Mathematics: School of Physical Sciences - UC Irvine


  Selected Publications of Frederic Wan  
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1. Comparative analyses of thin paraboloidal shells of revolution under gravity, Proc. World Conference on Shell Structures (San Francisco, 1962), Nat. Acad. Sci., 1964, Pgs 487-500. (With J.W. Mar.)

2. Rotating shallow elastic shells of revolution, J. of SIAM 13, 1965, Pgs 333-352. (Presented at SIAM Symp.: "Theodore v. Karman - in Memoriam," Washington D.C., 1964.) (With E. Reissner.)

3. The influence of shell behavior on the design of large antennas, Proc. 16th International Astronautical Congress, 1965, (Athens, Greece) Pgs 183-212. (With J. W. Mar.)

4. The use of sandwich shells in large steerable aerials, Design and construction of Large Steerable Aerials (Proc. Conference on Large Steerable Aerials for Satellite Communication, Radio Astronomy and Radar), IEE Conference Publication 21, London 1966, Pgs 125-129. (With J.W. Mar.)

5. A note on stress strain relations of the linear theory of shells, J. of Appl. Math. and Phys. (ZAMP) 17, 1966, Pgs 676-681. (With E. Reissner.)

6. On the stress strain relations and strain displacement relations of the linear theory of shells, Recent Progress in Applied Mechanics (The Folke Odqvist Volume), Almqvist and Wiksell, Stockholm, 1967, Pgs 487-500. (With E. Reissner.)

7. A class of unsymmetric stress distributions in helicoidal shells, Quart. of Applied Math. 24, 1967, Pgs 374-379.

8. Membrane and bending stresses in shallow spherical shells, Intern'l. J. of Solids and Structures 3, 1967, Pgs 353-366.

9. A note on Günther's analysis of couple stress, Mechanics of Generalized Continua (Proc. IUTAM Symp., Stuttgart, Germany 1967), Springer-Verlag, 1968, Pgs 83-86. (With E. Reissner.)

10. On axial extension and torsion of helicoidal shells, J. Math. and Phys. 47, 1968, Pgs 1-30. (With E. Reissner.)

11. Pure bending of shallow helicoidal shells, J. of Applied Mechanics 35, 1968,
Pgs 387-392. (Presented at the ASME Summer Meeting, Providence.)

12. On the displacement boundary value problem of shallow spherical shells, Intern'l. J. of Solids and Structures 4, 1968, Pgs 661-666.

13. Two variational theorems for thin shells, J. Math. and Phy. 47, 1968, Pgs 429-431.

14. Rotationally symmetric stress and strain in shells of revolution, Studies in Applied Math.* 48, 1969, Pgs 1-17. (Also presented at the 12th International Congress of Applied Mechanics, 1968, Stanford; at the 3rd USSR Congress of Applied Mechanics, 1968, Moscow.) (With E. Reissner.)

15. On the equations of linear shallow shell theory, Studies in Applied Math.* 48, 1969, Pgs 133-145. (With E. Reissner.)

16. The side force problem for shallow helicoidal shells, J. Applied Mechanics 36, 1969, Pgs 292-295. (Presented at the ASME Summer Meeting, Evanston.)

17. Stress functions for nonlinear shallow shell theory, Studies in Applied Math. 48, 1969, Pgs 177-179.

18. St. Venant flexure of pretwisted rectangular plates, Intern'l. J. of Engineering Sciences 7, 1969, Pgs 351-360.

19. Exact reductions of equations of linear theory of shells of revolution, Studies in Applied Math. 48, 1969, Pgs 361-375. (Also presented at the 6th U.S. Congress of Applied Mechanics, Cambridge.)

20. On the equations of the linear theory of elastic conical shells, Studies in Appl. Math. 49, 1970, Pgs 69-83. (Also presented at the 6th U.S. Congress of Applied Mechanics, Cambridge.)

21. Circumferentially sinusoidal stress and strain in shells of revolution, Intern'l. J. Solids and Structures (IJSS) 6, 1970, Pgs 959-973.

22. Rotationally symmetric shearing and bending of helicoidal shells, Studies in Appl. Math. 49, 1970, Pgs 351-369.

23. On stretching, twisting, pure bending and flexure of pretwisted elastic plates, Intern'l. J. Solids and Structures 7, 1971, Pgs 625-637. (With E. Reissner.)

24. On rotationally symmetric stress and strain in anisoptropic shells of revolution, Studies in Appl. Math. 50, 1971, Pgs 391-394. (With E. Reissner.)

25. Spirally sinusoidal stress distributions in elastic helicoidal shells, J. Appl. Math. & Phys. (ZAMP) 22, 1971, Pgs 1029-1043. (With R.L. Mallett.)

26. Rotor blade response to random loads: a direct time domain approach, AIAA Journal 11, 1973, Pgs 24-28. (Also presented at the AIAA 10th Aerospace Science Meeting, San Deigo, Jan 1972.) (With C. Lakshmikantham.)

27. Linear partial differential equations with random forcing, Studies in Appl. Math. 51, 1972, Pgs 163-178.

28. A direct method for linear dynamical problems in continuum mechanics with random loads, Studies in Appl. Math. 52, 1973, Pgs 259-275. (Also presented at the 13th International Congress of Theoretical and Applied Mechanics, August, 1972, Moscow.)

29. Laterally loaded shells of revolutions, Ingenieur Archiv. 42, 1973, Pgs 245-258.

30. Nonstationary response of linear time-varying dynamical systems to random excitations, J. Appl.Mech. 40, 1973, Pgs 422-428. (Also presented at the ASME Summer Meeting, Atlanta.)

31. The static-geometric duality and a staggered mesh difference scheme for some shell problems, Studies in Appl. Math. 52, 1973, Pgs 21-38. (With R.L. Mallett.)

32. An algebraic method for linear dynamical systems with stationary excitations, J. Sound and Vibration 28, 1973, Pgs105-120. (With C. Lakshmikantham.)

33. An in-core finite difference method for separable boundary value problems on a rectangle, Studies in Appl. Math. 52, 1973, Pgs 103-113.

34. The spatial-correlation method and a time-varying flexible structure, AIAA J. 12, 1974, Pgs 700-707. (Also presented at AIAA-ASME Struc. Dyn. Mat. Conf., 1973, Williamsburg.) (With C. Lakshmikantham.)

35. Lateral bending and twisting of thin-walled curved tubes, Studies in Appl. Math. 53, 1974, Pgs 73-89. (With W.J. Seaman.)

36. Dynamical problems of continuous media with random boundary data, IJSS 10, 1974,
Pgs 35-44.

37. Effect of spanwise load-correlation on rotor blade flapping, presented at AIAA-ASME-ASCE Struc. Dyn. Mat. Conf. (Las Vegas, 1974) AIAA Paper No. 74-418. (Published later as journal article under item 54.)

38. Snowplow problems, Appl. Math. Notes 1, 1975, Pgs 6-11. (An educational note.)

39. An eigenvalue problem for a semi-infinite pretwisted strip, Studies in Applied Mathematics 54, 1975, Pgs 351-358.

40. Interdisciplinary graduate programs in Applied Mathematics at UBC, Proc. of the CMC Conference on Curriculum Alternatives, University of Regina (Ed. P. Binding), 1975, Pgs

41. Aging linear springs, Appl. Math. Notes 2, 1976, Pgs 27-31. (an educational note.)

42. Extraction costs in the theory of exhaustible resources, Bell J. of Economics 7, 1976,
Pgs 359-370. (Also presented at U.S. National Bureau of Economics Research Workshop on Resource Economics, Stanford, May, 1975). (With R.M. Solow.)

43. A note on factoring linear differential operators, Appl. Math. Notes 2, 1976, Pgs 98-101. (An educational note.)

44. Perturbation and asymptotic solutions for problems in the theory of urban land rent, Studies in Applied Mathematics 56, 1977, Pgs 219-239. (Also presented at the 2nd CFMC, Vancouver, May, 1976.)

45. Falling into the sun, Appl. Math. Notes 3, 1977, Pgs 49-51. (An educational note.)

46. Bifurcation theory and the two-hundred mile fishing limit, Appl. Math. Notes 4, 1978,
Pgs 74-87.

47. The response of a spatially distributed neuron to a white noise current injection, Biological Cybernetics 33, 1979, Pgs 39-55. (With H.C. Tuckwell.)

48. Eulerian Wobble, Appl. Math. Notes 4, 1979, Pgs 33-41. (An educational note.)

49. The dimpling of spherical caps, Mechanics Today 5 (The Eric Reissner Anniversary Volume, 1980, Pgs 495-508.

50. Polar dimpling of complete spherical shells, "Theory of Shells," Proc. of 3rd IUTAM Shell Symposium (Tbilisi; August, 1978), Ed. W.T. Koiter & G.K. Mikhailov, North Holland, 1980, Pgs 191-207.

51. Constant sustainable consumption rate in optimal growth with exhaustible resources, Studies in Applied Mathematics 63, 1980, Pgs 47-66. (Also presented by invitation to the 1977 A.M.S. Summer Meeting in Seattle.)

52. Numerical solutions for maximum sustainable consumption growth with a multi-grade exhaustible resource, SIAM J. Scientific & Statistical Computing 1, 1980, Pgs 160-172. (With U. Ascher.)

53. Horizontal and flat points in shallow cap dimpling, Proc. Conf. on Boundary & Interior Layers, Comp. & Asympt. Methods (Dublin, Ireland), Ed. J. Miller, 1980, Pgs 415-419. (Also published as I.A.M.S. Tech. Rep. 80-5). (With U. Ascher.)

54. Flapping response of lifting rotor blades to spanwise non-uniform random excitations, J. Eng. Math. 14, 1980, Pgs 241-261.

55. The buckling of flexible columns, Appl. Math. Notes 5, 1980, Pgs 109-122. (An educational note.)

56. The response of a nerve cylinder to spatially distributed white noise inputs, J. Theo. Biology 87, 1980, Pgs 275-295. (With H.C. Tuckwell.)

57. Re-entry into the Earth's atmosphere, Appl. Math. Notes 6, 1981, Pgs 80-85. (An educational note.)

58. Neuronal firing and input variability, J. Theoret. Neurobiol. 1, 1982, Pgs 197-218. (With H.C. Tuckwell.)

59. A note on the linear theory of shallow shear-deformable shells, J. Appl. Math. & Phys. (ZAMP) 33, 1982, Pgs 425-427. (With E. Reissner.)

60. Numerical solutions of boundary value problems in ODE, Appl. Math. Notes 7, 1982,
Pgs 40-52. (An educational note.)

61. Fundamentals of Linear Theory of Elasticity, I.A.M.S. Tech. Report 82-17, UBC, Vancouver, November, 1982. (Lecture notes.)

62. Mathematical models and their formulation, Handbook of Applied Mathematics, Chapter XIX (2nd Ed.), Ed. C. Pearson, Van Nostrand Reinhold Co., New York, 1983, Pgs 1044-1138.

63. Optimal forest harvesting with ordered site access, Studies in Appl. Math. 68, 1983, Pgs 189-226. (Also presented at the 3rd CFMC, London (Ontario), May, 1980.) (With K. Anderson.)

64. Long time behavior, Appl. Math. Notes 8, 1983, Pgs 45-58. (An educational note.)

65. Lecture Notes on the Theory of Thin Elastic Shells, I.A.M.S. Tech. Report Pgs 83-11, UBC, Vancouver, July, 1983. (Lecture Notes.)

66. Linear Plate Theory, I.A.M.S. Tech. Report Pgs 83-15, UBC, Vancouver, September, 1983. (Lecture notes.)

67. Finite polar dimpling of shallow caps under sub-buckling axistmmetric pressure distributions, SIAM J. of Appl. Math. 44, 1984, Pgs 301-326. (Also presented at the XVth ICTAM, Toronto, 1980.) (With D.F. Parker.)

68. The interspike interval of a cable model neuron with white noise input, Biological Cybernetics 49, 1984, Pgs 155-167. (With H.C. Tuckwell and Y.S. Wong.)

69. Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory, J. of Elasticity 4, 1984, Pgs 27-64. (Also presented at CAMS/SCMA Annual Meeting, Vancouver, May, 1984.) (With R.D. Gregory.)

70. Optimal harvesting of ongoing forest, Math. Models of Renewable Resources, II, (Proc. 2nd Pacific Coast Conf. on Math. Modelling of Renewable Resources, Univ. of Victoria, May 5-7, 1983), Ed. R. Lamberson, Humboldt State Univ. Math. Modeling Group, 1984, Pgs 117-122.

71. Shallow caps with a localized axisymmetric load distribution, Flexible Shells (Proc. of European Mechanics Colloq. No. 165, Munich, July, 1983), Ed. E.L. Axelrad & F.A. Emmerling, Springer-Verlag, Berlin-Heidelberg-New York, 1984, Pgs 124-145.

72. First passage time of Markov processes to moving barriers, J. Appl. Probability 21, 1984, Pgs 695-709. (With Henry C. Tuckwell.)

73. The linear theory of elastic plates, Applied Math. Notes 9, 1984, Pgs 19-37. (Revised version published as Appl. Math. Tech. Rep. No. 85-3, Part I, Univ. of Wash., Seattle, March, 1985.) (An educational note.)

74. Lecture notes on shallow shell theory, I.A.M.S. Tech. Report 84-8, UBC Vancouver, B.C., July, 1984. (Lecture notes.)

75. Lecture notes on the linear theory of thin elastic shells of revolution, I.A.M.S. Tech. Report 84-9, UBC, Vancouver, August, 1984. (Lecture notes.)

76. Asymptotic solutions of steadily spinning shallow shells of revolution under uniform pressure, Int'l. J. Solids & Structures 21, 1985, Pgs 27-53. (Also presented at SIAM Summer Meeting, Seattle, July, 1984.) (With Y. H. Lin.)

77. On plate theories and Saint-Venant's Principle, Int'l. J. Solids & Structures 21, 1985,
Pgs 1005-1024. (Also presented at a Symposium in Honor of E. Reissner, Vancouver, June, 1983.) (With R.D. Gregory.)

78. Edge effects in the stretching of plates, Local Effects in the Analysis of Structures (Proc. Euro. Mech. Colloq. No. 191, Cachan, August, 1984), Ed. P. Ladevèze, Elsevier Science Publ. BV. Amsterdam, 1985, Pgs 35-54. (With R.D. Gregory.)

79. Dynamic stability of polar dimpling, Proc. of Int'l. Conf. Nonlinear Mechanics. Ed. W.-z. Chien, Science Press, Beijing, China, 1985, Pgs 340-345. (With T.-q. Yun.)

80. Ordered site access and optimal forest rotation, Studies in Applied Math. 73, 1985, Pgs 155-175. (Also presented at CAMS/SCMA Annual Meeting, Edmonton, June, 1985.)

81. Stress function methods in plate theory, Applied Math. Notes 11, 1986, Pgs 5-24. (An educational note.)

82. On the effect of transverse shear deformability on stress concentration factors for twisted and sheared shallow spherical shells, J. Appl. Mech. 53, 1986, Pgs 597-601. (Also presented at ASME Winter Meeting, Anaheim, December, 1986.) (With E. Reissner.)

83. Boundary layer solutions for some nonlinear elastic membrane problems, J. Appl. Math. and Phys. (ZAMP) 38, 1987, Pgs 79-91. (With H.J. Weinitschke.)

84. Bounded domain approximation of unbounded domain problems, Proc. Can. Congr. Appl. Mech. (Edmonton) 1987, D62-D63. (With J. Yu.)

85. On lateral buckling of end-loaded cantilevers, including the effect of warping stiffness, Computational Mechanics 2, 1987, Pgs 137-147. (With E. Reissner and J.E. Reissner.)

86. Stress singularities at a rim of orthotropic cylinders, Appl. Math., Fluid Mech., Astrophys. (Proc. Symp. to Honor C.C. Lin, Cambridge, 1987), D.J. Benney, F. Shu and C. Yuan, eds., World Scientific, Singapore-N.J.-Hong Kong, 1988, Pgs 49-56. (With Y.H. Lin.)

87. First integrals and the interior solution for orthotropic plates in plane strain or axisymmetric deformations, Studies in Appl. Math. 79, 1988, Pgs 93-125. (Also presented at the ASME Summer Meeting, Berkeley, June, 1988.) (With Y.H. Lin.)

88. The interior solution for linear problems of elastic plates, J. Appl. Mech. 55, 1988, Pgs 551-559. (Also presented at the 10th U.S. National Congr. of Appl. Mech. Austin, June, 1986.) (With R.D. Gregory.)

89. Shells of revolution with the Love-Kirchhoff hypotheses, J. Engr. Math. 22, 1988, Pgs 285-334. (With H.J. Weinitschke.)

90. On the equations of flexual motions for shear-deformable plates, Proc. of Pan American Congress of Applied Mechanics (Rio de Janeiro, 1989), C.R. Steele and L. Bevilacqua, eds., Amer. Acad. Mech., 1989, Pgs 616-619.

91. Mathematical Models and Their Analysis, Harper and Row, February, 1989.

92. Interior solutions for slender and thin elastic bodies with prescribed displacement end data, Proc. ASME Symp. on Analytical and Computational Models for Shells (San Francisco, 1989), ed. A.K. Noor et al., ASME Publ., New York, 1989, Pgs 55-70.

93. Semi-infinite cantilevered orthotropic strips and the foundations of plate theories, Studies in App. Math. 82, 1990, Pgs 217-244. (With Y.H. Lin.)

94. Boundary layers and Saint-Venant's Principle for slender and thin elastic bodies, Advances in the Theories of Plates and Shells. G.Z. Voyiadjis and D. Karamanlidis, eds., Elsevier Sci. Publ. B.V., Amsterdam, 1990, Pgs 153-173.

95. Finite axial extension and torsion of elastic helicoidal shells, Proc. of a Symp. of Asymptotic and Computational Analysis (in honor of F. Olver, Winnipeg, 1989), ed. R. Wong, Marcel Dekker, New York and Basel, 1990, Pgs 491-516.

96. Bending and flexure of semi-infinite cantilevered strips, Frontiers in Computational Mechanics (Proc. Symp. in Honor of T.H.H. Pian, Cambridge, 1989, S.N. Atluri and P. Tong, guest eds.), Computers & Structures 35, 1990, Pgs 349-359. (With Y.H. Lin.)

97. Cylindrical bending of thick plates, Int. J. Solids and Structures 29, 1992, Pgs 547-557. (Also, presented at the Symposium on Contemporary Developments in Solid Mechanics, Pasadena, 1991.)

98. A follower load buckling problem for rectangular plates, J. Appl. Mech. 59, 1992, Pgs 674-676. (With E. Reissner.)

99. Perturbation solutions for the second-best land use problem, Can. Appl. Math. Quart. 1, 1993, Pgs 1-35. (Also presented at the International Symp. on Nonlinear Problems in Science and Engineering, Beijing, Oct. 1991.)

100. Correct asymptotic theories for the axi-symmetric deformation of thin and moderately thick cylindrical shells, Int. J. Solids Structures 30, 1993, Pgs 1957-1981. (with R.D. Gregory)

101. Torsion of slender prismatic elastic bodies, Studies in Appl. Math. 89, 1993, Pgs 63-94.

102. Shear center for plates of variable thickness, Proc. of Pan American Congress of Applied Mechanics, III (Sao Paolo, Brazil, January 8-16, 1993), D.T. Mook and D.L. Zagottis, eds., Amer. Acad. Mech., 1993, Pgs 604-607. (with C. H. Gu)

103. Circular elastic plates with prescribed axi-symmetric edge displacements, Can. Appl. Math. Quart. 1, 1993, Pgs 311-342. (With Y.H. Lin.)

104. Approximate solutions for the shear center of orthotropic plates, Arch. Appl. Mech. 63, 1993, Pgs 513-521. (With C. H. Gu)

105. Further consideration of the stress concentration problems for twisted or sheared shallow spherical shells, Int. J. solids Structures 31, 1994, Pgs 2153-2165. (With E. Reissner)

106. Boundary conditions at the edge of a thin or thick plate bonded to an elastic support, J. Elasticity 39, 1994, Pgs 155-182. (with R.D. Gregory)

107. Introduction to the Calculus of Variations and Its Applications, Chapman & Hall, January, 1995

108. Outer asymptotic solution without matching, A World of Shell, Festschrift in Honor of
Peter G. Glockner, ed. M. Epstein, University of Calgary (Mechanical Engineering),
April, 1995, Pgs 93-143.

109. On shear center for plates of variable thickness, Proc. 3rd Asian-Pacific Conference on Computational Mechanics (Seoul/September), Vol. 1, ed. C-K Choi, C-B Yun and D-G Lee, Techno-Press (Korea), 1996, Pgs 299-304. (with R.D. Gregory and C.H. Gu)

110. The cantilever strip plate under torsion, bending or flexure at infinity, J. Elasticity 43, 1997, Pgs 109-136. (with R.D. Gregory and C.H. Gu)

111. The axi-symmetric deformation of a thin, or moderately thick, elastic spherical cap,
Studies in Appl. Math. 100, 1998, Pgs 67-94. (with R.D. Gregory and T.I. Milac)

112. A thick hollow sphere compressed by equal and opposite concentrated axial loads; an asymptotic solution, SIAM J. Appl. Math. 59(3), 1999, Pgs 1080-1097. (with R.D. Gregory and T.I. Milac)

113. Static-geometric duality and stress concentration in twisted and sheared shallow spherical shells, Computational Mechanics, 22, 1999, Pgs 437-442. (with E. Reissner)

114. Locational equilibrium models for publicly owned residential land, Natural Resource Modeling 13 (2), 2000, Pgs 219-246. (Also issued as a special volume on Application of Asymptotic Methods to Resource Modeling Problems, ed. L. Kalachev.)

115. First passage time to detection in stochastic population dynamical models for HIV-1,
Applied Math. Letters 13, 2000, Pgs 79-83. (with H.C. Tuckwell)

116. Professor Eric Reissner (January 5, 1913 - November 1, 1996), Z. angew. Math. Phys. 51 (4), 2000, Pgs 1-2.

117. Outer solution for elastic torsion by the method of boundary layer residual states,
Z. angew. Math. Phys. 51 (4), 2000, Pgs 509-529.

118. Nature of equilibria and effects of drug treatments in some viral population dynamical models, IMA J. Math. Appl. Med. & Biol. 17, 2000, Pgs 311-327. (with H.C. Tuckwell)

119. Effect of non-linearity on lateral buckling of end-loaded cantilevers with transverse shear deformations, Advances in the Mechanics of Plates and Shells, the Libai Festschrift, eds. D. Durban, D. Givoli, & J.G. Simmonds, Kluwer Academic Publishers, 2001, Pgs 343-350.

120. An asymptotic analysis of the three-dimensional displacements and stresses in a spherical shell under inward radially opposed concentrated surface loads, Int. J. Solids Structures 38, 2001, Pgs 6869-6887. (with J.G. Simmonds)

121. The Nonlinear Theory of Elastic Shells, 2nd Ed., SIAM Reviews 43, 2001, Pgs 744-747.

122. The cantilever strip plate of varying thickness and the centre of shear, Quart. J. Mech. App. Math. 55, 2002, Pgs. 29-48. (with R.D. Gregory and C.Gu)

123. A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current, Biol. Cybern. 86, 2002, Pgs 137-145. (with H.C. Tuckwell & J.-P. Rospars)

124. Analytical determination of firing times in stochastic nonlinear neural models, Letters, Neurocomuting, 48, 2002, Pgs. 1003-1007. (with H.C. Tuckwell and Rodriguez)

125. Do morphogen gradients arise by diffusion?, Dev. Cell, 2, 2002, Pgs. 785-796. (with A.D. Lander and Q. Nie)

126. Determination of Firing Times for the Stochastic Fitzhugh-Nagumo Neuronal Model, Neural Comp., 15, 2003, Pgs. 143-159. (with H.C. Tuckwell and Rodriguez)

127. Stress Boundary conditions for plate bending, Int. J. Solids Structures, 40, 2003, Pgs. 4107-4123.

128. Can morphogen activity be enhanced by its inhibitors?, Proc. 2nd MIT Conf. on Comp. Mech., 2, Ed. K.J. Bathe, Elsevier Science Ltd, 2003, Pgs. 1729-1734.

129. Bifurcation Analysis of Shallow Spherical Shells with Meridionally Nonuniform Loading, Proc. IUTAM Sympo. on Complementary, Duality and Symmetry, Ed. David Gao, Kluwer 2004 Academic Publ. Norwell MA, Pgs. 141-157.

130. Nonlinear Eigenvalue Problems in the Stability Analysis of Morphogen Gradients, Studies in Appl. Math., 113, 2004, Pgs. 183-215. (with Y. Lou Q. Nie)

131. On the behavior of solutions in viral dynamical models, BioSystems, 73 (No. 3), 2004, Pgs. 157-161. (with H.C. Tuckwell)

132. Aggregation of a distributed ligand source and morphogen gradients, Studies in Appl. Math., 114, 2005, Pgs. 343-374. (with A.D. Lander, Q. Nie. and B. Varga)

133. Spatially distributed morphogen synthesis and morphogen gradient formation, Math. Biosci. & Eng. (MBE), 2 , 2005, Pgs. 239 – 262. (with A.D. Lander and Q. Nie)

134. Formation of the BMP activity gradient in the Drosophila embryo, Dev. Cell, 8, 2005, Pgs. 1-10 [plus supplement]. (with C.M. Mizutani, Q. Nie, Y.-T. Zhang, P. Vilmos, E. Bier, J.L. Marsh and A.D. Lander) (Supplemental on Materials)

135. Effects of Sog on Dpp-receptor binding, SIAM J. Appl. Math., 65, 2005, Pgs. 1748 - 1771. (with Y. Lou and Q. Nie)

136. Time to first spike in Hodgkin-Huxley stochastic systems, Physica A - Stat. Mech. Applic., 351 (2-4), 2005, Pgs. 427-438. (with H.C. Tuckwell)

137. Internalization and end flux in morphogen gradient formation, J. Comp. Appl. Math, 190, 2006, Pgs. 232-251. (with A.D. Lander and Q. Nie)

138. Membrane associated non-recptors and morphogen gradients, Bulletin of Math. Bio., 69, 2007, Pgs. 33-54. (with A.D. Lander and Q. Nie)

139. Wingless directly represses DPP morphogen expression via an Armadillo/TCF/Brinker complex, PLoS ONE, 2007, 1 (e142, doi:10.1371/journal.pone.0000142), Pgs. 1-10 [plus supplement, 1-14, and figures, S1-S6]. (with H. Theisen, A. Syed, B.T. Nguyen, T. Lukacsovich, J. Purcell, G.P. Srivastava, D. Iron, K. Gaudenz, Q. Nie,M.L. Waterman, and J. L. Marsh)

140. Elastodynamics of embryonic epidermal wound closure, Studies in Appl. Math., 118, 2007, Pgs. 365-395. (with A. Sadovsky)

141. Negative feedback in morphogen gradients, Frontiers of Applied Mathematics (Proc. of 2nd International Symposium, June, 2006, Beijing, Ed. D.-Y. Hsieh, M. Zhang & W. Sun), World Scientific, NJ, 2007, Pgs. 29-51. (with M. Khong)

142. Experimental methods for measuring in vivo mechanical properties of Angiosperm Roots, J. Engrg Mat. & Tech., 2007, 129, 2007, 483-487. (with P. Baldi and A. Sadovsky)

143.Selective pressures for and against genetic instability in cancer: a time-dependent problem, J. Royal Society, Interface, 5, 2008, Pgs. 105-121 (Online, June 19, 2007, doi: 10.1098/rsif.2007.1054). (with N. Komarova and A. Sadovsky)

144. The role of feedback in the formation of morphogen territories, Math. Biosci. & Eng. (MBE), 5 (No.2), 2008, Pgs. 277 –298. (with D. Iron, A. Syed, H. Theisen, T. Lukacsovich, M. Naghibi, J.L. Marsh, and Q. Nie)

145. Compact integration factor methods in high spatial dimension, J. Comp. Phys., 227, 2008, Pgs. 5238-5525. (with Q. Nie, F.Y.M. Wan, Y.-T. Zhang and X.-F. Liu)

146. Feedback regulation in multistage cell lineages, Math. Biosci. & Eng., 6(1), 2009, Pgs. 59-82. (W.-C. Lo, C.-S. Chou, K. Gokoffski, A.D. Lander, A.L. Calof and Q. Nie)

147. Localized ectopic expression of Dpp receptors in a Drosophila embryo, Studies in Appl. Math., 123, 2009, Pgs. 175 - 214. (with A.D. Lander, Q. Nie and Y.-T. Zhang)

148. Cell lineages and the logic of proliferative control, PLoS Biology, 7(1), 2009, Pgs. 0084 - 0100. (with A.D. Lander, K. Gokoffski, Q. Nie, and A.L. Calof)

149. The measures of success: constraints, objective, and tradeoffs in morphogen-mediated patterning, Cold Soring Harbor Perspect. in Biol. 2009; 1:a002022. (with A.D. Lander, W.-C. Lo, and Q. Nie)

150. Genetic instability in cancer: an optimal control problem, Studies in Appl. Math., Vol. 125(1), 2010, Pgs. 1 - 10. (with A. Sadovsky and N. L. Komarova)

151. Spatial dynamics of multi-state cell lineages in tissue stratification, Biophysical J. Vol. 99 (10), 2010, Pgs. 3145-3154. (with C.-S. Chiou, W. Lo, K. Gokoffski,Y.-T.Zhang, A.D. Lander, A.L. Calof, and Q. Nie)

152. Size-normalized robustness of Dpp gradient in Drosophila wing imaginal disc, JoMMS Vol. 6 (1-4), 2011, Pgs. 321-350. (with A.D. Lander, Q, Nie, and B. Vargas)

153. Robustness of signaling gradient in Drosophila wing imaginal disc, J. DCDS-B (Discrete and Continuous Dynamical Systems, Series B), 16 (3) 2011, Pgs. 835-866. (with J. Lei, A.D. Lander, and Q. Nie)

154. Robustness of morphogen gradients with "Bucket Brigade" transport througD. Wang,h membrane-associated non-receptors, J. DCDS-B (Discrete and Continuous Dynamical Systems, Series B) Vol. 18(3), 2013, Pgs. 721-739. (with J.-Z. Lei, D. Wang, Y. Song and Q. Nie)

155. A new approach to feedback for robust signaling gradients, Studies in Appl. Math. 133, 2014, 18-51. (with T. Kushner abd A. Simonyan)

156. Cell-surface bound non-receptors and morphogen gradients, Studies in Appl. Math. 133 (2), 2014, Pgs. 151-181. (DOI: 10.1111/sapm.12030)

157. Fastest time to cancer by loss of tumor suppressor genes, Bull. Math Bio.. 76. 2014, 2737-2784. (with C. Sanchez-Tapia)

158. Robust and precise morphogen-mediated patterning: trade-offs, constraints and mechanisms, Interface, J. Royal Soc. 12 . 2014, Pgs. 1014-. (with W.-C. Lo, S. Zhou, A.D. Lander and Q. Nie)

159. Transient Feedback and Robust Signaling Gradients, Int. J. Num. Anal. & Modeling, Series B, 13 (2), 2016, Pgs.175-200.  (with A. Simonyan)  

160.  Timing of CD8 T cell effector responses in viral infections, Royal Society Open Science, 2016, to appear.  (with S.R. Stipp, A. Iniguez, and D. Wodarz)









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