoughts on the nature of mathematical statements". (1981) I.M.A. Bulletin, 17, 21-25.
  17. "Asymptotic solutions and spectral theory of linear wave equations". (1982) Physics Reports 8 No. 5, 217-316.
  18. "Mechanical wave energy flux in magnetoatmospheres: discrete and continuous spectra". (1981) Astrophys. Sp. Sci. 78, 293 347.Addendum to the above paper (#18): (1981) Astrophys. Sp. Sci 78, 38-350.
  19. "Note on sigma-stability in hydromagnetics". (1982) Astrophys. Sp. Sci. 82, 115-121.
  20. "Complex eigenvalue bounds in magnetoatmospheric shear flow". (1983) (with P.S. Cally), Geophys.Astrophys. Fluid Dyn. 23, 57-67.
  21. "Mathematical methods in linear hydrodynamic stability theory". (1982) Int. J. Math. Ed. Sci.Tech 13, 405-422.
  22. "On a class of atmospheres occurring in stellar hydrodynamic theory". (1982) Z.A.M.P. 33, 473-486.
  23. "On photospheric and chromospheric penumbral waves". (With P.S Cally) (1983) Sol. Phys., 85, 97-111.
  24. "Green's functions, complex eigenvalues and the initial-value problem". (1984) I.M.A. Bulletin, 20, 171-176.
  25. "Some mathematical aspects of wave motion". (1984) Int. Jnl. Math. Ed Sci. Tech., 15, 719-725.
  26. "On complementary levels of description in applied mathematics" (1984) Int. Jnl. Math. Ed.Sci. Tech., 15, 672-673.
  27. "The critical layers and other singular regions in ideal hydrodynamics and MHD". (1984) Astrophys. Sp. Sci., 105, 401-412.
  28. "Magnetoatmospheric waves from a localized source". (With J.H. Thomas). (1984) Astrophys. Sp. Sci., 106, 125-150.
  29. "On the spectrum of some singular equations in MHD". (1985) Astrophys. Sp. Sci., 114, 249-258.
  30. "Critical layer singularities and complex eigenvalues in some differential equations of mathematical physics". (1986) Physics Reports, 142, 263-356.
  31. "A simplified mathematical model of tumor growth". (1986) Mathematical Biosciences., 81, 229-244.
  32. "Spectral theory and stability in astrophysics. I. Ideal MHD". (1986) Astrophys. Sp. Sci. 127, 163-178.
  33. "Spectral theory and stability in astrophysics. II. Rotating stars". (1986) Astrophys. Sp. Sci., 127, 309-320.
  34. "A linear scattering problem in magnetohydrodynamics: transmission resonances in a magnetic slab". (1987) Astrophys. Sp. Sci. 133 317-337
  35. "A mathematical model of tumor growth: II. Effects of geometry and spatial non-uniformity on stability". (1987) Math. Biosci., 86, 183-211.
  36. "A mathematical model of tumor growth: III. Comparison with experiment". (1987) Math.Biosci., 86, 213-227.
  37. On complementary levels or description in applied mathematics. II. Mathematical models in cancer biology". 1988 Int. J. Math. Ed. Sci. Tech., 19, 519-535.
  38. "On Liouville's equation and its occurrence in mathematical astrophysics". (1988) Int. J.Math. Ed. Sci. Tech., 19, 881-890.
  39. "Complementary levels of description in applied mathematics. III. Equilibrium models of cities". (1988) Math. Comput. Modelling, 10, 321-339.
  40. "Mathematical model of tumor growth by diffusion". (1988) Proceedings of the 6th International Conference on Mathematical Modelling, St. Louis, 1987. Published in Math.Comput. Modelling, 11, 455-456.
  41. "Integral Invariants and Complex Eigenvalue Bounds". Applied Math. Lett. ( 1988) 1, 203-206.
  42. "A nonlinear eigenvalue problem in astrophysical magnetohydrodynamics: some properties of the spectrum". J. Math. Phys. ( 1989) 30, 744-756.
  43. "Some results on the spectrum of a magnetoatmospheric wave operator". Applied Math. Lett. (1989)2, 11-14.
  44. "Note on a class of nonlinear time-independent diffusion equations". (With S.A. Maggelakis), Applied Math. Lett. (1989) 2, 141-145.
  45. "A Mathematical Model of Tumor Growth. IV. Effects of a Necrotic Core" (With S.A. Maggelakis), Mathematical Biosci . 97 (1989) 121-136.
  46. "Note on a Diffusion Model of Tissue Growth", (with S.A. Maggelakis), Applied Math. Lett.3 (1990) 27-31.
  47. "A Mathematical Model of Preascular Growth of a Spherical Carcinoma" (with S.A. Maggelakis), Math. Comput. Modelling 1990 5 13, 2338.
  48. "Diffusion Regulated Growth Characteristics of A Prevascular Carcinoma" (with S.A. Maggelakis), Bull. Math. Biology. 1990, 52 549-582
  49. "An Initial-Value Problem for Magnetoatmospheric Waves. I. Theory". Wave Motion 1990, 12 385-399.
  50. "A Generalization of a Solvable Model in Population Dynamics", (with G. DeRise), J. Phys.:Math. & Gen. (1990), L727-L731.
  51. "Diffusion Models of Prevascular and Vascular Tumor Growth: A Review". Lecture Notes inPure and Applied Mathematics, 1991, Vol.131, Chapter 41, p.625-642 (Marcel Dekker, Inc.).
  52. "Self-Activation and Inhibition: Simple Nonlinear Model". Appl. Math. Letters, 4, 2 (1991), 85-87.
  53. "Self-Activation and Inhibition: The Effect of a Zero-Flux Boundary", Appl. Math. Letters, 4, 3 (1991) 45-47.
  54. "Activator-Inhibitor Control of Tissue Growth". SIAM Review, 33, (1991), 462-466
  55. "Solution Uniqueness and Stability Criteria for a Model of Growth Factor Production", Appl.Math. Letters, 5 (1992) 89-92.
  56. "The Dynamics of Growth Factor-Modified Immune Response to Cancer Growth: One-Dimensional Models", Mathematical and Computer Modelling, 17 (1993), 83-106.
  57. "The Scattering Potential for a Polytrope of Degree n=5". Appl. Math. Letters, 6, #4 (1993) 9-1 1 .
  58. "Scattering Parameters for an Epstein Profile in a Half-Space", Appl. Math. Letters, 6, #4, (1993), 13-15.
  59. "Propagation of Magnetoacoustic-Gravity Waves in a Horizontally Stratified Medium: IV. Kinematics". Astrophys. Sp. Sci. 202 (1993), 259-271. (With I. McKaig).
  60. "Equilibrium Model of a Vascularized Spherical Carcinoma with Central Necrosis: Some Properties of the Solution". J. Math. Biol. 31 (1993), 735-745. (With R. Noren).
  61. "Non-Radial Stellar Oscillations from the Perspective of Potential Scattering Theory: Theoretical Aspects." Astrophys. Sp. Sci. 220 (1994), 179-233.
  62. "Mathematical Model of Cycle-Specific Chemotherapy" (With Carl Panetta). Mathematicaland Computer Modelling 22 (1995), 67-82.
  63. "A Simple Mathematical Model and Alternative Paradigm for Certain Chemotherapeutic Regimens." (With Carl Panetta). Mathematical and Computer Modelling, 22 (1995), 49-60.
  64. "Educated Guesses". Quantum – A Journal of Mathematics and Science. Sept/Oct. 1995.
  65. "The Effects of Vascularization on Lymphocyte-Tumor Cell Dynamics: Qualitative Features", Math. Comp. Modelling 23 (1996), 1-10.
  66. "General Aspects of Modeling Tumor Growth and Immune Response", Chapter 2 in the book cited below(Adam & Bellomo, Eds.)
  67. “Mathematical Models of Spheroid Growth and Catastrophe-Theoretic Description of Rapid Metastatic Growth/Remission”, Invasion & Metastasis, 16 (1996), 247-267.
  68. “N-Space, Dimensional Interface Phenomena and an Adventure in Flatland”, Hyperspace, 5(1996), 10-23. 
  69. “Scattering from Stellar Acoustic-Gravity Potentials: II. Phase Shifts via the First Born Approximation”, (with Iain McKaig), Appl. Math. Lett., 10 (1997), 39-42.
  70. “Limiting Spheroid Size as a Function of Growth Factor Source Location”, (with Kim Ward), Appl. Math. Lett., 10 (1997), 43-46.
  71. “Post-Surgical Passive Response of Local Environment to Primary Tumor Removal”, (with Carryn Bellomo), Math. Comp. Modelling, 25 (1997), 7-17.
  72. “The Pekeris Waveguide: A Case Study in Classical Applied Mathematics”, Math. Meth. Mod. App. Sci., 8 (1998), 157-186.
  73. “ (A Note on)2 the Shape of the Erythrocyte”, Math. Comp. Modeling, 27 (1998), 73-77.
  74. “Post-Surgical Passive Response of Local Environment to Primary Tumor Removal. II. Heterogeneous Environment”, (with Carryn Bellomo), Math. Meth. Mod. Appl. Sci. 9 (1999), 617-626.
  75. “The Mathematical Modeling of Cancer: A Review”, (with Carl Panetta and Mark Chaplain), Conference Proceedings, 281-310, 1999,Vanderbilt University Press.
  76. “A Simplified Model of Wound Healing, with particular reference to the Critical Size Defect: One-dimensional model.” Math. Comp. Mod. 30 (1999), 23-32.
  77. “A Simplified Model of Wound Healing, with particular reference to the Critical Size Defect: Two-dimensional model.” Math. Comp. Mod. 30 (1999), 47-60. (with J.S. Arnold)
  78. “A mathematical model of wound healing in bone.” In the Proceedings of the 2000 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS ’00), p.97-103, Las Vegas, June 2000.
  79. “Nutrient concentration in and around a vascularized tumor with a necrotic core.” (With Carryn Bellomo). In the Proceedings of the 2000 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS ’00), p.105-110, Las Vegas, June 2000. 
  80. “The Mathematical Physics of Rainbows and Glories”. Physics Reports 356 (Nos. 4-5) (2002), 229-366.
  81. “Healing times for circular wounds on plane and spherical bone surfaces”. Applied Mathematics Letters, 15 (2002), 55-58.
  82. “The effect of surface curvature on wound healing in bone”. Applied Mathematics Letters, 15 (2002), 59-62.
  83. “The effect of surface curvature on wound healing in bone: II. The critical size defect”. Mathematical and Computer Modelling, 35 (2002), 085-1094.
  84. “Like a bridge over colored water: a mathematical review of The Rainbow Bridge: Rainbows in Art, Myth and Science” by R. Lee and A. Fraser, Notices of the AMS, Dec. 2002, 49 (No. 11), 1360-1371.
  85. “Mathematical Models of Tumors and Their Remote Metastases”; C. Bellomo, J.A. Adam. In Computational Methods in Biophysics, Biomaterials, Biotechnology and Medical Systems: Algorithm Development, Mathematical Analysis and Diagnostics, published by Kluwer Press, 2002.
  86. “Mathematical models of tumor growth: from empirical description to biologicalmechanism”, in vol. 537 of Advances in Experimental Medicine and Biology, entitled Mathematical Modeling in Nutrition and the Health Sciences (Kluwer Academic/Plenum Publishers, 2003).
  87. “Inside mathematical modeling: building models in the context of wound healing in bone “ in Discrete and Continuous Dynamical Systems, 4 (2004), 1-24.
  88. "Flowers of Ice - Beauty, Symmetry, and Complexity: A Review of The Snowflake: Winter's Secret Beauty." Notices of the AmericanMathematical Society, 52, #4, 402-416 (2005).
  89. "A simplified model for growth factor induced healing of circular wounds" Mathematical & Computer Modeling, 44(2006), 887-898. (Co-authors Fred VErmolen and Esther Van Baaren.)
  90. "On Rainbows from Inhomogeneous Transparent Spheres: A Ray-Theoretic Approach.” (With Philip Laven), Applied Optics, 46 (2007), 922-929.
  91. F.J. Vermolen, W.G. van Rossum, E. Javierre and J.A. Adam. Modeling of self-healing of skin tissue. In: Self-healing materials: an alternative approach to 20 centuries of materials science, Springer, Dordrecht, the Netherlands, 2007.
  92. F.J. Vermolen and J.A. Adam. A finite element model for epidermal wound healing involving angiogenesis. Proceedings of the ICCS conference, Springer-Verlag, Beijing, China, 2007. Proceedings part I, Edited by Y. Shi, G.D. van Albada, J. Dongarra and P.M.A. Sloot, Springer-Verlag, Berlin-Heidelberg, 2007
  93. F.J. Vermolen, W.G. van Rossum, E. Javierre and J.A. Adam. A numerical model for epidermal wound healing. Proceedings of the ECCOMAS conference on Coupled Problems, Ibiza, Spain, 2007.
  94. Rainbows, Geometrical Optics, and a Generalization of a result of Huygens”, Applied Optics, 47, H11 - H13.
  95. “A Two-Population Insurgency In Colombia: Quasi-Predator-Prey Models -- A Trend Towards Simplicity” (with John A. Sokolowski and Catherine M. Banks); Mathematical and Computer Modelling, 49 (2009),p. 1115–1126.”
  96. A review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Manahan, MIT Press, Cambridge, MA., in The American Journal of Physics, 78 (2010), 1230-1232.
  97. "Blood Vessel Branching: Going Beyond the Standard Calculus Problem", Mathematics Magazine, 84 (2011), 196 – 207.
  98. "Zero-order bows in radially inhomogeneous spheres: direct and inverse problems." Applied Optics, 50 (2011) F50 - F59.
  99. "Putting the X in Biology: A Review of The Mathematics of Life by Ian Stewart." Notices of the American Mathematical Society, 58 (2011), 1572-1578.
  100. A review of A Wealth of Numbers: An Anthology of 500 years of Popular Mathematics Writing, edited by Benjamin Wardhaugh. American Journal of Physics (August 2012) volume 80(8), 745-746.
  101. 'Rainbows' in homogeneous and radially inhomogeneous spheres: connections with ray, wave and potential scattering theory. Mathematical & Statistical Research with Applications to Physical & Life Sciences, Engineering & Technology. Springer Proceedings in Mathematics and Statistics, vol. 37, 2013, Ed. Bourama Toni.
  102. "Electromagnetic and Potential Scattering from a Radially Inhomogeneous Sphere" 2013; co-author: Umaporn Nuntaplook, http://arxiv.org/abs/1307.1647
  103. "Scattering of electromagnetic plane waves in radially inhomogeneous media: ray theory, exact solutions and connections with potential scattering theory”, Chapter 3 in Volume 9 of Light Scattering Reviews, Editor, Alexander Kokhanovsky. Springer, 2014.
  104. "Scalar wave scattering by two-layer radial inhomogeneities” (with U. Nuntaplook) Applied Mathematics E-Notes, 14 (2014), 185-192.
  105. "Scattering of a Plane Electromagnetic Wave by a Generalized Luneburg Sphere. Part 1: Ray Scattering” (with James Lock and Philip Laven). Journal of Quantitative Spectroscopy and Radiative Transfer, 162 (2015), 154-163.
  106. “Scattering of a Plane Electromagnetic Wave by a Generalized Luneburg Sphere. Part 2: Wave Scattering and Time-Domain Scattering” (with James Lock and Philip Laven). Journal of Quantitative Spectroscopy and Radiative Transfer, 162 (2015), 164-174.
  107. “Ray- and wave-theoretic problems in radially inhomogeneous media” (with M. Pohrivchak & U. Nuntaplook): invited chapter for Volume 11 of Light Scattering Reviews, Editor, Alexander Kokhanovsky. Springer, 2016, 339 – 361.
  108. “Scattering of Plane Electromagnetic Waves by Radially Inhomogeneous Spheres: Asymptotics and Special Functions” (with M. Pohrivchak & U. Nuntaplook): invited chapter for Mathematical & Statistical Research with Applications to Physical & Life Sciences, Engineering & Technology, Springer Proceedings in Mathematics and Statistics, vol. 39, 2016, Ed. Bourama Toni, (Chapter 17, p. 383 – 417).
  109. “Evaluation of Ray-Path Integrals in Geometrical Optics”, International Journal of Applied and Experimental Mathematics, 1, 108 (2016) (7 pages, With M. Pohrivchak).
  110. “Mountain Shadows Revisited”. Applied Optics 56(19), (2017) G26 – G35.
  111. “An Example of Nature’s Mathematics: The Rainbow.” Submitted to The Virginia Mathematics Teacher.
  112. “Morphology-dependent resonances in two concentric spheres with variable refractive index in the outer layer: analytic solutions.” (With U. Nuntaplook) Submitted to Applied Mathematics E-Notes.