Transport phenomena in living systems and continuum physics

Rivista del Nuovo Cimento

Volumn 30, Issue 11, 2007, Pages 485-564

  Grillo, A ^a,b   Zingali, G ^c   Borrello, D ^c   Giaquinta, G ^b,c  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b CNISM Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia   (Italy)

^c UNIVERSITY OF CATANIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44449091622     PISSN: 0393697X     EISSN: None     Source Type: Journal    
DOI: 10.1393/ncr/i2007-10026-6     Document Type: Article

References (130)

1. MARSDEN J. E. and HUGHES T. G. R., Mathematical Foundations of Elasticity (Dover Publications Inc., New York) 1983.
2. ERINGEN A. C., Mechanics of Continua (John Wiley & Sons, Inc:, New York) 1980.
3. LANCZOS C., The Variational Principles of Mechanics, 4th edition (Dover Publications Inc., New York) 1970.
4. LANDAU L. D. and LIFSHITZ E. M., Mechanics (Pergamon Press, Oxford, London, Paris).
5. LIU I-SHIH, Continuum Mechanics (Springer, Berlin-Heidelberg-New York) 2002.
6. MAUGIN G. A., Material Inhomogeneities in Elasticity (Chapman & Hall/CRC, CRC Press Company, London, New York) 1993.
7. HOLZAPFEL G. A., GASSER T. C. and OGDEN R., J. Elasticity, 61 (2000) 1.
8. EPSTEIN M. and MAUGIN G. A., Int. J. Plast., 16 (2000) 951.
9. LANDAU L. D. and LIFSHITZ E. M., Theory of Elasticity (Pergamon Press, Oxford, London, Paris) 1960.
10. OGDEN R. W., Non-linear Theory of Elasticity (Dover, New York) 1997.
11. SMIRNOV V. I., A Course of Higher Mathematics: Integral Equations and Partial Differential Equations (Pergamon Press, Oxford, London) 1964.
12. TRUESDELL C. and TOUPIN R., in The Classical Field Theories. Handbuch der Physik, edited by FLÜGGE S., Vol. III/3 (Springer, Berlin-Heidelberg-New York) 1960.
13. TRUESDELL C. and NOLL W., in The non-Linear Field Theories of Mechanics, Handbuch der Physik, edited by FLÜGGE S., Vol. III/3 (Springer, Berlin-Heidelberg-New York) 1965.
14. ŠILAVY M., The Mechanics and Thermodynamics of Continuous Media (Springer, Berlin, New York) 1997.
15. DAY W. A., The Thermodynamics of Simple Materials with Fading Memory (Springer-Verlag, New York, Heidelberg, Berlin) 1972.
16. ERINGEN A. C., Non-local Continuum Field Theories (Springer-Verlag, New York, Inc.) 2002.
17. REED M. and SIMON B., Methods of Modern Mathematical Physics: I Functional Analysis (Academic Press, San Diego, New York) 1980.
18. TRUESDELL C., Rational Thermodynamics, 2nd edition (Springer-Verlag, New York-Berlin) 1984.
19. MAUGIN G. A., The Thermomechanics of Nonlinear Irreversible Behaviours - An Introduction (World Scientific, Singapore) 1999.
20. GILES R., Mathematical Foundations of Thermodynamics (Pergamon Press, Oxford) 1964.
21. CALLEN H. B., Thermodynamics - An Introduction to Thermostatics, 2nd edition (John Wiley & Sons, Inc., New York) 1985.
22. COLEMAN B. D. and NOLL W., Rev. Mod. Phys., 33 (1961) 239.
23. FABRIZIO M. and MORRO A., Mathematical Problems in Linear Viscoelasticity (Society for Industrial and Applied Mathematics, Philadelphia) 1992.
24. MAUGIN G. A., Nonlinear Waves in Elastic Crystals (Oxford University Press, New York, Inc.) 1999.
25. FOSDIK R. L. and SERRIN J., J. Elasticity, 9 (1979) 83.
26. FEDERICO S., GRILLO A., IMATANI S., GIAQUINTA G. and HERZOG W., Int. J. Eng. Sci., 46 (2007) 164.
27. FEDERICO S., GRILLO A., GIAQUINTA G. and HERZOG W., Meccanica DOI 10 1007/s11012-007-9090-6.
28. COWIN S. C., J. Biomech. Eng., 122 (2000) 553.
29. COWIN S. C., Annu. Rev. Biomed. Eng, 6 (2004) 77.
30. HUMPHREY J. D., Proc. R. Soc. London, Ser. A, 459 (2003) 3.
31. FUNG Y. C., Biomechanics-Motion Flow, Stress and Growth (Springer-Verlag Inc., New York) 1990.
32. DAVYDOV A. S., Solitons in Molecular Systems (Kluwer Academic, Dordrecht) 1991.
33. BEDFORD A., Hamilton's Principle in Continuum Mechanics (Pitman Advanced Publishing Program, Boston, London, Melbourne) 1985.
34. MAUGIN G. A. and TRIMARCO C., Acta Mech., 94 (1992) 1.
35. MAUGIN G. A., Rend. Sem. Mat. Univ. Pol. Torino, Geom., Cont. and Micros. II, 58 (2000).
36. MAUGIN G. A., Theor. Appl. Mech., 28-20 (2002) 221.
37. MAUGIN G. A., Tech. Mech., 22, Heft 2 (2002) 98.
38. MAUGIN G. A., Theor. Appl. Mech., 27 (2002) 1.
39. MAUGIN G. A., Nonlinear Waves in Elastic Crystals (Oxford University Press, New York, Inc.) 1999.
40. YAPPA Y. A. and NOVOZHILOV Y. V., Electrodynamics (MIR Publishers, Moscow) 1981.
41. MAUGIN G. A. and KALPAKIDES V. K., Tech. Mech., 22 (2002) 98.
42. HILL E. L., Rev. Mod. Phys., 23 (1951) 253.
43. TABER L. A., Appl. Mech. Rev., 48 (1995) 487.
44. AMBROSI D. and MOLLICA F., Int. J. Eng. Sci., 40 (2002) 1297.
45. AMBROSI D. and MOLLICA F., J. Math. Biol., 48 (2004) 477.
46. RODRIGUEZ E. K., HOGER A. and MCC ULLOCH A. D., J. Biomech., 27 (1994) 455.
47. COWIN S. C. and HEGEDUS D. H., J. Elasticity, 6 (1976) 313.
48. EPSTEIN M. and MAUGIN G. A., Acta Mech., 83 (1990) 127.
49. GRILLO A., FEDERICO S., GIAQUINTA G., HERZOG W. and LA ROSA G., Theor. Appl. Mech., 30 (2003) 311.
50. GRILLO A., ZINGALI G., FEDERICO S., HERZOG W. and GIAQUINTA G., Theor. Appl. Mech., 1 (2005) 21.
51. FELSAGER B., Geometry, Particles, and Fields (Springer, New York, Berlin, Heidelberg) 1998.
52. MARSDEN J. E., PEKARSKY S., SHKOLLER S. and WEST M., J. Geom. Phys., 38 (2001) 253.
53. STRUCKMEIER J. and RIEDEL C., Phys. Rev. E, 66 (2002) 1.
54. IMATANI S. and MAUGIN G. A., Mech. Res. Commun., 29 (2002) 477.
55. LUBARDA V. A. and HOGER A., Int. J. Solids Struct., 39 (2002) 4627.
56. BAKŠA A., Theor. Appl. Mech., 26 (2001) 169.
57. BOWEN R. M., Part I: Theory of Mixtures in Continuum Physics, Vol. III - Mixtures and EF Field Theories, edited by ERINGEN A. C. (Academic Press, New York) 1976.
58. KIENZLER R. and HERMANN G., Acta Mech., 161 (2003) 103.
59. KIENZLER R. and HERMANN G., Mechanics in Material Space With Applications in Defect and Fracture Mechanics (Springer-Verlag, Berlin) 2000.
60. BOGOLIUBOV N. N. and SHIRKOV D. V., Introduction to the Theory of Quantized Fields, Vol. III (Interscience Publishers Ltd, London) 1959.
61. PENFIELD P. and HAUS H. A., Electrodynamics of Moving Media Research Monograph No. 40 (MIT Press, Cambridge, Massachussets) 1967.
62. RAJAGOPAL K. R., Rep. Inst. Comput Appl. Mech., 6 (1995).
63. RAJAGOPAL K. R. and SRINIVASA A. R., J. Non-Newton Fluid, 88 (2000) 207.
64. QUILIGOTTI S., Theor. Appl. Mech., 28-29 (2002) 277.
65. KANNAN K., RAO I. J. and RAJAGOPAL K. R., J. Rheol., 46 (2002) 977.
66. YAVARI A., MARSDEN J. E. and ORTIZ M., J. Math. Phys., 47 (2006) 042903-1.
67. DOYLE T. C. and ERICKSEN J. L., Adv. Appl. Mech., 4 (1956) 4.
68. NELSON D. F., Phys. Rev., 44 (1991) 3985.
69. AMBROSI D. and PREZIOSI L., Math. Mod. Meth. Appl. S., 12 (2002) 737.
70. BYRNE H. M. and PREZIOSI L., Math. Med. Biol., 20 (2003) 341.
71. BELLOMO N., DE ANGELIS E. and PREZIOSI L., J. Theor. Med., 5 (2003) 111.
72. MOFFATT H. K., Rep. Prog. Phys., 46 (1983) 621.
73. WIEGEL F. V., Introduction to Path Integral Methods in Physics and Polymer Science (World Scientific Publishing Co., Pte., Ltd., Singapore, USA) 1986.
74. DE ANGELIS E. and PREZIOSI L., Math. Mod. Meth. App. S., 10 (2000) 379.
75. MIKHAILOV M. D. and ÖZIŞK M. N., Unified Analysis and Solutions of Heat and Mass Diffusion (Dover Publications Inc., New York) 1984.
76. DITTIRICH W. and REUTER M., Classical and Quantum Mechanics (Springer, Berlin, New York) 2001
77. KAC M., Probability and Related Topics in Physical Sciences (Interscience Publishers, Ltd., London) 1959.
78. KLEINERT H., Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific Publishing Co., Pte., Ltd., New York, London, Hong Kong) 1995.
79. RAJAGOPAL K. R. and TAO L., Mechanics of Mixtures (World Scientific, Singapore) 1995.
80. FARINA A. and PREZIOSI L., Int. J. Nonlinear Mech., 37 (2002) 485.
81. KLISCH S. M., CHEN S. S., SAH R. L. and HOGER A., J. Biomech. Eng., 125 (2003) 169.
82. GARIKIPATI K., ARRUDA E. M., GROSH K., NARAYANAN H. and CALVE S., J. Mech. Phys. Solids, 52 (2004) 1595.
83. HAKEN H., Quantum Field Theory of Solids. An Introduction (North-Holland Publishing Company) 1983.
84. MARSDEN J. E., MONTGOMERY R. and RATIU T., Reduction, Symmetry and Phases in Mechanics (First of two numbers) (American Mathematical Society) 1990.
85. MUSKAT M., The Flow of Homogeneous Fluids through Porous Media (Ann Arbor, MI Edwards) 1937.
86. POLUBORINOVA-KOCHINA P. YA., The Theory of Ground Water Movement (Princeton University Press, Princeton, New Jersey) 1962.
87. SCHEIDEGGER A. E., Physics of Flow through Porous Media (University of Toronto Press, Toronto) 1974.
88. JOST W., Diffusion in Solids, Liquids, and Gases (Academic Press, New York) 1952.
89. BOSWORTH R. C. L., Transport Processes in Applied Chemistry (Pitman, London) 1956.
90. CARMAN P. C., Flow of Gases through Porous Media (Academic Press, New York) 1956.
91. CRANK J., The Mathematics of Diffusion (Clarendon Press, Oxford) 1956.
92. RAJAGOPAL K. R., Mater. Sci. Tech. Ser., 19 (2003) 1175.
93. HASSANIZADEH S. M., Adv. Water Res., 9 (1986) 196.
94. HASSANIZADEH S. M. and GRAY W. G., Adv. Water Res., 2 (1979) 131.
95. HASSANIZADEH S. M. and GRAY W. G., Adv. Water Res., 2 (1979) 191.
96. HASSANIZADEH S. M. and GRAY W. G., Adv. Water Res., 3 (1980) 25.
97. LORET B. and SIMÕES F. M. F., Eur. J. Mech. A-Solids, 24 (2005) 757.
98. BEAR J., Dynamics of Fluids in Porous Media (American Elsevier, New York) 1972.
99. GRAY W. G., Chem. Eng. Sci., 30 (1975) 229.
100. BLAKE T. R. and GARG S. K., Water Resour. Res., 12 (1976) 798.
101. BEAR J. and BACHMAT Y., Transport Phenomena in Porous Media. The Basic Equation in Fundamentals of Transport Phenomena in Porous Media, edited by BEAR J. J. and CORRAPCIOGLU M. Y. (Martinus Nijhof, Dordrecht) 1984.
102. CARBONELL R. G. and WHITAKER S., Heat and Mass Transfer in Fundamentals of Transport Phenomena in Porous Media, edited by BEAR J. J. and CORRAPCIOGLU M. Y. (Martinus Nijhof, Dordrecht) 1984.
103. HUMPHREY J. D. and RAJAGOPAL K. R., Biomech. Model. Mechanobiol., 2 (2003) 109.
104. KLISCH S. M. and HOGER A., Math. Mech. Solids, 8 (2003) 377.
105. AURIAULT J.-L. and ADLER P. M., Adv. Water Resour., 18 (1995) 217.
106. BYRNE H. M., KING J. R., MCELWAIN D. L. S. and PREZIOSI L., Appl. Math. Lett., 16 (2002) 567.
107. KING P. R., J. Phys. A: Math. Gen., 20 (1987) 3935.
108. CHAPLIA Y. and CHERNUKHA O., Int. J. Eng. Sci., 43 (2005) 1337.
109. GRILLO A., ZINGALI G., BORRELLO D., FEDERICO S., HERZOG W. and GIAQUINTA G., J. Phys.: Conf. Ser., 62 (2007) 43.
110. HASSANIZADEH S. M. and GRAY W. G., Adv. Water Res., 13 (1990) 169.
111. ATESHIAN G. A., Biomechan. Model. Mechanobiol., DOI: 10.1007/s10237-006-0070-x (2007).
112. GRILLO A., ZINGALI G., BORRELLO D., FEDERICO S., HERZOG W. and GIAQUINTA G., Theor. Appl. Mech., 34 (2007) 51.
113. DORMIEUX L., KONDO D. and ULM F.-J., Microporomechanics (John Wiley & Sons Ltd., England) 2006.
114. RUGGERI T., Continuum Mech. Therm., 1 (1989) 3.
115. RUGGERI T. and SIMIĆ S., Math. Meth. Appl. Sci., 30 (2007) 827.
116. QUILIGOTTI S., MAUGIN G. A. and DELL'ISOLA F., Acta Mech., 160 (2003) 45.
117. BENSOUSSAN A., LIONS J. L. and PAPANICOLAOU G. C., Asymptotic Analysis for Periodic Structures (North Holland, New York) 1978.
118. CIORANESCU D. and DONATO P., An Introduction to Homogenization (Oxford University Press, Oxford) 1999.
119. LUNATI P., ATTINGER S. and KINZELBACH W., Water Resour. Res., 30 (2002) 1187.
120. DE BOER R., Trends in Continuum Mechanics of Porous Materials - Theory and Applications of Transport in Porous Media (Springer, The Netherlands) 2005.
121. NICHOLSON C., Rep. Prog. Phys., 64 (2001) 815.
122. LEHNER F. K., Chem. Eng. Sci., 34 (1979) 821.
123. BIFERALE L., CRISANTI A., VERGASSOLA M. and VULPIANI A., Phys. Fluids, 7 (1995) 2725.
124. WU J. Z. and HERZOG W., J. Biomech., 35 (2002) 931.
125. FEERICO S., GRILLO A. and HERZOG W., J. Mech. Phys. Solids, 52 (2004) 2309.
126. FEDERICO S., GRILLO A., LA ROSA G., GIAQUINTA G. and HERZOG W., J. Biomech., 38 (2005) 2008.
127. THIFFEAULT J. L., Phys. Lett A, 309 (2003) 451.
128. CHAPLAIN M. A. J., Math. Comput Modelling, 23 (1996) 47.
129. SCALERANDI M., CAPOGROSSO SANSONE B. and CONDAT C., Phys. Rev. E, 65 (2001) 011902.
130. BULLOUGH W. S. and DEOL J. U., Symp. Soc. Exp. Biol., 25 (1971) 255.