JOURNAL ARTICLES:

Equilibrium Statistical Mechanics

Greenberg, W., "Correlation Functionals of Infinite Volume Quantum Spin Systems," Communications in Mathematical Physics 11, 314-320 (1969).

Greenberg, W., "Critical Temperature Bounds of Quantum Lattice Gases," Communications in Mathematical Physics 13, 335-344 (1969).

Greenberg, W., "Quantum Potentials on Lattices," Journal of Mathematical Physics 12, 1770-1771 (1971).

Greenberg, W., "Thermodynamic States of Classical Systems," Communications in Mathematical Physics 22, 259-268 (1971).

Gruber, G., D. Merlini and W. Greenberg, "Spin 1/2 Lattice Systems: Duality Transformations and Correlation Functionals," Physika 65, 28-40 (1973).

Greenberg, W., "Thermodynamic Duality for Classical Systems of Arbitrary Spin," Communications in Mathematical Physics 29, 163-175 (1973).

Greenberg, W., "The Conditional Entropy in the Microcanonical Ensemble," Journal of Mathematical Physics 16, 1667-1671 (1975).

Greenberg, W., "The Interaction Function and Lattice Duals," Journal of Mathematical Physics 18, 1985-1986 (1977).

Dietz, D. and W. Greenberg, "Conditional Entropy in the Microcanonical Ensemble: the Quantum Lattice," Physica 69A, 511-530 (1979).

Nonequilibrium Statistical Mechanics

Greenberg W., "Functional Calculus for the Symmetric Multi-Group Transport Operator," Journal of Mathematical Physics 17, 159-162. (1976).

Greenberg, W. and P.F. Zweifel, "The Case Eigenfunction Expansion for a Conservative Medium," Journal of Mathematical Physics 17, 163-167 (1976).

Ball, J. and W. Greenberg, "A Pontrjagin Space Analysis of the Supercritical Transport Equation," Journal of Transport Theory and Statistical Physics 4, 143-154 (1975).

Greenberg, W. and S. Sancaktar, "Solution of the Multi-group Transport Equation in Lp Spaces," Journal of Mathematical Physics 17, 2092-2097 (1976).

Greenberg, W. and P.F. Zweifel, "Recent Developments in Kinetic Theories," Journal of Transport Theory and Statistical Physics 5, 207-218 (1976).

Greenberg, W. and P.F. Zweifel, "Functional Analytic Treatment of the Transport Equation," Journal of Transport Theory and Statistical Physics 5, 219-254 (1976)..

Arthur, M.D., W. Greenberg and P.F. Zweifel, "Vlasov Theory of Plasma Oscillations:Linear Theory," Physics of Fluids 20, 1296-1301 (1977).

Bowden, R., W. Greenberg and P.F. Zweifel, "Critical Multigroup Transport," SIAM Journal of Applied Mathematics 32, 765-777 (1977).

Greenberg, W. and P.F. Zweifel, "Fifth Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 6, 159-168 (1977).

Greenberg, W. and P.F. Zweifel, "Transport Theoretical Methods in Physics," Journal of Transport Theory and Statistical Physics 6, 219-226 (1977).

Freede-Garbanti, L., W. Greenberg and P.F. Zweifel, "Uniqueness of Solutions to the Linear Boltzmann Equation." Journal of Mathematical Physics 19, 249-252 (1978).

Arthur, M.D., W. Greenberg and P.F. Zweifel, "Kinetic Theory of Plasma Stability," in Proceedings of the 15th Annual Meeting of the Society of Engineering Science, R.L. Sierakowski, ed., University of Florida, Gainesville (1978), pp. 135-138.

Greenberg, W., "Numerical Transport Methods," Journal of Transport Theory and Statistical Physics 7, 135-138 (1978).

Cercignani, C., W. Greenberg and P.F. Zweifel, "Global Solutions of the Boltzmann Equation on a Lattice," Journal of Statistical Physics 20, 449-462 (1979).

Bowden, R., W. Greenberg and P.F. Zweifel, "Resolvent Integration Techniques for Generalized Transport Equations," Journal of Mathematical Physics 20, 1099-1108 (1979).

Greenberg, W., J. Voigt and P.F. Zweifel, "Convergence of a Lattice Model of the Boltzmann Equation," Letters in Mathematical Physics 3, 293-296 (1979).

Arthur, M.D., W. Greenberg and P.F. Zweifel, "Transverse Plasma Oscillations," Physics of Fluids 22, 1465-1470 (1979).

Greenberg, W., J. Voigt and P.F. Zweifel, "Discretized Boltzmann Equation: Lattice Limit and Non-Maxwellian Gases," Journal of Statistical Physics 21, 649-657 (1979).

Burnap, C., W. Greenberg and P.F. Zweifel, "Eigenvalue Problems for Singular Potentials," Il Nuovo Cimento 50A, 457-465 (1979).

Greenberg, W. and P.F. Zweifel, "Sixth (Inter)National Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 8, 117-124 (1979).

Greenberg, W., "Mathematical Problems in the Kinetic Theory of Gases," Journal of Transport Theory and Statistical Physics 8, 246-252 (1979).

Greenberg, W., "A Discrete Model Boltzmann Equation," Annals of Nuclear Energy 7, 201 (1980).

Greenberg, W. and G. Spiga, "New Results in Transport Theory," Journal of Transport Theory and Statistical Physics 9, 146 (1980).

Greenberg, W., "Kinetic Equations in Weak Topologies," Progress in Nuclear Energy 8, 171-175 (1981).

Greenberg, W., M. Williams and P.F. Zweifel, "Report on the Seventh International Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 10, 115-130 (1981).

Greenberg, W. and P.F. Zweifel, "Resolvent Integration Methods in Transport Theory," Integral Equations and Operator Theory 5, 25-539 (1982).

Greenberg, W. and C. van der Mee, "Abstract Boundary Value Problems from Kinetic Theory," Journal of Transport Theory and Statistical Physics 11, 155-181 (1982).

Greenberg, W., J. Polewczak and P.F. Zweifel, "Global Existence Proofs for the Boltzmann Equation," in Nonequilibrium Phenomena I. The Boltzmann Equation (Studies in Statistical Mechanics, vol. X), E.W. Montroll and J.L.Lebowitz, eds., North-Holland, New York (1983), pp. 19-49.

Greenberg, W. and P.F. Zweifel, "Mathematical Problems in Kinetic Theory," Journal of Transport Theory and Statistical Physics 12, 85-101 (1983).

Greenberg, W., "Half Space Problems in Neutron Transport," in Atti del Convegno Nazionale di Fisica del Reattore Nucleare, Pitagora, Bologna (1983), 10 pp.

Greenberg, W. and J. Polewczak, "Some Remarks About Continuity Properties of Local Maxwellians and the BGK Model of the Boltzmann Equation," Journal of Statistical Physics 33, 307-316 (1983).

Greenberg, W., C. van der Mee and P.F. Zweifel, "Generalized Kinetic Equations," Integral Equations and Operator Theory 7, 60-95 (1984).

Greenberg, W. and C. van der Mee, "Stationary Transport Processes with Unbounded Collision Operators," Letters in Mathematical Physics 8, 7-12 (1984).

Greenberg, W. and C. van der Mee, "Abstract Kinetic Equations Relevant to Supercritical Media," Journal of Functional Analysis 57, 111-142 (1984).

Greenberg, W. and C. van der Mee, "An Abstract Approach to Strong Evaporation Models in Rarefied Gas Dynamics," Journal of Applied Mathematics and Physics (Z.A.M.P.) 35, 156-165 (1984).

Greenberg, W. and C. van der Mee, "Problems in the Abstract Theory of Stationary One Dimensional Transport," Journal of Transport Theory and Statistical Physics 12, 413-420 (1984).

Cavalier, J.F. and W. Greenberg, "Analytical Solutions of Model Equations for Two Phase Gas Mixtures: Transverse Velocity Perturbations," Physics of Fluids 26, 1114-1124 (1984).

Greenberg, W. and C. van der Mee, "An Abstract Model for Radiative Transfer in an Atmosphere with Reflection by the Planetary Surface," S.I.A.M. Journal of Mathematical Analysis 16, 695-702 (1985).

Greenberg, W., "Mathematical Methods in Kinetic Theory," Journal of Transport Theory and Statistical Physics 15, 345-352 (1986).

Greenberg, W. and W. Walus, "Abstract Kinetic Equations Relevant to Transport in Multiplying Media in Slab Geometry," in Proceedings of the Fifteenth International Symposium on Rarefied Gas Dynamics, V. Boffi, C. Cercignani, eds., Teubner, Stuttgart (1986), pp.134-143.

Ganchev, A., W. Greenberg and C. van der Mee, "Perturbation of Bisemigroups and Boundary Value Problems for Abstract Kinetic Equations," in Proceedings of the Fifteenth International Symposium on Rarefied Gas Dynamics, V. Boffi, C. Cercignani, eds., Teubner, Stuttgart (1986), pp.125-133.

Greenberg, W., and P.F. Zweifel, "Tenth International Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 16, 1107-1175 (1987).

Greenberg, W., C. van der Mee and W. Walus, "Strong Solutions of Stationary Kinetic Equations in Abstract Kinetic Theory," Integral Equations and Operator Theory 11, 186-204 (1988).

Ganchev, A. and W. Greenberg, "Linear Half Space Transport Equations with Accretive Invertible Collision Operators," Journal of Transport Theory and Statistical Physics 17, 93-105 (1988).

Ganchev, A., W. Greenberg and C. van der Mee, "Abstract Kinetic Equations with Accretive Collision Operators," Integral Equations and Operator Theory 11, 332-350 (1988).

Ganchev, A., W. Greenberg and C. van der Mee, "A Class of Linear Kinetic Equations in a Krein Space Setting," Integral Equations and Operator Theory 11, 518-535 (1988).

Ganchev, A., W. Greenberg and C. van der Mee, "Perturbation Analysis of Analytic Bisemigroups and Applications to Linear Transport Theory," in Special Classes of Linear Operators and Other Topics (Operator Theory: Advances and Applications, vol. 28) H. Helson, ed., Basel, Birkhäuser (1988), pp. 83-99.

Greenberg, W. and P.F. Zweifel, "Mathematical Problems in the Kinetic Theory of Gases," Journal of Transport Theory and Statistical Physics 17, 651-658 (1988).

Greenberg, W., and J. Polewczak, "A Global Existence Theorem for the Nonlinear B.G.K. Equation, Journal of Statistical Physics 55, 1313-1321 (1989).

Greenberg, W., and J. Polewczak, "Transport Equations in Weak * Topologies of Dual Banach Spaces," Journal of Transport Theory and Statistical Physics 18, 115-124 (1989).

Greenberg, W., and C. van der Mee, "A Tensor Banach Algebra Approach to Abstract Kinetic Equations," in Rarefied Gas Dynamics: Theoretical and Computational Techniques, E.P. Muntz, D.P. Weaver, D.H. Campbell, eds., American Institute of Aeronautics and Astronautics, Washington, 1989, pp. 29-38.

Greenberg, W., and J. Polewczak, "Averaging Techniques for the Transport Operator and an Existence Theorem for the B.G.K. Equation in Kinetic Theory," in The Gohberg Anniversary Collection, vol. II (Operator Theory: Advances and Applications, vol. 41), H. Dym, S. Goldberg, M.A. Kaashoek, P. Lancaster, eds., Basel, Birkhäuser (1989), pp. 299-309.

Greenberg, W. and J. Polewczak, "Eleventh International Transport Theory Conference," Journal of Transport Theory and Statistical Physics 19, 75-85 (1990).

Peng, L. and W. Greenberg, "Abstract Parametric Equations without Positivity," Journal of Transport Theory and Statistical Physics 19, 29-41 (1990).

Greenberg, W., "Analytical and Semi-analytical Methods in Transport Theory," in Modern Mathematical Methods in Transport Theory, W. Greenberg, J. Polewczak, eds., Birkhäuser Verlag, Basel (1990), pp. 1-5.

Greenberg, W., P.F. Zweifel and S. Paveri-Fontana, "The Riemann-Hilbert Problem for Nonsymmetric Systems," Journal of Mathematical Physics 32, 3540-3545 (1991).

Greenberg, W. and J. Polewczak, "Twelfth International Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 21, 277-290 (1992).

Greenberg, W., P. Lei and R. Liu, "Stability Theory for the Kinetic Equations of a Moderately Dense Gas," in Rarefied Gas Dynamics: Theory and Simulations (Progress in Astronautics and Aeronautics, vol. 159), B.D. Shizgal and D.P. Weaver, eds., American Institute of Aeronautics and Astronautics, Washington (1994), pp. 599-607.

Greenberg, W. and P.F. Zweifel, "Thirteenth International Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 23, 541-552 (1993).

Greenberg, W., P. Lei and R. Liu, " Solution of Kinetic Equations for Dense Gases," in Proceedings of the Nineteenth International Symposium on Rarefied Gas Dynamics, J. Harvey and G. Lord, eds., Oxford University Press, Oxford (1995), pp. 192-197.

Greenberg, W. and P.F. Zweifel, "Fourteenth International Conference on Transport Theory," Journal of Transport Theory and Statistical Physics 24, 1423-1433 (1995).

Greenberg, W. and A. Yao, "Kinetic Equations for Gases with Piecewise Constant Intermolecular Potentials," Journal of Transport Theory and Statistical Physics 27, 137-150 (1997).

Greenberg, W. and P. Lei, "Solutions of a Vlasov-Enskog Equation," in Proceedings of International Scientific Conference, Russian Academy of Science (Institute for Mathematical Biology), Tver, (1997), pp. 41-48

Greenberg, W., L. Uvarova and T. Naumovich, "Mathematical Models in Nonlinear Statistical Mechanics," Journal of Transport Theory and Statistical Physics 26, 379-382 (1997).

Greenberg, W. and J. Polewczak, “Nonlinear Transport Equations in Weak Banach Space Topologies,” in Rarefied Gas Dynamics, C. Shen, ed., Peking University Press, Beijing, (1997), pp. 97-101.

Chen, J., W. Greenberg and R.L. Bowden, "Existence of Solutions and Dynamical Models of Chandrasekhar H-Equations," in Mathematical Models of Non-Linear Excitations, Transfer, Dynamics and Control in Condensed Systems and Other Media, L.A. Uvarova, A.E. Arinstein and A.V. Latyshev, eds., Plenum, New York, 1999.

Greenberg, W. "Mathematical Models in Nonlinear Statistical Mechanics," Transport Theory and Statistical Physics 28, 191-194 (1999).

Dorning, J., W. Greenberg, P. Nelson, D. Song and P. Zweifel, "Particle Transport in Gases, Plasmas, Semiconductors and Nuclear Systems," Transport Theory and Statistical Physics 30, 91-118 (2001)

Greenberg, W. and D. Song, "Asymptotics of the Neutron Transport Equation for Spherical Geometry in L2 with Reflecting Boundary Conditions," in Mathematical Models of Nonlinear Excitations, Transfer, Dynamics and Control in Condensed Systems and Other Media, L.A. Uvarova, A.E. Arinstein, A.V. Latyshev, eds., Kluwer Academic/Plenum Publ., New York, 2001, 12 pp. 

Song, D. and W. Greenberg, "Spectral Properties of Transport Equations for Slab Geometry in L1 with Reentry Boundary Conditions," Transport Theory and Statistical Physics 30, 325-356 (2001).

Greenberg, W., "Stationary Kinetic Equations: Existence, Uniqueness and Representation of Solutions," Research Trends in Statistical Physics 4, 45-59 (2004). 

Greenberg, W. and D. Song, "Spectral Properties of the Neutron Transport Equation for Spherical Geometry in the Setting of L1," Transport Theory and Statistical Physics 34, 1-20 (2005).

Greenberg, W., "Models of Boltzmann-like Nonlinear Kinetic Equations for Moderately Dense Gases," in Proceedings del II Congreso International de Matematica Aplicada y Computacional (CIMAC II), D. Mauricio, ed., SPMAC, to appear

Greenberg, W., "Kinetic Equations with Intermolecular Potentials: Avoiding the Boltzmann Assumption," in les Comptes-rendus du IIIme Symposium Malien sur les Sciences Appliques (MSAS2004), F. Seydou, ed., Oulu University Press, Oulu, Finland, 2005.

Greenberg, W. and P. Lei, "A Vlasov-Enskog Equation with Thermal Background in Gas Dynamics," Differential and Difference Equations and Applications, R.P. Agarwal and K. Perera, eds., Hindawi Publ., New York, 2006, pp. 423-432.

Greenberg, W. and P. Lei, "Cauchy Problem for an Enskog Equation with Attractive Tail and Fokker-Planck Scattering," to appear in Dynamics of Continuous, Discrete and Impulsive Systems, Series A, 13 pp.

Lei, P. and W. Greenberg, "Nonlinear Kinetic Equations for Rigid Spheres with Weak Poisson Coupling and Diffusion," International Journal of Evolution Equations 1, 345-372 (2005).

Greenberg, W. and M. Williams, "Kinetic Equations on a Lattice with Nearest Neighbor Interaction: Discrete and Semi-Discrete Modeling," in Proceedings of International Conference in Mathematics and Applications ICMA-MU 2005, Y. Lenbury, ed., National Research Council, Bangkok, 2005, pp. 19 - 36; also East-West Journal of Mathematics 9, 369 - 383 (2007).

Greenberg, W. and M. Williams, "Global Solutions of the Enskog Lattice Equation with Square Well Potential," CUBO Mathematical Journal 9, 13-26 (2007).

Greenberg, W. and M. Williams, "A New Algorithm for BLE (Boltzmann Lattice Equation) Numerics," in Proceedings of MSAS2006, F. Seydou, ed., to appear, 10 pp.

Greenberg, W. "New Models, Existence Theorems and Open Problems in the Kinetic Theory of Dense Gases," in Mathematical Modeling, Simulation, Visualization and E-learning, D. Konate, ed., Springer Verlag, Berlin, to appear, 18 pp.

Greenberg, W. and D. Song, "Lp Interpolation of Planar Neutron Transport with Reentry Boundary Conditions," Dynamics of Continuous, Discrete and Impulsive Systems A, to appear, 5 pp.

Biological Systems

Greenberg, W., "A Tanganyikan Cichlid Community," Journal of the American Cichlid Association 129, 8-12 (1988).

Jones, J., W. Greenberg and M. Ayers, "Computed Tomographic Evaluation of Dinosaur Egg Shell Integrity," Journal of Veterinary Radiology and Ultrasound 39, 133-136 (1998)

Mathematics Education

Loganathan, G.V., W. Greenberg, L. Holub and C. Moore, "The Deflected Beam in Differential Calculus," in 1999 American Society of Engineering Education Conference, sess. 3565, CD-ROM, ASEE, 1999.

Greenberg, W., “Mathematical Analysis in Engineering: Reform of the Calculus in the United States,” in International Conference on Engineering and Computer Education: Technology-Based Education and Globalization, H.H. Figueroa, ed., CD-ROM, ABENGE, Rio de Janiero, 1999.

Greenberg, W. and M. Williams, "Reform in the Teaching of Mathematics at the University Level: the Computer Emporium," in Proceedings of the RAMAD International Conference on Environmental Modeling and Simulation (RAMAD5), submitted for publication.

Williams, M. and W. Greenberg, "A High Volume Test Engine and Pedagogy for Computer Emporium Instruction," in les Comptes-rendus du IIIme Symposium Malien sur les Sciences Appliques (MSAS2004), F. Seydou, ed., Oulu University Press, Oulu, Finland, 2005, 6 pp.. 

BOOKS:

Greenberg, W., C. van der Mee and V. Protopopescu, Boundary Value Problems in Abstract Kinetic Theory (Operator Theory: Advances and Applications, vol. 23), Birkhäuser Verlag, Basel, 1987, 526 pp.

Greenberg, W. and J. Polewczak, eds., Modern Mathematical Methods in Transport Theory (Operator Theory: Advances and Applications, vol. 51), Birkhäuser Verlag, Basel, 1990, 327 pp.

Greenberg, W. (ed.), Proceedings of the Fourteenth International Conference on Transport Theory, as Transport Theory and Statistical Physics, vol. 27(1&2), Marcel Dekker, New York, 1997, 285 pp.