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Volumn 49, Issue 1, 2005, Pages 79-94

Exploiting the second law in weakly non-local continuum physics

Author keywords

Ginzburg Landau equation; Liu's procedure; Non equilibrium thermodynamics; Weakly non load

Indexed keywords

ENTROPY; FUNCTIONS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; THERMODYNAMICS;

EID: 22944451829     PISSN: 03246051     EISSN: 1587379X     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (24)

References (56)
  • 1
    • 0001799940 scopus 로고
    • Sur la forme que prennant les équations du mouvement des fluides si l'on tient compte des froces capillaires causées par des variations de densité
    • KORTEWEG, D. J., Sur la forme que prennant les équations du mouvement des fluides si l'on tient compte des froces capillaires causées par des variations de densité, Archives Nerlandaises des Sciences Exactes et Naturelles, Series II, 6 (1901), pp. 1-16.
    • (1901) Archives Nerlandaises des Sciences Exactes et Naturelles, Series II , vol.6 , pp. 1-16
    • Korteweg, D.J.1
  • 2
    • 2342642518 scopus 로고
    • Solution of the linearized phonon boltzmann equation
    • GUYER, R. A. - KRUMHANSL, J. A. Solution of the Linearized Phonon Boltzmann Equation, Physical Review, 148 (2) (1966), pp. 766-778.
    • (1966) Physical Review , vol.148 , Issue.2 , pp. 766-778
    • Guyer, R.A.1    Krumhansl, J.A.2
  • 3
    • 0348114801 scopus 로고
    • Evolution hyperbolic equations for heat conduction
    • W. Kosiński, W. Larecki, A. Morro, and H. Zorski, editors, Thermodynamics and Kinetic Theory, Singapore - New Jersey - London-Hong Kong. World Scientific
    • CIMMELLI, V. A. - KOSIŃSKI, W., Evolution Hyperbolic Equations for Heat Conduction, In W. Kosiński, W. Larecki, A. Morro, and H. Zorski, editors, Thermodynamics and Kinetic Theory, volume 12 of Series on Advanced Mathematics and Applied Sciences, pages 11-22, Singapore - New Jersey - London-Hong Kong, 1992. World Scientific.
    • (1992) Series on Advanced Mathematics and Applied Sciences , vol.12 , pp. 11-22
    • Cimmelli, V.A.1    Kosiński, W.2
  • 6
    • 0028602836 scopus 로고
    • Thermodynamics with internal variables. Part I. General concepts
    • MAUGIN, G. A. - MUSCHIK, W., Thermodynamics with Internal Variables. Part I. General concepts, Journal of Non-Equilibrium Thermodynamics, 19 (1994), pp. 217-249.
    • (1994) Journal of Non-equilibrium Thermodynamics , vol.19 , pp. 217-249
    • Maugin, G.A.1    Muschik, W.2
  • 8
    • 0004079016 scopus 로고    scopus 로고
    • Rational extended thermodynamics
    • Springer Verlag, New York-etc., 2nd edition
    • MÜLLER, I. - RUGGERI, T., Rational Extended Thermodynamics, volume 37 of Springer Tracts in Natural Philosophy. Springer Verlag, New York-etc., 2nd edition, 1998.
    • (1998) Springer Tracts in Natural Philosophy , vol.37
    • Müller, I.1    Ruggeri, T.2
  • 9
    • 0004235867 scopus 로고    scopus 로고
    • Akadémiai Kiadó and Kluwer Academic Publisher, Budapest
    • VERHÁS, J., Thermodynamics and Rheology, Akadémiai Kiadó and Kluwer Academic Publisher, Budapest, 1997.
    • (1997) Thermodynamics and Rheology
    • Verhás, J.1
  • 10
  • 11
    • 0001158204 scopus 로고    scopus 로고
    • Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
    • GURTIN, M. G., Generalized Ginzburg-Landau and Cahn-Hilliard Equations Based on a Microforce Balance, Physica D, 92 (996), pp. 178-192.
    • Physica D , vol.92 , Issue.996 , pp. 178-192
    • Gurtin, M.G.1
  • 13
    • 0029250596 scopus 로고
    • A non-local thermodynamic analysis of second sound propagation in crystalline dielectrics
    • LEBON, G. - TORRISI, M. - VALENTINI, A., A Non-local Thermodynamic Analysis of Second Sound Propagation in Crystalline Dielectrics, Journal of Physics: Condensed Matter, 7 (1995), pp. 1461-1474.
    • (1995) Journal of Physics: Condensed Matter , vol.7 , pp. 1461-1474
    • Lebon, G.1    Torrisi, M.2    Valentini, A.3
  • 15
    • 0002735169 scopus 로고    scopus 로고
    • Weakly nonlocal heat conduction in rigid solids
    • LEBON, G. - GRMELA, M., Weakly Nonlocal Heat Conduction in Rigid Solids, Physics Letters A, 214 (1996), pp. 184-188.
    • (1996) Physics Letters A , vol.214 , pp. 184-188
    • Lebon, G.1    Grmela, M.2
  • 16
    • 0031391656 scopus 로고    scopus 로고
    • Heat conduction at low temperature: A non-linear generalization of the Guyer-Krumhansl equation
    • LEBON, G. - JOU, D. - CASAS-VÁZQUEZ, J. - MUSCHIK, W., Heat Conduction at Low Temperature: A Non-linear Generalization of the Guyer-Krumhansl Equation, Periodica Polytechnica Chemical Engineering, 41 (2) (1997), pp. 185-196.
    • (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
  • 18
    • 0001714097 scopus 로고
    • Existence of caloric equation of state in thermodynamics
    • COLEMAN, B. D.- MIZEL, V. J., Existence of Caloric Equation of State in Thermodynamics, Journal of Chemical Physics, 40 (1964), pp. 1116-1125.
    • (1964) Journal of Chemical Physics , vol.40 , pp. 1116-1125
    • Coleman, B.D.1    Mizel, V.J.2
  • 20
    • 0038711960 scopus 로고    scopus 로고
    • Weakly nonlocal irreversible thermodynamics
    • cond-mat/0112214
    • VAN, P., Weakly Nonlocal Irreversible Thermodynamics, Annalen der Physik (Leipzig), 12 (3) (2003), pp. 142-169 (cond-mat/0112214).
    • (2003) Annalen der Physik (Leipzig) , vol.12 , Issue.3 , pp. 142-169
    • Van, P.1
  • 23
    • 0000781812 scopus 로고    scopus 로고
    • Gradient generalization to internal state variables and a theory of superfluidity
    • CIMMELLI, V. A. - KOSIŃSKI, W., Gradient Generalization to Internal State Variables and a Theory of Superfluidity, Journal of Theoretical and Applied Mechanics, 35 (4) (1997), pp. 763-779.
    • (1997) Journal of Theoretical and Applied Mechanics , vol.35 , Issue.4 , pp. 763-779
    • Cimmelli, V.A.1    Kosiński, W.2
  • 25
    • 0032097110 scopus 로고    scopus 로고
    • Multifield description of microcracked continua: A local model
    • MARIANO, P. M. - AUGUSTI, G., Multifield Description of Microcracked Continua: A Local Model, Mathematics and Mechanics of Solids, 3 (1998), pp. 183-200.
    • (1998) Mathematics and Mechanics of Solids , vol.3 , pp. 183-200
    • Mariano, P.M.1    Augusti, G.2
  • 26
    • 77956697542 scopus 로고    scopus 로고
    • Multifield theories in mechanics of solids
    • MARIANO, P. M., Multifield Theories in Mechanics of Solids, Advances in Applied Mechanics, 38 (2002), pp. 1-94.
    • (2002) Advances in Applied Mechanics , vol.38 , pp. 1-94
    • Mariano, P.M.1
  • 28
    • 17744384437 scopus 로고    scopus 로고
    • Exploiting the dissipation inequality in case of constrained state space variables
    • B. T. Maruszewski, W. Muschik, and Radowicz A., editors, Singapure-etc.. World Scientific
    • HERRMANN, H. - MUSCHIK, W. - PAPENFUSS, C. - RÜCKNER, G., Exploiting the Dissipation Inequality in Case of Constrained State Space Variables, In B. T. Maruszewski, W. Muschik, and Radowicz A., editors, Trends in Continuum Physics, pages 156-163, Singapure-etc., 1999. World Scientific.
    • (1999) Trends in Continuum Physics , pp. 156-163
    • Herrmann, H.1    Muschik, W.2    Papenfuss, C.3    Rückner, G.4
  • 31
    • 3042547390 scopus 로고    scopus 로고
    • Remarks on thermodynamical terminology
    • MUSCHIK, W., Remarks on Thermodynamical Terminology, Journal of Non-Equilibrium Thermodynamics, 29 (2) (2004), pp. 199-203.
    • (2004) Journal of Non-equilibrium Thermodynamics , vol.29 , Issue.2 , pp. 199-203
    • Muschik, W.1
  • 32
    • 0036013603 scopus 로고    scopus 로고
    • The World of the complex Ginzburg-Landau equation
    • ARANSON, I. S. - KRAMER, L., The World of the Complex Ginzburg-Landau Equation, Reviews of Modern Physics, 74 (1) (2002), pp. 99-143.
    • (2002) Reviews of Modern Physics , vol.74 , Issue.1 , pp. 99-143
    • Aranson, I.S.1    Kramer, L.2
  • 33
    • 45149136070 scopus 로고
    • Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
    • PENROSE, O. - FIFE, P. C., Thermodynamically Consistent Models of Phase-Field Type for the Kinetics of Phase Transitions, Physica D, 43 (1990), pp. 44-62.
    • (1990) Physica D , vol.43 , pp. 44-62
    • Penrose, O.1    Fife, P.C.2
  • 34
    • 4243308858 scopus 로고    scopus 로고
    • Weakly nonlocal irreversible thermodynamics - The Ginzburg -Landau equation
    • cond-mat/0111307
    • VÁN, P., Weakly Nonlocal Irreversible Thermodynamics - the Ginzburg -Landau Equation, Technische Mechanik, 22 (2) (2002), pp. 104-110, (cond-mat/0111307).
    • (2002) Technische Mechanik , vol.22 , Issue.2 , pp. 104-110
    • Ván, P.1
  • 35
    • 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, Archive of Rational Mechanics and Analysis, 46 (1972), pp. 131-148.
    • (1972) Archive of Rational Mechanics and Analysis , vol.46 , pp. 131-148
    • Liu, I.-S.1
  • 36
    • 0019204411 scopus 로고
    • On the problem of diffusion in solids
    • AIFANTES, E. C., On the Problem of Diffusion in Solids, Acta Mechanica, 37 (1980), pp. 256-296.
    • (1980) Acta Mechanica , vol.37 , pp. 256-296
    • Aifantes, E.C.1
  • 37
    • 0034347157 scopus 로고    scopus 로고
    • On the mathematical structure of thermodynamics
    • MATOLCSI, T., On the Mathematical Structure of Thermodynamics, Journal of Mathematical Physics, 41 (4) (2000), pp. 2021-2042.
    • (2000) Journal of Mathematical Physics , vol.41 , Issue.4 , pp. 2021-2042
    • Matolcsi, T.1
  • 38
    • 0000313595 scopus 로고    scopus 로고
    • Dynamics and thermodynamics of complex fluids. I. Development of a general formalism
    • GRMELA, M. - ÖTTINGER, H. C., Dynamics and Thermodynamics of Complex Fluids. I. Development of a General Formalism, Physical Review E, 56 (6) (1997), pp. 6620-6632.
    • (1997) Physical Review E , vol.56 , Issue.6 , pp. 6620-6632
    • Grmela, M.1    Öttinger, H.C.2
  • 39
    • 5344263088 scopus 로고    scopus 로고
    • Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism
    • ÖTTINGER, H. C. - GRMELA, M., Dynamics and Thermodynamics of Complex Fluids. II. Illustrations of a General Formalism, Physical Review E, 56 (6) (1997), pp. 6633-6655.
    • (1997) Physical Review E , vol.56 , Issue.6 , pp. 6633-6655
    • Öttinger, H.C.1    Grmela, M.2
  • 40
    • 0001637562 scopus 로고    scopus 로고
    • General projection operator formalism for the dynamics and thermodynamics of complex fluids
    • ÖTTINGER, H. C., General Projection Operator Formalism for the Dynamics and Thermodynamics of Complex Fluids, Physical Review E, 57 (2) (1998), pp. 1416-1420.
    • (1998) Physical Review E , vol.57 , Issue.2 , pp. 1416-1420
    • Öttinger, H.C.1
  • 41
    • 0009549931 scopus 로고
    • The structure of variational principles in nonequilibrium thermodynamics
    • VÁN, P. - MUSCHIK, W., The Structure of Variational Principles in Nonequilibrium Thermodynamics, Physical Review E, 52 (4) (1995), pp. 3584-3590.
    • (1995) Physical Review E , vol.52 , Issue.4 , pp. 3584-3590
    • Ván, P.1    Muschik, W.2
  • 42
    • 35949034972 scopus 로고
    • Theory of dynamic critical phenomena
    • HOHENBERG, P. C. - HALPERIN, B. I., Theory of Dynamic Critical Phenomena, Reviews of Modem Physics, 49 (3) (1977), pp. 435-479.
    • (1977) Reviews of Modem Physics , vol.49 , Issue.3 , pp. 435-479
    • Hohenberg, P.C.1    Halperin, B.I.2
  • 43
    • 12044252828 scopus 로고
    • Pattern formation outside equilibrium
    • CROSS, M. C. - HOHENBERG, P. C., Pattern Formation Outside Equilibrium, Reviews of Modern Physics, 65 (3) (1993), pp. 851-1106.
    • (1993) Reviews of Modern Physics , vol.65 , Issue.3 , pp. 851-1106
    • Cross, M.C.1    Hohenberg, P.C.2
  • 46
    • 0036011703 scopus 로고    scopus 로고
    • A historical note on the entropy principle of Müller and Liu
    • HAUSER, R. A. - KIRCHNER, N. P., A Historical Note on the Entropy Principle of Müller and Liu, Continuum Mechanics and Thermodynamics, 14 (2002), pp. 223-226.
    • (2002) Continuum Mechanics and Thermodynamics , vol.14 , pp. 223-226
    • Hauser, R.A.1    Kirchner, N.P.2
  • 47
    • 85022120553 scopus 로고    scopus 로고
    • Lecture held on, Berlin, 3-6 September
    • Lecture held on CIMRF'01, Berlin, 3-6 September, 2001.
    • (2001) CIMRF'01
  • 48
    • 0000471616 scopus 로고
    • A Fourier-féle mechanikai elv alkalmazásai
    • in Hungarian
    • FARKAS, GY., A Fourier-féle mechanikai elv alkalmazásai, Mathematikai és Természettudományi Értesíto, 12 (1894), pp. 457-472. (in Hungarian.)
    • (1894) Mathematikai és Természettudományi Értesíto , vol.12 , pp. 457-472
    • Farkas, Gy.1
  • 50
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 53
    • 0038379935 scopus 로고
    • A lineáris egyenlotlenség kovetkezményei
    • in Hungarian
    • FARKAS, GY., A lineáris egyenlotlenség kovetkezmé nyei, Mathematikai és Természettudományi Értesíto, 36 (1918), pp. 397-408. (in Hungarian.)
    • (1918) Mathematikai és Természettudományi Értesíto , vol.36 , pp. 397-408
    • Farkas, Gy.1
  • 54
    • 0344785925 scopus 로고
    • Discussion of a maximum principle
    • A. H. Taub, editor, New York and Oxford, Pergamon Press
    • VON NEUMAN, J., Discussion of a Maximum Principle, In A. H. Taub, editor, Collected Works, volume VI, pages 89-95, New York and Oxford, 1961. Pergamon Press.
    • (1961) Collected Works , vol.6 , pp. 89-95
    • Von Neuman, J.1
  • 55
    • 0002069505 scopus 로고
    • Akadémiai Kiadó Publishing House of the Hungarian Academy of Sciences, Budapest
    • MATOLCSI, T., Spacetime Without Reference Frames, Akadémiai Kiadó Publishing House of the Hungarian Academy of Sciences), Budapest, 1993.
    • (1993) Spacetime Without Reference Frames
    • Matolcsi, T.1
  • 56
    • 41349122394 scopus 로고    scopus 로고
    • Variational theory for thermodynamics of thermal waves
    • 046132
    • SIENIUTYCZ, S. - BERRY, R. S., Variational Theory for Thermodynamics of Thermal Waves, Physical Review E, 65 (046132), 2002.
    • (2002) Physical Review E , vol.65
    • Sieniutycz, S.1    Berry, R.S.2


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