# Publications

### Publications Listed in Chronological Order

- "Viscous damping of nonlinear magnetoacoustic waves"
*(1975), Astrophysics and Space Science 36,**479-487.* - "Steady magnetogravity flow"
*(1975)*,*Quarterly Journal of Mechanics and Applied Mathematics 28, 397-103.* - "Alfven wave reflection at a density transition region"
*(1976)*,*Journal of Physics A: Mathematical and General 9, L193-L194.* - "Maximum growth rates of magnetoatmospheric instabilities"
*(1977)*,*Astrophysics and Space Science 47, L5-L7.* - "On the occurrence of critical levels in solar magnetohydrodynamics"
*(1977), Solar Physics 52, 293-307.* - "Hydrodynamic instability of convectively unstable atmospheres in shear flow"
*(1977), Astrophysics and Space Science, 50, 493-514.* - "Solar magnetoatmospheric waves -a simplified mathematical treatment". (1977)
*Astronomy and**Astrophysics 60, 171-179.* - "Solutions of the inhomogeneous acoustic-gravity wave equation". (1977),
*Journal of Physics A: Mathematical and General*, 10, L169-L173. - "Stability of aligned magnetoatmospheric flow" (1978),
*J. Plasma Phys*. 19, 77-86. - "Magnetohydrodynamic wave energy flux in a stratified compressible atmosphere with shear" (1978)
*Q.J. Mech. Appl. Math*. 31 77-98. - "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. - "Explosive resonant wave interactions in a three-layer fluid flow". (With A.D.D. Craik) (1979)
*J. Fluid Mech*. 92, 15-33. - "Maximum growth rate of magnetoatmospheric instabilities. II: Hilbert space approach". (1980
*J. Phys. A. Math. & Gen.*13, 373-378. - "Some wave reflection problems in solar physics". (1981)
*The Irish Astronomical Journal*, 14, 133-137. - "Eigenvalue bounds in magnetoatmospheric shear flow". (1980)
*J. Phys. A. Math. & Gen*. 13, 3325-3338. - "Some thoughts on the nature of mathematical statements". (1981)
*I.M.A. Bulletin*, 17, 21-25. - "Asymptotic solutions and spectral theory of linear wave equations". (1982)
*Physics Reports*8 No. 5, 217-316. - "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. - "Note on sigma-stability in hydromagnetics". (1982)
*Astrophys. Sp. Sci*. 82, 115-121. - "Complex eigenvalue bounds in magnetoatmospheric shear flow". (1983) (with P.S. Cally),
*Geophys.Astrophys. Fluid Dyn.*23, 57-67. - "Mathematical methods in linear hydrodynamic stability theory". (1982)
*Int. J. Math. Ed. Sci.**Tech*13, 405-422. - "On a class of atmospheres occurring in stellar hydrodynamic theory". (1982)
*Z.A.M.P*. 33, 473-486. - "On photospheric and chromospheric penumbral waves". (With P.S Cally) (1983)
*Sol. Phys*., 85, 97-111. - "Green's functions, complex eigenvalues and the initial-value problem". (1984)
*I.M.A. Bulletin*, 20, 171-176. - "Some mathematical aspects of wave motion". (1984)
*Int. Jnl. Math. Ed Sci. Tech*., 15, 719-725. - "On complementary levels of description in applied mathematics" (1984)
*Int. Jnl. Math. Ed.**Sci. Tech.*, 15, 672-673. - "The critical layers and other singular regions in ideal hydrodynamics and MHD". (1984)
*Astrophys. Sp. Sci*., 105, 401-412. - "Magnetoatmospheric waves from a localized source". (With J.H. Thomas). (1984)
*Astrophys. Sp. Sci*., 106, 125-150. - "On the spectrum of some singular equations in MHD". (1985)
*Astrophys. Sp. Sci*., 114, 249-258. - "Critical layer singularities and complex eigenvalues in some differential equations of mathematical physics". (1986)
*Physics Reports*, 142, 263-356. - "A simplified mathematical model of tumor growth". (1986)
*Mathematical Biosciences*., 81, 229-244. - "Spectral theory and stability in astrophysics. I. Ideal MHD". (1986)
*Astrophys. Sp. Sci*. 127, 163-178. - "Spectral theory and stability in astrophysics. II. Rotating stars". (1986)
*Astrophys. Sp. Sci*., 127, 309-320. - "A linear scattering problem in magnetohydrodynamics: transmission resonances in a magnetic slab". (1987)
*Astrophys. Sp. Sci*. 133 317-337 - "A mathematical model of tumor growth: II. Effects of geometry and spatial non-uniformity on stability". (1987)
*Math. Biosci.*, 86, 183-211. - "A mathematical model of tumor growth: III. Comparison with experiment". (1987)
*Math.**Biosci*., 86, 213-227. - On complementary levels or description in applied mathematics. II. Mathematical models in cancer biology". 1988
*Int. J. Math. Ed. Sci. Tech*., 19, 519-535. - "On Liouville's equation and its occurrence in mathematical astrophysics". (1988)
*Int. J.**Math. Ed. Sci. Tech*., 19, 881-890. - "Complementary levels of description in applied mathematics. III. Equilibrium models of cities". (1988)
*Math. Comput. Modelling*, 10, 321-339. - "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. - "Integral Invariants and Complex Eigenvalue Bounds".
*Applied Math. Lett.*( 1988) 1, 203-206. - "A nonlinear eigenvalue problem in astrophysical magnetohydrodynamics: some properties of the spectrum".
*J. Math. Phys*. ( 1989) 30, 744-756. - "Some results on the spectrum of a magnetoatmospheric wave operator".
*Applied Math. Lett.*(1989)2, 11-14. - "Note on a class of nonlinear time-independent diffusion equations". (With S.A. Maggelakis),
*Applied Math. Lett*. (1989) 2, 141-145. - "A Mathematical Model of Tumor Growth. IV. Effects of a Necrotic Core" (With S.A. Maggelakis),
*Mathematical Biosci*. 97 (1989) 121-136. - "Note on a Diffusion Model of Tissue Growth", (with S.A. Maggelakis),
*Applied Math. Lett.*3 (1990) 27-31. - "A Mathematical Model of Preascular Growth of a Spherical Carcinoma" (with S.A. Maggelakis),
*Math. Comput. Modelling*1990 5 13, 2338. - "Diffusion Regulated Growth Characteristics of A Prevascular Carcinoma" (with S.A. Maggelakis),
*Bull. Math. Biology*. 1990, 52 549-582 - "An Initial-Value Problem for Magnetoatmospheric Waves. I. Theory".
*Wave Motion*1990, 12 385-399. - "A Generalization of a Solvable Model in Population Dynamics", (with G. DeRise),
*J. Phys.:**Math. & Gen.*(1990), L727-L731. - "Diffusion Models of Prevascular and Vascular Tumor Growth: A Review".
*Lecture Notes in**Pure and Applied Mathematics*, 1991, Vol.131, Chapter 41, p.625-642 (Marcel Dekker, Inc.). - "Self-Activation and Inhibition: Simple Nonlinear Model".
*Appl. Math. Letters*, 4, 2 (1991), 85-87. - "Self-Activation and Inhibition: The Effect of a Zero-Flux Boundary",
*Appl. Math. Letters*, 4, 3 (1991) 45-47. - "Activator-Inhibitor Control of Tissue Growth".
*SIAM Review*, 33, (1991), 462-466 - "Solution Uniqueness and Stability Criteria for a Model of Growth Factor Production",
*Appl.**Math. Letters*, 5 (1992) 89-92. - "The Dynamics of Growth Factor-Modified Immune Response to Cancer Growth: One-Dimensional Models
*", Mathematical and Computer Modelling*, 17 (1993), 83-106. - "The Scattering Potential for a Polytrope of Degree n=5".
*Appl. Math. Letters*, 6, #4 (1993) 9-1 1 . - "Scattering Parameters for an Epstein Profile in a Half-Space",
*Appl. Math. Letters*, 6, #4, (1993), 13-15. - "Propagation of Magnetoacoustic-Gravity Waves in a Horizontally Stratified Medium: IV. Kinematics".
*Astrophys. Sp. Sci*. 202 (1993), 259-271. (With I. McKaig). - "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). - "Non-Radial Stellar Oscillations from the Perspective of Potential Scattering Theory: Theoretical Aspects."
*Astrophys. Sp. Sci*. 220 (1994), 179-233. - "Mathematical Model of Cycle-Specific Chemotherapy" (With Carl Panetta).
*Mathematical**and Computer Modelling*22 (1995), 67-82. - "A Simple Mathematical Model and Alternative Paradigm for Certain Chemotherapeutic Regimens." (With Carl Panetta).
*Mathematical and Computer Modelling*, 22 (1995), 49-60. - "Educated Guesses".
*Quantum*– A Journal of Mathematics and Science. Sept/Oct. 1995. - "The Effects of Vascularization on Lymphocyte-Tumor Cell Dynamics: Qualitative Features",
*Math. Comp. Modelling*23 (1996), 1-10. - "General Aspects of Modeling Tumor Growth and Immune Response", Chapter 2 in the book cited below(Adam & Bellomo, Eds.)
- “Mathematical Models of Spheroid Growth and Catastrophe-Theoretic Description of Rapid Metastatic Growth/Remission”,
*Invasion & Metastasis*, 16 (1996), 247-267. - “N-Space, Dimensional Interface Phenomena and an Adventure in Flatland”,
*Hyperspace*, 5(1996), 10-23. - “Scattering from Stellar Acoustic-Gravity Potentials: II. Phase Shifts via the First Born Approximation”, (with Iain McKaig),
*Appl. Math. Lett*., 10 (1997), 39-42. - “Limiting Spheroid Size as a Function of Growth Factor Source Location”, (with Kim Ward),
*Appl. Math. Lett.,*10 (1997), 43-46. - “Post-Surgical Passive Response of Local Environment to Primary Tumor Removal”, (with Carryn Bellomo),
*Math. Comp. Modelling*, 25 (1997), 7-17. - “The Pekeris Waveguide: A Case Study in Classical Applied Mathematics”,
*Math. Meth.**Mod. App. Sci*., 8 (1998), 157-186. - “ (A Note on)
^{2}the Shape of the Erythrocyte”,*Math. Comp. Modeling*, 27 (1998), 73-77. - “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. - “The Mathematical Modeling of Cancer: A Review”, (with Carl Panetta and Mark Chaplain), Conference Proceedings, 281-310, 1999,Vanderbilt University Press.
- “A Simplified Model of Wound Healing, with particular reference to the Critical Size Defect: One-dimensional model.”
*Math. Comp. Mod*. 30 (1999), 23-32. - “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) - “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.
- “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.
- “The Mathematical Physics of Rainbows and Glories”.
*Physics Reports*356 (Nos. 4-5) (2002), 229-366. - “Healing times for circular wounds on plane and spherical bone surfaces”.
*Applied Mathematics Letters*, 15 (2002), 55-58. - “The effect of surface curvature on wound healing in bone”.
*Applied Mathematics Letters*, 15 (2002), 59-62. - “The effect of surface curvature on wound healing in bone: II. The critical size defect”.
*Mathematical and Computer Modelling*, 35 (2002), 085-1094. - “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. - “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. - “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).
- “Inside mathematical modeling: building models in the context of wound healing in bone “ in
*Discrete and Continuous Dynamical Systems*, 4 (2004), 1-24. - "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).
- "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.)
- "On Rainbows from Inhomogeneous Transparent Spheres: A Ray-Theoretic Approach.” (With Philip Laven), Applied Optics, 46 (2007), 922-929.
- 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.
- 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
- 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.
- “Rainbows, Geometrical Optics, and a Generalization of a result of Huygens”, Applied Optics, 47, H11 - H13.
- “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.”
- 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. - "Blood Vessel Branching: Going Beyond the Standard Calculus Problem", Mathematics Magazine, 84 (2011), 196 – 207.
- "Zero-order bows in radially inhomogeneous spheres: direct and inverse problems." Applied Optics, 50 (2011) F50 - F59.
- "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.
- 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. - '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.
- "Electromagnetic and Potential Scattering from a Radially Inhomogeneous Sphere" 2013; co-author: Umaporn Nuntaplook, http://arxiv.org/abs/1307.1647
- "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.
- "Scalar wave scattering by two-layer radial inhomogeneities” (with U. Nuntaplook) Applied Mathematics E-Notes,
**14**(2014), 185-192. - "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. - “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. - “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.
- “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). - “Evaluation of Ray-Path Integrals in Geometrical Optics”, International Journal of Applied and Experimental Mathematics,
**1**, 108 (2016) (7 pages, With M. Pohrivchak). - “Mountain Shadows Revisited”. Applied Optics
**56**(19), (2017) G26 – G35. - “An Example of Nature’s Mathematics: The Rainbow.” Submitted to The Virginia Mathematics Teacher.
- “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.