• For a current list of publications and other information, go to https://fs.wp.odu.edu/jadam/ Dr. John A. Adam has been Professor of Mathematics at Old Dominion University since 1984. His Ph.D. from the University of London was in theoretical astrophysics (an exceedingly long time ago). As an undergraduate he was exposed to a concentrated diet of Monty Python’s Flying Circus, and he has never fully recovered, even at his advanced age. His first introduction to the USA was through the humor of The Far Side cartoons by Gary Larson. He has broad interests in mathematical modeling and applied mathematics, ranging from mathematical biology to meteorological optics. He is a frequent contributor to Earth Science Picture of the Day (http://epod.usra.edu/). In 2007 he was winner of an Outstanding Faculty Award for the State of Virginia. In 2012 he was a recipient of a Carl B. Allendoerfer Award from the Mathematical Association of America (MAA). The Award is made to authors of expository articles published in the MAA journal Mathematics Magazine. He has published approximately 110 papers in mathematical and scientific journals, and given over 160 talks and presentations to professional and university/college groups. He has written several books (all published by Princeton University Press): Mathematics in Nature: Modeling Patterns in the Natural World, X and the City: Modeling Aspects of Urban Life and A Mathematical Nature Walk. He is also co-author (with physicist Lawrence Weinstein) of Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. His latest book, Rays, Waves and Scattering: Topics in Classical Mathematical Physics was published in June 2017.
  • Selected Publications

    Articles In Academic Journals

    Year Title
    2017 An Example of Nature’s Mathematics: The RainbowThe Virginia Mathematics Teacher. 12-19.
    2017 Mountain shadows revisitedApplied Optics. G26-G35.
    2016 Evaluation of Ray - Path Integrals in Geometrical OpticsInt'l Journal of Applied and Experimental Mathematics. 7.
    2015 Scattering of a plane electromagnetic wave by a generalized Luneburg sphere–Part 1: Ray scatteringJournal of Quantitative Spectroscopy and Radiative Transfer. 154-163.
    2015 Scattering of a plane electromagnetic wave by a generalized Luneburg sphere–Part 2: Wave scattering and time-domain scatteringJournal of Quantitative Spectroscopy and Radiative Transfer. 164-174.
    2014 Scalar wave scattering by two-layer radial inhomogeneitiesApplied Mathematics E-Notes. 185-192.
    2013 Electromagnetic and Potential Scattering from a Radially Inhomogeneous Sphere
    2011 Zero-order bows in radially inhomogeneous spheres: direct and inverse problemsApplied Optics. F50-F59.
    2009 A two-population insurgency in Colombia: Quasi-predator-prey models - A trend towards simplicityMathematical & Computer Modeling. 1115-1126.
    2008 Geometric optics and rainbows: generalization of a result by HuygensApplied Optics. H11-H13.
    2008 Rainbow, geometrical optics, and a generalization of a result of HuygensApplied Optics. H11-H13.
    2007 On rainbows from inhomogeneous transparent spheres: A ray-theoretic approachApplied Optics. 922-929.
    2007 Rainbows from inhomogeneous transparent spheres: a ray-theoretic approachApplied Optics. 922-929.
    2006 A simplified model for growth factor induced healing of circular woundsMathematical & Computer Modeling. 887-898.
    2005 Flowers of Ice?Beauty, Symmetry, and Complexity: A Review of The Snowflake: Winter?s Secret BeautyNotices Amer. Math. Soc. 402-416.
    2005 Mathematics in nature. modeling patterns in the natural worldThe Mathematical Intelligencer. 81-82.
    2004 Inside mathematical modeling: building models in the context of wound healing in boneDiscrete and Continuous Dynamical Systems Series B. 1-24.
    2003 Mathematical models of tumors and their remote metastases.Kluwer Academic/Plenum Publishers.
    2002 Healing times for circular wounds on plane and spherical bone surfacesApplied mathematics letters. 55-58.
    2002 Like a Bridge over Colored Water: A Mathematical Review of The Rainbow Bridge: Rainbows in Art, Myth, and ScienceNotices of the AMS.
    2002 Mathematical models of tumors and their remote metastases.Kluwer Press.
    2002 The effect of surface curvature on wound healing in boneApplied mathematics letters. 59-62.
    2002 The effect of surface curvature on wound healing in bone: II. The critical size defectMathematical and Computer Modelling. 1085-1094.
    2002 The mathematical physics of rainbows and gloriesPhysics Reports. 229-365.
    1999 A simplified model of wound healing (with particular reference to the critical size defect)Mathematical and Computer Modelling. 23-32.
    1999 A simplified model of wound healing II: The critical size defect in two dimensionsMathematical and Computer Modelling. 47-60.
    1999 Post-surgical passive response of local environment to primary tumor removal II: Heterogeneous modelMathematical Models and Methods in Applied Sciences. 617-626.
    1998 (A note on) 2 the shape of the erythrocyteMathematical and Computer Modelling. 73-77.
    1998 The Pekeris Waveguide: A Case Study in Classical Applied MathematicsMathematical Models and Methods in Applied Sciences. 157-186.
    1997 Limiting spheroid size as a function of growth factor source locationApplied mathematics letters. 43-46.
    1997 Post-surgical passive response of local environment to primary tumor removalMathematical and Computer Modelling. 7-17.
    1997 Scattering from stellar acoustic-gravity potentials: II. Phase shifts via the first Born approximationApplied mathematics letters. 39-42.
    1996 Effects of vascularization on lymphocyte/tumor cell dynamics: Qualitative featuresMathematical and Computer Modelling. 1-10.
    1996 Mathematical Models of Spheroid Growth and Catastrophe-Theoretic Description of Rapid Metastatic Growth/RemissionInvasion & metastasis. 247-267.
    1996 N-Space, Dimensional Interface Phenomena and an Adventure in FlatlandHyper space. 10.
    1995 A mathematical model of cycle-specific chemotherapyMathematical and Computer Modelling. 67-82.
    1995 A simple mathematical model and alternative paradigm for certain chemotherapeutic regimensMathematical and Computer Modelling. 49-60.
    1995 Educated Guesses. QuantumJournal of Mathematics and Science.
    1994 Non-radial stellar oscillations: a perspective from potential scattering (I)Astrophysics and Space Science. 179-233.
    1993 Equilibrium model of a vascularized spherical carcinoma with central necrosis?Some properties of the solutionJournal of mathematical biology. 735-745.
    1993 Propagation of magnetoacoustic-gravity waves in a horizontally-stratified medium: IV. kinematicsAstrophysics and Space Science. 259-271.
    1993 Scattering parameters for an Epstein profile in a half-spaceApplied mathematics letters. 13-15.
    1993 The dynamics of growth-factor-modified immune response to cancer growth: One dimensional modelsMathematical and Computer Modelling. 83-106.
    1993 The scattering potential for a polytrope of degree 5Applied mathematics letters. 9-11.
    1992 Solution uniqueness and stability criteria for a model of growth factor productionApplied mathematics letters. 89-92.
    1991 Activator–Inhibitor Control of Tissue GrowthSIAM Review. 462-466.
    1991 Diffusion models of prevascular and vascular tumor growth. A reviewLect. Notes Pure Appl. Math. 625.
    1991 Self Activation and Inhibition: Simple Nonlinear ModelApplied mathematics letters. 85 87.
    1991 Self-activation and inhibition: The effect of a zero-flux boundaryApplied mathematics letters. 45-47.
    1990 A generalisation of a solvable model in population dynamicsJournal of Physics A: Mathematical and General. L727S.
    1990 An initial value problem for magnetoatmospheric waves: I. TheoryWave Motion. 385-399.
    1990 Diffusion regulated growth characteristics of a spherical prevascular carcinomaBulletin of Mathematical Biology. 549-582.
    1990 Mathematical model of prevascular growth of a spherical carcinomaMathematical and Computer Modelling. 23-38.
    1990 Note on a diffusion model of tissue growthApplied mathematics letters. 27-31.
    1989 A Mathematical Model of Tumor Growth. IV. Effects of a Necrotic CoreMathematical Biosci. 121 136.
    1989 A nonlinear eigenvalue problem in astrophysical magnetohydrodynamics: Some properties of the spectrumJournal of mathematical physics. 744-756.
    1989 Mathematical computer and modelling reportsMathematical and Computer Modelling: An International Journal. 911.
    1989 Note on a class of nonlinear time independent diffusion equationsApplied mathematics letters. 141-145.
    1989 Some results on the spectrum of a magnetoatmospheric wave operatorApplied mathematics letters. 11-14.
    1988 A mathematical model of tumor growth by diffusionMathematical and Computer Modelling. 455-456.
    1988 Complementary levels of description in applied mathematics. III. Equilibrium models of citiesMath. Comput. Modelling. 321 339.
    1988 Integral invariants and complex eigenvalue boundsApplied mathematics letters. 203-206.
    1988 On Liouville’s equation and its occurrence in mathematical astrophysicsInternational Journal of Mathematical Education in Science and Technology. 881-890.
    1988 On complementary levels of description in applied mathematics II. Mathematical models in cancer biologyInternational Journal of Mathematical Education in Science and Technology. 519-535.
    1987 A linear scattering problem in magnetohydrodynamics: Transmission resonances in a magnetic slabAstrophysics and Space Science. 317-337.
    1987 A mathematical model of tumor growth. II. Effects of geometry and spatial nonuniformity on stabilityMathematical Biosciences. 183-211.
    1987 A mathematical model of tumor growth: III. Comparison with experimentMathematical Biosciences. 213 227.
    1986 A simplified mathematical model of tumor growthMathematical Biosciences. 229-244.
    1986 Critical layer singularities and complex eigenvalues in some differential equations of mathematical physicsPhysics Reports. 263-356.
    1986 Initial-value problem for the 1-D wave equation in an inhomogeneous mediumInstitute of Plasma Physics, Czechoslovak Academy of Sciences, Report IPPCZ-268.
    1986 Spectral theory and stability in astrophysics. I. Ideal MHDAstrophysics and Space Science. 163-178.
    1986 Spectral theory and stability in astrophysics. II. Rotating starsAstrophysics and Space Science. 309 320.
    1985 On the spectrum of some singular equations in magnetohydrodynamicsAstrophysics and Space Science. 249-258.
    1984 Magneto-atmospheric waves from a localized sourceAstrophysics and Space Science. 125-150.
    1984 On complementary levels of description in applied mathematicsInternational Journal of Mathematical Education in Science and Technology. 667-673.
    1984 Some mathematical aspects of wave motionInternational Journal of Mathematical Education in Science and Technology. 719-725.
    1984 The critical layers and other singular regions in ideal hydrodynamics and magnetohydrodynamicsAstrophysics and Space Science. 401-412.
    1983 Complex eigenvalue bounds in magnetoatmospheric shear flow. IIGeophysical & Astrophysical Fluid Dynamics. 57-67.
    1983 On photospheric and chromospheric penumbral wavesSolar Physics. 97-111.
    1982 A note on sigma-stability in hydromagneticsAstrophysics and Space Science. 115-121.
    1982 Asymptotic solutions and spectral theory of linear wave equationsPhysics Reports. 217-316.
    1982 Mathematical methods in linear inviscid hydrodynamic stability theoryInternational Journal of Mathematical Education in Science and Technology. 405-422.
    1981 Mechanical wave-energy fluxin magnetoatmospheres: Discrete and continuous spectraAstrophysics and Space Science. 293-350.
    1980 Eigenvalue bounds in magnetoatmospheric shear flowJournal of Physics A: Mathematical and General. 3325.
    1980 Maximum growth rate of magnetoatmospheric instabilities. II. A Hilbert space approachJournal of Physics A: Mathematical and General. 373.
    1980 Some wave reflection problems in solar physicsIrish Astronomical Journal. 133-137.
    1979 ‘Explosive’ resonant wave interactions in a three-layer fluid flowJournal of Fluid Mechanics. 15-33.
    1978 Evolution in space and time of resonant wave triads - I. The \textquoterightpump-wave approximation\textquoterightProceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 243.
    1978 Magnetohydrodynamic wave-energy flux in a stratified compressible atmosphere with shearThe Quarterly Journal of Mechanics and Applied Mathematics. 77-98.
    1978 Stability of aligned magnetoatmospheric flowJournal of plasma physics. 77-86.
    1977 Hydrodynamic instability of convectively unstable atmospheres in shear flowAstrophysics and Space Science. 493-514.
    1977 Maximum growth rates of magnetoatmospheric instabilitiesAstrophysics and Space Science. L5-L7.
    1977 On the occurrence of critical levels in solar magnetohydrodynamicsSolar Physics. 293-307.
    1977 Solar magnetoatmospheric waves-A simplified mathematical treatmentAstronomy and Astrophysics. 171-179.
    1977 Solutions of the inhomogeneous acoustic-gravity wave equationJournal of Physics A: Mathematical and General. L169.
    1976 Alfven wave reflection at a density transition regionJournal of Physics A: Mathematical and General. L193.
    1975 Steady magnetogravity flowThe Quarterly Journal of Mechanics and Applied Mathematics. 397-403.
    1975 Viscous damping of nonlinear magneto-acoustic wavesAstrophysics and Space Science. 479-487.


    Year Title
    2017 Rays, Waves, and Scattering: Topics in Classical Mathematical Physics.  Princeton University Press.
    2012 A mathematical nature walk-Slovenian translation.  Princeton University Press.
    2012 X and the City: Modeling Aspects of Urban Life.  Princeton University Press.
    2011 A mathematical nature walk-Paperback Edition.  Princeton University Press.
    2009 A Mathematical Nature Walk.  Princeton University Press.
    2008 Guesstimation - Solving the World's Problems on the Back of a Cocktail Napkin.  Princeton University Press.
    2003 Mathematics in nature. modeling patterns in the natural world.  Princeton University Press.
    1997 A Survey of Models for Tumor Immune Systems Dynamics.  Birkhäuser.


    Year Title
    2016 Some Wave-Theoretic Problems in Radially Inhomogeneous MediaLight Scattering Reviews, Volume 11. Springer.
    2016 “Scattering of Plane Electromagnetic Waves by Radially Inhomogeneous Spheres: Asymptotics and Special Functions”Mathematical & Statistical Research with Applications to Physical & Life Sciences, Engineering & Technology. Springer Proceedings in Mathematics and Statistics.
    2015 Scattering of electromagnetic plane waves in radially inhomogeneous media: ray theory, exact solutions and connections with potential scattering theoryLight Scattering Reviews 9. Springer.
    2013 Rainbows in Homogeneous and Radially Inhomogeneous Spheres: Connections with Ray, Wave, and Potential Scattering TheoryAdvances in Interdisciplinary Mathematical Research. Springer.
    2007 Modeling of Self Healing of Skin TissueSelf Healing Materials. Springer.
    2003 Mathematical models of tumor growth: from empirical description to biological mechanismMathematical Modeling in Nutrition and the Health Sciences. Springer.
    1997 General aspects of modeling tumor growth and immune responseA survey of models for tumor-immune system dynamics. Springer.

    Conference Papers

    Year Title
    2014 Scattering of a plane electromagnetic wave by a radially inhomogeneous generalized Luneburg lens
    2007 A finite element model for epidermal wound healing.  70-77.
    2007 A finite element model for epidermal wound healing involving angiogenesis. In: Proceedings Part 1, of the ICCS Conference
    2007 A numerical model for epidermal wound healing
    2000 A mathematical model of wound healing in bone.  97-103.
    2000 Nutrient concentration in and around a vascularized tumor with a necrotic core.  105-110.
    1999 The mathematical modelling of cancer: a review.  281-310.
    1983 Photospheric and Chromospheric Penumbral Waves.  706.

    Research Overview

  • Mathematical Theory of Waves; Magnetohydrodynamic Waves and Stability in Astrophysics; Spectral Theory of Singular Ordinary Differential Equations Arising in Mathematical Physics, Mathematical Biology, Mathematical Modeling, especially in the context of cancer biology, and wound healing in bone, Meteorological Optics
  • Education And Training

  • Ph.D. in Theoretical Astrophysics/Applied Mathematics, University of London, University College 1975
  • B.S. in Theoretical Physics, Queen Elizabeth College, University of London 1971
  • Full Name

  • John Adam