메뉴 건너뛰기




Volumn 12, Issue 3, 2003, Pages 146-173

Weakly nonlocal irreversible thermodynamics

Author keywords

Cahn Hilliard; Ginzburg Landau; Guyer Krumhansl; Irreversible; Nonlocality

Indexed keywords

BOUNDARY CONDITIONS; CONTINUUM MECHANICS; DEGREES OF FREEDOM (MECHANICS); ENTROPY; FUNCTIONS; LAGRANGE MULTIPLIERS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING;

EID: 0038711960     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/andp.200310002     Document Type: Article
Times cited : (71)

References (92)
  • 1
    • 0038718190 scopus 로고
    • Geometrical and dynamical nonlocality
    • D. Rogula, Geometrical and dynamical nonlocality, Archives of Mechanics (Stosowanej) 31(1), 65-75 (1979).
    • (1979) Archives of Mechanics (Stosowanej) , vol.31 , Issue.1 , pp. 65-75
    • Rogula, D.1
  • 3
    • 0016079832 scopus 로고
    • Irreversible thermodynamics of nonlocal systems
    • D. G. B. Edelen, Irreversible thermodynamics of nonlocal systems, Int. J. Eng. Sci. 12, 607-631 (1974).
    • (1974) Int. J. Eng. Sci. , vol.12 , pp. 607-631
    • Edelen, D.G.B.1
  • 4
    • 0002877039 scopus 로고
    • Introduction to nonlocal theory of material media
    • edited by D. Rogula (Springer Verlag, Wien-New York)
    • D. Rogula, Introduction to nonlocal theory of material media, in: Nonlocal Theory of Material Media, Vol. 268 of CISM Courses and Lectures, edited by D. Rogula (Springer Verlag, Wien-New York, 1982), pp. 123-222.
    • (1982) Nonlocal Theory of Material Media, Vol. 268 of CISM Courses and Lectures , pp. 123-222
    • Rogula, D.1
  • 5
    • 0002795062 scopus 로고
    • Nonlocal theories or gradient-type theories: A matter of convenience?
    • G. A. Maugin, Nonlocal theories or gradient-type theories: a matter of convenience?, Archives of Mechanics (Stosowanej) 31(1), 15-26 (1979).
    • (1979) Archives of Mechanics (Stosowanej) , vol.31 , Issue.1 , pp. 15-26
    • Maugin, G.A.1
  • 6
    • 0002565890 scopus 로고
    • The non-linear field theories of mechanics
    • (Springer Veralg, Berlin, Heidelberg, New York)
    • C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics, Handbuch der Physik III/3 (Springer Veralg, Berlin, Heidelberg, New York, 1965).
    • (1965) Handbuch der Physik III/3
    • Truesdell, C.1    Noll, W.2
  • 7
    • 0004235867 scopus 로고    scopus 로고
    • Thermodynamics and Rheology
    • (Akadémiai Kiadó and Kluwer Academic Publisher, Budapest)
    • J. Verhás, Thermodynamics and Rheology (Akadémiai Kiadó and Kluwer Academic Publisher, Budapest, 1997).
    • (1997)
    • Verhás, J.1
  • 8
    • 0001235241 scopus 로고
    • A gradient generalization to internal state variable approach
    • W. Kosiński and W. Wojno, A gradient generalization to internal state variable approach, Arch. Mech. 47(3), 523-536 (1995).
    • (1995) Arch. Mech. , vol.47 , Issue.3 , pp. 523-536
    • Kosiński, W.1    Wojno, W.2
  • 10
    • 0000781812 scopus 로고    scopus 로고
    • Gradient generalization to internal state variables and a theory of superfluidity
    • V. A. Cimmelli and W. Kosiński, Gradient generalization to internal state variables and a theory of superfluidity, J. Theor. Appl. Mech. 35(4), 763-779 (1997).
    • (1997) J. Theor. Appl. Mech. , vol.35 , Issue.4 , pp. 763-779
    • Cimmelli, V.A.1    Kosiński, W.2
  • 11
    • 0029694917 scopus 로고    scopus 로고
    • A gradient theory of internal variables
    • K. C. Valanis, A gradient theory of internal variables, Acta Mech. 116, 1-14 (1996).
    • (1996) Acta Mech. , vol.116 , pp. 1-14
    • Valanis, K.C.1
  • 12
    • 0031683297 scopus 로고    scopus 로고
    • A gradient thermodynamic theory of self-organization
    • K. C. Valanis, A gradient thermodynamic theory of self-organization, Acta Mech. 127, 1-23 (1998).
    • (1998) Acta Mech. , vol.127 , pp. 1-23
    • Valanis, K.C.1
  • 13
    • 0028464449 scopus 로고
    • On the role of microstructure in behaviour of solids: Effects of higher order gradients and internal inertia
    • I. Vardoulakis and E. C. Aifantis, On the role of microstructure in behaviour of solids: effects of higher order gradients and internal inertia, Mech. Mater. 18, 151-158 (1994).
    • (1994) Mech. Mater. , vol.18 , pp. 151-158
    • Vardoulakis, I.1    Aifantis, E.C.2
  • 14
    • 0343353890 scopus 로고    scopus 로고
    • Dynamic systems, rate and gradient effects in material instability
    • P. B. Béda, Dynamic systems, rate and gradient effects in material instability, Int. J. Mech. Sci. 42, 2101-2114 (2000).
    • (2000) Int. J. Mech. Sci. , vol.42 , pp. 2101-2114
    • Béda, P.B.1
  • 15
    • 34147165059 scopus 로고
    • Internal variables and dissipative structures
    • G. A. Maugin, Internal variables and dissipative structures, J. Non-Equilib. Thermodyn. 15, 173-192 (1990).
    • (1990) J. Non-Equilib. Thermodyn. , vol.15 , pp. 173-192
    • Maugin, G.A.1
  • 16
    • 0018918541 scopus 로고
    • The principle of virtual power in continuum mechanics. Application to coupled fields
    • G. A. Maugin, The principle of virtual power in continuum mechanics. Application to coupled fields, Acta Mech. 35, 1-70 (1980).
    • (1980) Acta Mech. , vol.35 , pp. 1-70
    • Maugin, G.A.1
  • 17
    • 0038041658 scopus 로고    scopus 로고
    • Multifield theories: An introduction
    • Preface to a special issue dedicated to multifield theories
    • G. Capriz and P. M. Mariano, Multifield theories: an introduction, International Journal of Solids and Structures 38, 939-941 (2001), Preface to a special issue dedicated to multifield theories.
    • (2001) International Journal of Solids and Structures , vol.38 , pp. 939-941
    • Capriz, G.1    Mariano, P.M.2
  • 18
    • 77956697542 scopus 로고    scopus 로고
    • Multifield theories in mechanics of solids
    • P.M. Mariano, Multifield theories in mechanics of solids, Advances in Applied Mechanics 38, 1-94 (2002).
    • (2002) Advances in Applied Mechanics , vol.38 , pp. 1-94
    • Mariano, P.M.1
  • 19
    • 0003652415 scopus 로고
    • Non-equilibrium thermodynamics
    • North-Holland Publishing Company, Amsterdam
    • S. R. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North-Holland Publishing Company, Amsterdam, 1962.
    • (1962)
    • De Groot, S.R.1    Mazur, P.2
  • 20
    • 0004071351 scopus 로고
    • Non-equilibrium thermodynamics field theory and variational principles
    • Springer Verlag
    • I. Gyarmati, Non-equilibrium Thermodynamics Field Theory and Variational Principles, Springer Verlag, 1970.
    • (1970)
    • Gyarmati, I.1
  • 21
    • 34250963757 scopus 로고
    • The thermodynamics of elastic materials with heat conduction and viscosity
    • B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Ration. Mech. Anal. 13, 167-178 (1963).
    • (1963) Arch. Ration. Mech. Anal. , vol.13 , pp. 167-178
    • Coleman, B.D.1    Noll, W.2
  • 22
    • 34250446889 scopus 로고
    • Method of lagrange multipliers for exploitation of the entropy principle
    • I-Shih Liu, Method of Lagrange multipliers for exploitation of the entropy principle, Arch. Ration. Mech. Anal. 46, 131-148 (1972).
    • (1972) Arch. Ration. Mech. Anal. , vol.46 , pp. 131-148
    • I-Shih, L.1
  • 23
    • 0017631054 scopus 로고
    • The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics
    • K. Hutter, The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics, Acta Mech. 27, 1-54 (1977).
    • (1977) Acta Mech. , vol.27 , pp. 1-54
    • Hutter, K.1
  • 24
    • 0004077459 scopus 로고    scopus 로고
    • The mechanics and thermodynamics of continuous media
    • (Springer Verlag, Berlin)
    • M. Šilhavý, The Mechanics and Thermodynamics of Continuous Media (Springer Verlag, Berlin, 1997).
    • (1997)
    • Šilhavý, M.1
  • 26
    • 21144467086 scopus 로고
    • Dynamical laws in thermodynamics
    • T. Matolcsi, Dynamical laws in thermodynamics, Phys. Essays 5(3), 320-327 (1992).
    • (1992) Phys. Essays , vol.5 , Issue.3 , pp. 320-327
    • Matolcsi, T.1
  • 27
    • 0003539783 scopus 로고
    • Thermodynamic theory of structure, stability and fluctuations
    • (Wiley-Interscience, London)
    • P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley-Interscience, London, 1971).
    • (1971)
    • Glansdorff, P.1    Prigogine, I.2
  • 28
    • 0006724152 scopus 로고
    • A note on the relation between the hypothesis of local equilibrium and the Clausius-Duhem inequality
    • J. Kestin, A note on the relation between the hypothesis of local equilibrium and the Clausius-Duhem inequality, J. Non-Equilib. Thermodyn. 15, 193-212 (1990).
    • (1990) J. Non-Equilib. Thermodyn. , vol.15 , pp. 193-212
    • Kestin, J.1
  • 29
    • 0027805123 scopus 로고
    • Internal variables in the local-equilibrium approximation
    • J. Kestin, Internal variables in the local-equilibrium approximation, J. Non-Equilib. Thermodyn. 18, 360-379 (1993).
    • (1993) J. Non-Equilib. Thermodyn. , vol.18 , pp. 360-379
    • Kestin, J.1
  • 30
    • 36149021145 scopus 로고
    • Fluctuations and irreversible processes
    • L. Onsager and S. Machlup, Fluctuations and irreversible processes, Physical Review 91, 1505-1512 (1953).
    • (1953) Physical Review , vol.91 , pp. 1505-1512
    • Onsager, L.1    Machlup, S.2
  • 31
    • 36149007093 scopus 로고
    • Fluctuations and irreversible processes II. Systems with kinetic energy
    • S. Machlup and L. Onsager, Fluctuations and irreversible processes II. Systems with kinetic energy, Physical Review 91, 1512-1515 (1953).
    • (1953) Physical Review , vol.91 , pp. 1512-1515
    • Machlup, S.1    Onsager, L.2
  • 32
    • 21844511679 scopus 로고
    • Reservoirs in thermodynamics
    • T. Matolcsi, Reservoirs in thermodynamics, Phys. Essays 8(3), 234-239 (1995).
    • (1995) Phys. Essays , vol.8 , Issue.3 , pp. 234-239
    • Matolcsi, T.1
  • 33
    • 21344438472 scopus 로고
    • Another dynamic laws in thermodynamics
    • P. Ván, Another Dynamic Laws in thermodynamics, Phys. Essays 8(4), 457-465 (1995).
    • (1995) Phys. Essays , vol.8 , Issue.4 , pp. 457-465
    • Ván, P.1
  • 34
    • 0030493651 scopus 로고    scopus 로고
    • On the classification of phase transitions
    • T. Matolcsi, On the classification of phase transitions, Z. Angew. Math. Phys. 47(6), 837-857 (1996).
    • (1996) Z. Angew. Math. Phys. , vol.47 , Issue.6 , pp. 837-857
    • Matolcsi, T.1
  • 35
    • 0030283404 scopus 로고    scopus 로고
    • On extended thermodynamics of discrete systems
    • W. Muschik and R. Domínguez-Cascante, On extended thermodynamics of discrete systems, Physica A 233, 523-550 (1996).
    • (1996) Physica A , vol.233 , pp. 523-550
    • Muschik, W.1    Domínguez-Cascante, R.2
  • 36
    • 0030518963 scopus 로고    scopus 로고
    • On the dynamics of phase transitions
    • T. Matolcsi, On the dynamics of phase transitions, Z. Angew. Math. Phys. 47 (6), 858-879 (1996).
    • (1996) Z. Angew. Math. Phys. , vol.47 , Issue.6 , pp. 858-879
    • Matolcsi, T.1
  • 37
    • 0034347157 scopus 로고    scopus 로고
    • On the mathematical structure of thermodynamics
    • T. Matolcsi, On the mathematical structure of thermodynamics, J. Math. Phys. 41(4), 2021-2042 (2000).
    • (2000) J. Math. Phys. , vol.41 , Issue.4 , pp. 2021-2042
    • Matolcsi, T.1
  • 38
    • 33746732370 scopus 로고
    • A thermodynamic theory of mixtures of fluids
    • I. Müller, A thermodynamic theory of mixtures of fluids, Arch. Ration. Mech. Anal. 28, 1-39 (1968).
    • (1968) Arch. Ration. Mech. Anal. , vol.28 , pp. 1-39
    • Müller, I.1
  • 39
    • 0003362738 scopus 로고    scopus 로고
    • Rational Extended Thermodynamics
    • 2nd ed. (Springer Verlag, New York)
    • I. Müller and T. Ruggeri, Rational Extended Thermodynamics, Springer Tracts in Natural Philosophy Vol. 37, 2nd ed. (Springer Verlag, New York, 1998).
    • (1998) Springer Tracts in Natural Philosophy , vol.37
    • Müller, I.1    Ruggeri, T.2
  • 41
    • 0031391656 scopus 로고    scopus 로고
    • Heat conduction at low temperature: A non-linear generalization of the Guyer-Krumhansl equation
    • Lecture held on 'Minisymposium on Non-Linear Thermodynamics and Reciprocal Relations', 22-26 September, Balatonvilágos, Hungary
    • G. Lebon, D. Jou, J. Casas-Vázquez, and W. Muschik, Heat conduction at low temperature: A non-linear generalization of the Guyer-Krumhansl equation, Periodica Polytechnica Chemical Engineering 41(2), 185-196, (1997); Lecture held on 'Minisymposium on Non-Linear Thermodynamics and Reciprocal Relations', 22-26 September, Balatonvilágos, Hungary.
    • (1997) Periodica Polytechnica Chemical Engineering , vol.41 , Issue.2 , pp. 185-196
    • Lebon, G.1    Jou, D.2    Casas-Vázquez, J.3    Muschik, W.4
  • 42
    • 0032097110 scopus 로고    scopus 로고
    • Multifield description of microcracked continua: A local model
    • P. M. Mariano and G. Augusti, Multifield description of microcracked continua: a local model, Math. Mech. Solids 3, 183-200 (1998).
    • (1998) Math. Mech. Solids , vol.3 , pp. 183-200
    • Mariano, P.M.1    Augusti, G.2
  • 44
    • 0037703900 scopus 로고
    • A concept of mathematical physics: Models for space time
    • (Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest)
    • T. Matolcsi, A Concept of Mathematical Physics: Models for Space Time (Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1984).
    • (1984)
    • Matolcsi, T.1
  • 45
    • 0022542664 scopus 로고
    • On material frame-indifference
    • T. Matolcsi, On material frame-indifference, Arch. Ration. Mech. Anal. 91(2), 99-118 (1986).
    • (1986) Arch. Ration. Mech. Anal. , vol.91 , Issue.2 , pp. 99-118
    • Matolcsi, T.1
  • 46
    • 24444475480 scopus 로고    scopus 로고
    • Lagrange formalism of point-masses
    • mat-ph/0205040 (2002)
    • M. Balázs and P. Ván, Lagrange formalism of point-masses, mat-ph/0205040 (2002).
    • Balázs, M.1    Ván, P.2
  • 47
    • 0017674959 scopus 로고
    • The wave approach of thermodynamics and some problems of non-linear theories
    • I. Gyarmati, The wave approach of thermodynamics and some problems of non-linear theories, J. Non-Equilib. Thermodyn. 2, 233-260 (1977).
    • (1977) J. Non-Equilib. Thermodyn. , vol.2 , pp. 233-260
    • Gyarmati, I.1
  • 48
    • 84971459084 scopus 로고
    • On the governing principle of dissipative processes and its extension to nonlinear problems
    • I. Gyarmati, On the governing principle of dissipative processes and its extension to nonlinear problems, Ann. Phys. (Germany) 23, 353-378 (1969).
    • (1969) Ann. Phys. (Germany) , vol.23 , pp. 353-378
    • Gyarmati, I.1
  • 51
    • 0006098842 scopus 로고    scopus 로고
    • Extended irreversible thermodynamics revisited (1988-98)
    • D. Jou, J. Casas-Vázquez, and G. Lebon, Extended irreversible thermodynamics revisited (1988-98), Rep. Prog. Phys. 62, 1035-1142 (1999).
    • (1999) Rep. Prog. Phys. , vol.62 , pp. 1035-1142
    • Jou, D.1    Casas-Vázquez, J.2    Lebon, G.3
  • 52
    • 0004004056 scopus 로고
    • Catastrophe theory for scientists and engineers
    • (John Wiley and Sons, New York)
    • R. Gilmore, Catastrophe Theory for Scientists and Engineers (John Wiley and Sons, New York, 1981).
    • (1981)
    • Gilmore, R.1
  • 53
  • 54
    • 0028602836 scopus 로고
    • Thermodynamics with internal variables. Part I. General concepts
    • G. A. Maugin and W. Muschik, Thermodynamics with internal variables. Part I. General concepts, J. Non-Equilib. Thermodyn. 19, 217-249 (1994).
    • (1994) J. Non-Equilib. Thermodyn. , vol.19 , pp. 217-249
    • Maugin, G.A.1    Muschik, W.2
  • 55
    • 0028581290 scopus 로고
    • Thermodynamics with internal variables. Part II. Applications
    • G. A. Maugin and W. Muschik, Thermodynamics with internal variables. Part II. Applications, J. Non-Equilib. Thermodyn. 19, 250-289 (1994).
    • (1994) J. Non-Equilib. Thermodyn. , vol.19 , pp. 250-289
    • Maugin, G.A.1    Muschik, W.2
  • 56
    • 36849104050 scopus 로고
    • Thermodynamics with internal state variables
    • B. D. Coleman and M. E. Gurtin, Thermodynamics with internal state variables, Journal of Chemical Physics 47(2), 597-613 (1997).
    • (1967) Journal of Chemical Physics , vol.47 , Issue.2 , pp. 597-613
    • Coleman, B.D.1    Gurtin, M.E.2
  • 57
    • 0021519485 scopus 로고
    • The macrodynamics of open systems and the variational principle of the local potential - I
    • V.N. Orlov and L. I. Rozonoer, The macrodynamics of open systems and the variational principle of the local potential - I, J. Franklin Inst. 318, 283-314 (1984).
    • (1984) J. Franklin Inst. , vol.318 , pp. 283-314
    • Orlov, V.N.1    Rozonoer, L.I.2
  • 58
    • 0021519484 scopus 로고
    • The macrodynamics of open systems and the variational principle of the local potential - II applications
    • V.N. Orlov and L. I. Rozonoer, The macrodynamics of open systems and the variational principle of the local potential - II Applications, J. Franklin Inst. 318, 315-347 (1984).
    • (1984) J. Franklin Inst. , vol.318 , pp. 315-347
    • Orlov, V.N.1    Rozonoer, L.I.2
  • 59
    • 0002898431 scopus 로고
    • Chan-Hilliard theory and irreversible thermodynamics
    • F. Falk, Chan-Hilliard theory and irreversible thermodynamics, J. Non-Equilib. Thermodyn. 17, 53-65 (1992).
    • (1992) J. Non-Equilib. Thermodyn. , vol.17 , pp. 53-65
    • Falk, F.1
  • 60
    • 0023827471 scopus 로고
    • On the localization an postlocalization behaviour of plastic deformation. I. On the initiation of shear bands
    • H. M. Zbib and E. C. Aifantis, On the localization an postlocalization behaviour of plastic deformation. I. On the initiation of shear bands, Res Mech. 23, 261-277 (1988).
    • (1988) Res Mech. , vol.23 , pp. 261-277
    • Zbib, H.M.1    Aifantis, E.C.2
  • 61
    • 35949034972 scopus 로고
    • Theory of dynamic critical phenomena
    • P.C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49(3), 435-479 (1977).
    • (1977) Rev. Mod. Phys. , vol.49 , Issue.3 , pp. 435-479
    • Hohenberg, P.C.1    Halperin, B.I.2
  • 62
    • 0000313595 scopus 로고    scopus 로고
    • Dynamics and thermodynamics of complex fluids. I. Development of a general formalism
    • M. Grmela and H. C. Öttinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism, Physical Review E 56(6), 6620-6632 (1997).
    • (1997) Physical Review E , vol.56 , Issue.6 , pp. 6620-6632
    • Grmela, M.1    Öttinger, H.C.2
  • 63
    • 5344263088 scopus 로고    scopus 로고
    • Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism
    • H. C. Öttinger and M. Grmela, Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism, Physical Review E 56(6), 6633-6655 (1997).
    • (1997) Physical Review E , vol.56 , Issue.6 , pp. 6633-6655
    • Öttinger, H.C.1    Grmela, M.2
  • 64
    • 0001158204 scopus 로고    scopus 로고
    • Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
    • M. G. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92, 178-192 (1996).
    • (1996) Physica D , vol.92 , pp. 178-192
    • Gurtin, M.G.1
  • 65
    • 4243308858 scopus 로고    scopus 로고
    • Weakly nonlocal irreversible thermodynamics - the Ginzburg-Landau equation
    • cond-mat/0111307
    • P. Ván, Weakly nonlocal irreversible thermodynamics - the Ginzburg-Landau equation, Technische Mechanik 22(2), 104-110 (2002) cond-mat/0111307
    • (2002) Technische Mechanik , vol.22 , Issue.2 , pp. 104-110
    • Ván, P.1
  • 66
    • 24444449607 scopus 로고    scopus 로고
    • Once again on the transport of dynamic degrees of freedom
    • J. Verhás, Once again on the transport of dynamic degrees of freedom, Atti Accademia Peloritana dei Pericolanti LXXII, 101-114 (1996).
    • (1996) Atti Accademia Peloritana dei Pericolanti , vol.72 , pp. 101-114
    • Verhás, J.1
  • 67
    • 0034884015 scopus 로고    scopus 로고
    • Internal thermodynamic variables and the failure of microcracked materials
    • P. Ván, Internal thermodynamic variables and the failure of microcracked materials, J. Non-Equilib. Thermodyn. 26(2), 167-189 (2001).
    • (2001) J. Non-Equilib. Thermodyn. , vol.26 , Issue.2 , pp. 167-189
    • Ván, P.1
  • 69
    • 0001044039 scopus 로고    scopus 로고
    • Some generalizations of the Cahn-Hilliard equation
    • A. Miranville, Some generalizations of the Cahn-Hilliard equation, Asymptotic Analysis 22(3-4), 235-259 (2000).
    • (2000) Asymptotic Analysis , vol.22 , Issue.3-4 , pp. 235-259
    • Miranville, A.1
  • 71
    • 0019204411 scopus 로고
    • On the problem of diffusion in solids
    • E.C. Aifantes, On the problem of diffusion in solids, Acta Mech. 37, 256-296 (1980).
    • (1980) Acta Mech. , vol.37 , pp. 256-296
    • Aifantes, E.C.1
  • 72
    • 2342642518 scopus 로고
    • Solution of the linearized phonon Boltzmann equation
    • R. A. Guyer and J. A. Krumhansl, Solution of the linearized phonon Boltzmann equation, Phys. Rev. 148(2), 766-778 (1966).
    • (1966) Phys. Rev. , vol.148 , Issue.2 , pp. 766-778
    • Guyer, R.A.1    Krumhansl, J.A.2
  • 73
    • 36049053285 scopus 로고
    • Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetallic crystals
    • R. A. Guyer and J. A. Krumhansl, Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetallic crystals, Phys. Rev. 148(2), 778-788 (1966).
    • (1966) Phys. Rev. , vol.148 , Issue.2 , pp. 778-788
    • Guyer, R.A.1    Krumhansl, J.A.2
  • 74
    • 0000227803 scopus 로고
    • The formulation of constitutive equations in continuum physics 1
    • A.C. Pipkin and R. S. Rivlin, The formulation of constitutive equations in continuum physics 1, Arch. Ration. Mech. Anal. 4, 129-144 (1959).
    • (1959) Arch. Ration. Mech. Anal. , vol.4 , pp. 129-144
    • Pipkin, A.C.1    Rivlin, R.S.2
  • 75
    • 0000779802 scopus 로고
    • On isotropic integrity bases
    • G.F. Smith, On isotropic integrity bases, Arch. Ration. Mech. Anal. 17, 282-292 (1964).
    • (1964) Arch. Ration. Mech. Anal. , vol.17 , pp. 282-292
    • Smith, G.F.1
  • 76
    • 0037703897 scopus 로고
    • Two-fluid hydrodynamics description of ordered systems
    • C. P. Enz, Two-fluid hydrodynamics description of ordered systems, Rev. Mod. Phys. 46(4), 705-753 (1974).
    • (1974) Rev. Mod. Phys. , vol.46 , Issue.4 , pp. 705-753
    • Enz, C.P.1
  • 77
    • 0019562199 scopus 로고
    • A systematic application of Gyarmati's wave theory of thermodynamics to thermal waves in solids
    • D. Fekete, A systematic application of Gyarmati's wave theory of thermodynamics to thermal waves in solids, phys. status solidi B 105, 161-174 (1981).
    • (1981) Phys. Status Solidi B , vol.105 , pp. 161-174
    • Fekete, D.1
  • 78
    • 4243694518 scopus 로고
    • The wave approach of irreversible thermodynamics
    • Doctoral Thesis, Hungarian Academy of Sciences, Budapest
    • D.K. Bhattacharya, The Wave Approach of Irreversible Thermodynamics, Doctoral Thesis, Hungarian Academy of Sciences, Budapest (1982).
    • (1982)
    • Bhattacharya, D.K.1
  • 79
    • 0001857490 scopus 로고
    • Heat transport in dielectric crystals at low temperature: A variational formulation based on extended irreversible thermodynamics
    • G. Lebon and P. C. Dauby, Heat transport in dielectric crystals at low temperature: a variational formulation based on Extended Irreversible Thermodynamics, Physical Review A 42(8), 4710-4715 (1990).
    • (1990) Physical Review A , vol.42 , Issue.8 , pp. 4710-4715
    • Lebon, G.1    Dauby, P.C.2
  • 80
    • 0002854152 scopus 로고
    • Reciprocity and consistency in non-local extended thermodynamics
    • R. E. Nettleton, Reciprocity and consistency in non-local extended thermodynamics, Open Systems and Information Dynamics 2(1), 41-47 (1993).
    • (1993) Open Systems and Information Dynamics , vol.2 , Issue.1 , pp. 41-47
    • Nettleton, R.E.1
  • 81
    • 0002735169 scopus 로고    scopus 로고
    • Weakly nonlocal heat conduction in rigid solids
    • G. Lebon and M. Grmela, Weakly nonlocal heat conduction in rigid solids, Phys. Lett. A 214, 184-188 (1996).
    • (1996) Phys. Lett. A , vol.214 , pp. 184-188
    • Lebon, G.1    Grmela, M.2
  • 85
    • 5444273657 scopus 로고    scopus 로고
    • Weakly nonlocal continuum physics - the Ginzburg-Landau equation
    • cond-mat/021402
    • P. Ván, Weakly nonlocal continuum physics - the Ginzburg-Landau equation, cond-mat/021402 (2002)
    • (2002)
    • Ván, P.1
  • 86
    • 45149136070 scopus 로고
    • Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
    • O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43, 44-62 (1990).
    • (1990) Physica D , vol.43 , pp. 44-62
    • Penrose, O.1    Fife, P.C.2
  • 87
    • 0009549931 scopus 로고
    • Structure of variational principles in nonequilibrium thermodynamics
    • P. Ván and W. Muschik, Structure of variational principles in nonequilibrium thermodynamics, Physical Review E E 5(4), 3584-3590 (1995).
    • (1995) Physical Review E , vol.5 , Issue.4 , pp. 3584-3590
    • Ván, P.1    Muschik, W.2
  • 88
    • 0000471616 scopus 로고
    • A Fourier-féle mechanikai elv alkalmazásai
    • in Hungarian
    • Gy Farkas, A Fourier-féle mechanikai elv alkalmazásai, Mathematikai és Természettudományi Értesíto 12, 457-472 (1894), in Hungarian.
    • (1894) Mathematikai és Természettudományi Értesíto , vol.12 , pp. 457-472
    • Farkas, G.1
  • 90
  • 91
    • 0036011703 scopus 로고    scopus 로고
    • A historical note on the entropy principle of Müller and Liu
    • Lecture held on CIMRF'01, Berlin, 3-6 September 2001
    • R. A. Hauser and N. P. Kirchner, A historical note on the entropy principle of Müller and Liu, Continuum Mechanics and Thermodynamics 14, 223-226 (2002); Lecture held on CIMRF'01, Berlin, 3-6 September 2001.
    • (2002) Continuum Mechanics and Thermodynamics , vol.14 , pp. 223-226
    • Hauser, R.A.1    Kirchner, N.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.