Mathematical and experimental modeling of physical and biological processes

Mathematical and Experimental Modeling of Physical and Biological Processes

Volumn , Issue , 2009, Pages 1-293

  Banks, H T ^a   Tran, H T ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85060575637     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (114)

1. R. Aster, B. Borchers and C. Thurber, Parameter Estimation and Inverse Problems, Academic Press, New York, 2004.
2. H.T. Banks, S. Dediu and S.E. Ernstberger, Sensitivity functions and their uses in inverse problems, J. Inverse and Ill-posed Problems, 15, 2007, pp. 683-708.
3. H.T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989.
4. W.E. Boyce and R.C. Di Prima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc., Hoboken, 8th ed., 2004.
5. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, Springer, Berlin, 4th ed., 1992.
6. J.A. David, Optimal Control, Estimation, and Shape Design: Analysis and Applications, Ph.D. Dissertation, North Carolina State University, Raleigh, 2007.
7. J.M. Gere and S.P. Timoshenko, Mechanics of Materials, PWS Pub. Co., Boston, 4th ed., 1997.
8. A. Gilat, MATLAB: An Introduction with Applications, John Wiley & Sons, Inc., Hoboken, 2nd ed., 2004.
9. E. Laporte and P. Le Tallec, Numerical Methods in Sensitivity Analysis and Shape Optimization, Birkhauser, Boston, 2002.
10. R.K. Nagle, E.B. Saff and A.D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Pearson Education, Inc., Boston, 2004.
11. S.S. Rao, Vibration of Continuous Systems, John Wiley & Sons, Inc., Hoboken, 2007.
12. A. Saltelli, K. Chan and E.M. Scott, Sensitivity Analysis, John Wiley & Sons, Inc., Hoboken, 2000.
13. H.T. Banks, J.E. Banks, L.K. Dick and J.D. Stark, Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides, CRSC-TR05-22, May, 2005; Bulletin of Mathematical Biology, 69, 2007, pp. 2139-2180.
14. H.T. Banks, M. Davidian, J.R. Samuels, Jr., and K.L. Sutton, An Inverse Problem Statistical Methodology Summary, CRSC-TR08-01, January, 2008; Chapter XX in Statistical Estimation Approaches in Epidemiology, (edited by Gerardo Chowell, Mac Hyman, Nick Hengartner, Luis M.A Bettencourt and Carlos Castillo-Chavez), Springer, Berlin Heidelberg New York, to appear.
15. H.T. Banks, S. Dediu and S.E. Ernstberger, Sensitivity functions and their uses in inverse problems, J. Inverse and Ill-posed Problems, 15, 2007, pp. 683-708.
16. H.T. Banks, S.L. Ernstberger and S.L. Grove, Standard errors and confidence intervals in inverse problems: Sensitivity and associated pitfalls, CRSC-TR06-10, March, 2006; J. Inverse and Ill-posed Problems, 15, 2006, pp. 1-18.
17. H.T. Banks and B.G. Fitzpatrick, Inverse problems for distributed systems: statistical tests and ANOVA, LCDS/CCS Rep. 88-16, July, 1988, Brown University; Proc. International Symposium on Math. Approaches to Envir. and Ecol. Problems, Springer Lecture Note in Biomath., 81, 1989, pp. 262-273.
18. H.T. Banks and B.G. Fitzpatrick, Statistical methods for model comparison in parameter estimation problems for distributed systems, CAMS Tech. Rep. 89-4, September, 1989, University of Southern California; J. Math. Biol., 28, 1990, pp. 501-527.
19. H.T. Banks and P. Kareiva, Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models, J. Math. Biol., 17, 1983, pp. 253-272.
20. H.T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989.
21. R.J. Carroll and D. Ruppert, Transformation and Weighting in Regression, Chapman & Hall, New York, 1988.
22. G. Casella and R.L. Berger, Statistical Inference, Duxbury, California, 2002.
23. M. Davidian and D. Giltinan, Nonlinear Models for Repeated Measurement Data, Chapman & Hall, London, 1998.
24. B. Fitzpatrick, Statistical Methods in Parameter Identification and Model Selection, Ph.D. Thesis, Division of Applied Mathematics, Brown University, Providence, RI, 1988.
25. A.R. Gallant, Nonlinear Statistical Models, Wiley, New York, 1987.
26. F. Graybill, Theory and Application of the Linear Model, Duxbury, North Scituate, MA, 1976.
27. R.I. Jennrich, Asymptotic properties of non-linear least squares estimators, Ann. Math. Statist., 40, 1969, pp. 633-643.
28. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, 2001.
29. G.A.F. Seber and C.J. Wild, Nonlinear Regression, J. Wiley & Sons, Hoboken, NJ, 2003.
30. J.J. Batzel, F. Kappel, D. Schneditz and H.T. Tran, Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control, SIAM, Philadelphia, 2006.
31. C.J. Geankoplis, Transport Processes and Unit Operations, Prentice Hall, Englewood Cliffs, 1993.
32. K. Godfrey, Compartmental Models and Their Applications, Academic Press, New York, 1983.
33. J.A. Jacquez, Compartmental Analysis in Biology and Medicine, The University of Michigan Press, Ann Arbor, 1985.
34. R.K. Nagle, E.B. Saff and A.D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Pearson Education, Inc., Boston, 2004.
35. M. Reddy, R.S. Yang, M.E. Andersen and H.J. Clewell, III, Physiologically Based Pharmacokinetic Modeling: Science and Applications, Wiley-Interscience, Malden, 2005.
36. S. Strauss and D.W.A. Bourne, Mathematical Modeling of Pharmacokinetic Data, CRC Press, Boca Raton, 1995.
37. G.G. Walter and M. Contreras, Compartmental Modeling with Networks, Birkhauser, Boston, 1999.
38. H.T. Banks, S.R. Durso, M.A. Goodhart and K. Ito, Nonlinear exothermic contributions to radio-frequency bonding of adhesives, Center for Research in Scientific Computation, North Carolina State University, Technical Report, CRSC-TR98-24, 1998; Nonlinear Analysis: Theory Method and Applications; Series B, 2, 2001, pp. 257-286
39. H.T. Banks and F. Kojima, Boundary shape identification problems in two-dimensional domains related to thermal testing of materials, Quarterly of Applied Mathematics, Vol. XLVII, No. 2, 1989, pp. 273-293.
40. W. Boyce and R. Diprima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc., Hoboken, 8th ed., 2004.
41. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, John Wiley & Sons, Inc., New York, 1960.
42. C.J. Geankoplis, Transport Processes and Unit Operations, Prentice Hall, Englewood Cliffs, 1993.
43. D.M. Heath, C.S. Welch and W.P. Winfree, Quantitative thermal diffu- sivity measurements of composites, in Review of Progress in Quantitative Nondestructive Evaluation, D.G. Thompson and D.E. Chimenti (eds.), Plenum Publ., 5B, 1986, pp. 1125-1132.
44. F. Incropera and D. Dewitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 1990.
45. W. Kaplan, Advanced Calculus, Addison-Wesley Publishing Co., Inc., New York, 1991.
46. NIST Monograph 175, Temperature-Electromotive Force Reference Functions and Tables for the Letter-Designated Thermocouple Types Based on the ITS-90, NIST Monograph 175, 1993.
47. W.A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons, New York, 1992.
48. H.T. Banks, W. Fang, R.J. Silcox and R.C. Smith, Approximation methods for control of acoustic/structure models with piezoceramic actuators, Journal of Intelligent Material Systems and Structures, 4(1), 1993, pp. 98-116.
49. H.T. Banks, N.G. Medhin and G.A. Pinter, Multiscale considerations in modeling of nonlinear elastomers, CRSC-TR03-42, North Carolina State University, Raleigh, North Carolina, October, 2003; Journal of Computational Methods in Science and Engineering, 8, 2007, pp. 53-62.
50. H.T. Banks, R.J. Silcox and R.C. Smith, The modeling and control of acoustic/structure interaction problems via piezoceramic actuators: 2-D numerical examples, ASME Journal of Vibration and Acoustics, 116(3), 1994, pp. 386-396.
51. W.E. Boyce and R.C. Di Prima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc., Hoboken, 8th ed., 2004.
52. A.J. Bullmore, P.A. Nelson, A.R.D. Curtis and S.J. Elliott, The active minimization of harmonic enclosed sound fields, part II: A computer simulation, Journal of Sound and Vibration, 117(1), 1987, pp. 15-33.
53. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. II, Wiley, New York, 1962.
54. J.M. Gere and S.P. Timoshenko, Mechanics of Materials, PWS Pub. Co., Boston, 4th ed., 1997.
55. W. Kaplan, Advanced Calculus, Addison-Wesley Publishing Co., Inc., New York, 1991.
56. H.C. Lester and C.R. Fuller, Active control of propeller induced noise fields inside a flexible cylinder, AIAA 10th Aeroacoustic Conference, Seattle, WA, 1986.
57. E.P. Popov, Introduction to Mechanics of Solids, Prentice-Hall, Inc., Englewood Cliffs, 1968.
58. J.N. Reddy, An Introduction to the Finite Element Method, McGraw Hill Series in Mechanical Engineering, New York, 3rd ed., 2005.
59. R.C.H. del Rosario, H.T. Tran and H.T. Banks, Proper orthogonal decomposition based control of transverse beam vibrations: Experimental implementation, CRSC-TR99-43, North Carolina State University, Raleigh, North Carolina, 1999; IEEE Trans. on Control Systems Technology, 10, 2002, pp. 717-726.
60. K.R. Symon, Mechanics, Addison-Wesley Publishing Co., Reading, 1971.
61. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, Inc., New York, 1987.
62. O.C. Zienkiewicz and R.C. Taylor, Finite Element Method: Volume 1, The Basis, Butterworth-Heinemann, Newbury (UK), 5th ed., 2000.
63. B.D.O. Anderson and J.B. Moore, Linear Optimal Control, Prentice Hall, Englewood Cliffs, 1971.
64. P.J. Antsaklis and A.N. Michel, Linear Systems, The McGraw-Hill Companies, Inc., New York, 1997.
65. H.T. Banks, R.C. Smith and Y. Wang, Smart Material Structures: Modeling, Estimation and Control, Masson/John Wiley, 1996.
66. S. Barnett and R.G. Cameron, Introduction to Mathematical Control Theory, Oxford Applied Mathematics and Computing Science Series, 2nd ed., 1985.
67. W.L. Brogran, Modern Control Theory, Prentice Hall, Englewood Cliffs, 3rd ed., 1991.
68. Chi-Tsong Chen, Linear System Theory and Design, Oxford University Press, Inc., New York, 1999.
69. R. Datko, Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks, SIAM J. Control and Optimization, 26(3), 1988, pp. 697-713.
70. R. Datko, J. Laguese and M.P. Polis, An Example on the effect of time delays in boundary feedback stabilization of wave equations, SIAM J. Control and Optimization, 24(1), 1986, pp. 152-156.
71. E.J. Davison, On pole assignment in multivariable linear systems, IEEE Trans. on AC, AC-13(6), 1968, pp. 747-748.
72. Jack K. Hale and Sjoerd M. Verduyn Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences 99, SpringerVerlag, New York, 1993.
73. R.E. Kalman, On the general theory of control systems, Proc. First Internl. Cong. IFAC, Moscow, 1960, Automatic and Remote Control, 1961, pp. 481-92.
74. R.E. Kalman, Mathematical description of linear dynamical systems, SIAM J. on Control, Ser. A, 1(2), 1963, pp. 152-192.
75. J.D. Lambert, Computational Methods in Ordinary Differential Equations, John Wiley & Sons, New York, 1973.
76. A. Manitius, G. Payre, R. Roy and H.T. Tran, Computation of eigenvalues associated with functional differential equations, SIAM J. Sci. Stat. Comput., 8(3), 1987, pp. 222-247.
77. R.C.H. del Rosario, H.T. Tran and H.T Banks, Proper orthogonal decomposition based control of transverse beam vibrations: Experimental implementation, IEEE Trans. on Control Systems Technology, 10, 2002, pp. 717-726.
78. W.M. Wonham, On pole assignment in multi-input, controllable linear systems, IEEE Trans. on AC, AC-12(6), 1967, pp. 660-665.
79. J. Zabczyk, Mathematical Control Theory: An Introduction, Birkhauser, Boston, 1992.
80. H.T. Banks, W. Fang, R.J. Silcox and R.C. Smith, Approximation methods for control of acoustic/structure models with piezoceramic actu- actors, Journal of Intelligent Material Systems and Structures, 4(1), 1993, pp. 98-116.
81. H.T. Banks, G. Propst and R.J. Silcox, A comparison of time domain boundary conditions for acoustic waves in wave guides, Quarterly of Applied Mathematics, LIV(2), 1996, pp. 249-265.
82. H.T. Banks, R.J. Silcox and R.C. Smith, The modeling and control of acoustic/structure interaction problems via piezoceramic actuators: 2-D numerical examples, ASME Journal of Vibration and Acoustics, 116(3), 1994, pp. 386-396.
83. H.T. Banks and R.C. Smith, Modeling and approximation of a coupled 3-D structural acoustics problem, in Progress in Systems and Control Theory, K.L. Bowers and J. Lund, eds., Birkhauser, Boston, 1993, pp. 29-48.
84. H.T. Banks, R.C. Smith and Y. Wang, Smart Material Structures: Modeling, Estimation and Control, John Wiley & Sons, Inc., 1996.
85. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, John Wiley & Sons, Inc., New York, 1960.
86. C.J. Geankoplis, Transport Processes and Unit Operations, Prentice- Hall, Inc., 1993.
87. K.F. Graff, Wave Motion in Elastic Solids, Dover Publications, Inc., 1991.
88. H. Schlichting, Boundary-layer Theory, MacGraw-Hill, New York, 1979.
89. H.T. Banks, J.E. Banks, L.K. Dick and J.D. Stark, Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides, CRSC-TR05-22, NCSU, May, 2005; Bull. Math. Biol., 69 (2007), pp. 2139-2180.
90. H.T. Banks, J.E. Banks, L.K. Dick and J.D. Stark, Time-varying vital rates in ecotoxicology: selective pesticides and aphid population dynamics, Ecological Modelling, 210, 2008, pp. 155-160.
91. H.T. Banks, V.A. Bokil, S. Hu, F.C.T. Allnutt, R. Bullis, A. K. Dhar and C.L. Browdy, Shrimp biomass and viral infection for production of biological countermeasures, CRSC-TR05-45, NCSU, December, 2005; Mathematical Biosciences and Engineering, 3, 2006, pp. 635-660.
92. H.T. Banks, D.M. Bortz, G.A. Pinter and L.K. Potter, Modeling and imaging techniques with potential for application in bioterrorism, CRSC- TR03-02, NCSU, January, 2003; Chapter 6 in Bioterrorism: Mathematical Modeling Applications in Homeland Security, (H.T. Banks and C. Castillo-Chavez, eds.), Frontiers in Applied Math, FR28, SIAM, Philadelphia, PA, 2003, pp. 129-154.
93. H.T. Banks and J.L. Davis, A comparison of approximation methods for the estimation of probability distributions on parameters, CRSC-TR05- 38, NCSU, October, 2005; Applied Numerical Mathematics, 57, 2007, pp. 753-777.
94. H.T. Banks and J.L. Davis, Quantifying uncertainty in the estimation of probability distributions with confidence bands, CRSC-TR07-21, NCSU, December, 2007; Math. Biosci. Engr., 5, 2008, pp. 647-667.
95. H.T. Banks, J.L. Davis, S.L. Ernstberger, S. Hu, E. Artimovich, A.K. Dhar and C.L. Browdy, Comparison of probabilistic and stochastic formulations in modeling growth uncertainty and variability, CRSC-TR08- 03, NCSU, February, 2008; J. Biological Dynamics, to appear.
96. H.T. Banks, L.W. Botsford, F. Kappel and C. Wang, Estimation of growth and survival in size-structured cohort data: An application to larval striped bass (Morone Saxatilis), J. Math. Biol., 30, 1991, pp. 125-150.
97. H.T. Banks, L.W. Botsford, F. Kappel and C. Wang, Modeling and estimation in size-structured population models, in Proceeding 2nd Course on Mathematical Ecology, Trieste, 1986, World Press, Singapore, 1988, pp. 521-541.
98. H.T. Banks and B.G. Fitzpatrick, Estimation of growth rate distributions in size-structured population models, Quart. Appl. Math., 49, 1991, pp. 215-235.
99. H.T. Banks, B.G. Fitzpatrick, L.K. Potter and Y. Zhang, Estimation of probability distributions for individual parameters using aggregate population observations, in Stochastic Analysis, Control, Optimization and Applications (W.Mceneaney, G. Yin, Q. Zhang, eds.), Birkhauser, 1998, pp. 353-371.
100. L.W. Botsford, B. Vandracek, T. Wainwright, A. Linden, R. Kope, D. Reed and J.J. Cech, Population development of the mosquitofish, Gam- busia Affinis, in rice fields, Environ. Biol. Fishes, 20, 1987, pp. 143-154.
101. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, Springer, Berlin, 4th ed., 1992.
102. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. II, Wiley, New York, 1962.
103. P.A. Hackney and J.C. Webb, A method for determining growth and mortality rates of ichthyoplankton, in Proc. Fourth National Workshop on Entrainment and Impringement (L.D. Jenson, ed.), Ecological Analysts Inc., Melville, New York, 1978, pp. 115-124.
104. W. Kaplan, Advanced Calculus, Addison-Wesley Publishing Co., Inc., New York, 1991.
105. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, 2001.
106. J.A.J. Metz and O. Diekmann (eds.), The Dynamics of Physiologically Structured Populations, Lecture Notes in Biomathematics, 68, Springer, 1986.
107. R. Pearl and L.J. Reed, On the rate of growth of the population of the United States since 1790 and its mathematical representation, Proceedings of the National Academy of Sciences of the United States of America, 6, pp. 275-288.
108. J.W. Sinko and W. Streifer, A new model for age-size structure of a population, Ecology, 48, 1967, pp. 910-918.
109. P.F. Verhulst, Recherches mathematiques sur la loi d'accroissement de la population, Noveaux Meoires de l'Academie Royale des Sciences et Belles Lettres de Bruxelles, 18, pp. 3-38.
110. V. Volterra, Fluctuation in the abundance of a species considered mathematically, Nature, 118, pp. 558-560.
111. R. Buck, Advanced Calculus, McGrawHill, New York, 1978.
112. R. Courant, Differential and Integral Calculus, translation by E.J. McShane, Interscience, New York, 1937.
113. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. II, Wiley, New York, 1962.
114. W. Kaplan, Advanced Calculus, Addison-Wesley Publishing Co., Inc., New York, 2003.