Erratum to: Thermodynamic approach to generalized continua
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Continuum Mech. Thermodyn. DOI 10.1007/s00161-014-0332-2 ERRATUM Peter Ván · Arkadi Berezovski · Christina Papenfuss Erratum to: Thermodynamic approach to generalized continua © Springer-Verlag Berlin Heidelberg 2014 Erratum to: Continuum Mech. Thermodyn. (2013) 118 DOI 10.1007/s00161-013-0311-z The evolution equations for the internal variables ψ ij and β ij in formula (5) on p. 4 are mistyped in the published article. The correct expressions are ˙ ψ ij + f ij = 0, ˙ β ij + g ij = 0. There are some consequent sign mistakes in the following. On p. 4 Eq. (9) for the derivative constraints and Eq. (10) for the entropy imbalance should be corrected as ∂ k ˙ ψ ij + ∂ k f ij = 0, ∂ k ˙ β ij + ∂ k g ij = 0, and ρ 0 ˙ s + ∂ j J j − Λ ji ( ˙ F ij − ∂ j v i ) − λ i ( ρ 0 ˙ v i − ∂ j t ij ) − κ ( ρ 0 ˙ e + ∂ i q i − t ij ∂ j v i ) + A ji ( ˙ ψ ij + f ij ) + A kji ( ∂ k ˙ ψ ij + ∂ k f ij ) + B ji ( ˙ β ij + g ij ) + B kji ( ∂ k ˙ β ij + ∂ k g ij ) ≥ 0. The online version of the original article can be found under doi:10.1007/s00161-013-0311-z. P. Ván (B ) Department of Theoretical Physics, Wigner RCP, HAS, Konkoly Thege Mikl ´ os ´ ut 29-33., 1121 Budapest, Hungary E-mail: [email protected] Tel.: +36-1-3922222 Fax: +36-1-3922727 P. Ván Department of Energy Engineering, Budapest University of Technology and Economics, Bertalan Lajos u. 4-6, 1111 Budapest, Hungary P. Ván Montavid Thermodynamic Research Group, Budapest, Hungary A. Berezovski Centre for Nonlinear Studies, Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia C. Papenfuss Technical University of Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany
Transcript of Erratum to: Thermodynamic approach to generalized continua
Continuum Mech. Thermodyn.DOI 10.1007/s00161-014-0332-2
ERRATUM
Peter Ván · Arkadi Berezovski · Christina Papenfuss
Erratum to: Thermodynamic approach to generalizedcontinua
© Springer-Verlag Berlin Heidelberg 2014
Erratum to: Continuum Mech. Thermodyn. (2013) 118DOI 10.1007/s00161-013-0311-z
The evolution equations for the internal variables ψi j and βi j in formula (5) on p. 4 are mistyped in thepublished article. The correct expressions are
ψi j + fi j = 0, βi j + gi j = 0.
There are some consequent sign mistakes in the following.On p. 4 Eq. (9) for the derivative constraints and Eq. (10) for the entropy imbalance should be corrected as
∂kψi j + ∂k fi j = 0, ∂k βi j + ∂k gi j = 0,
and
ρ0s + ∂ j J j −Λ j i(Fi j − ∂ jvi
) − λi(ρ0vi − ∂ j ti j
) − κ(ρ0e + ∂i qi − ti j∂ jvi
)
+ A ji(ψi j + fi j
) + Ak ji(∂kψi j + ∂k fi j
)
+ B ji(βi j + gi j
) + Bk ji(∂k βi j + ∂k gi j
) ≥ 0.
The online version of the original article can be found under doi:10.1007/s00161-013-0311-z.
P. Ván (B)Department of Theoretical Physics, Wigner RCP, HAS, Konkoly Thege Miklos ut 29-33., 1121 Budapest, HungaryE-mail: [email protected].: +36-1-3922222Fax: +36-1-3922727
P. VánDepartment of Energy Engineering, Budapest University of Technology and Economics, Bertalan Lajos u. 4-6,1111 Budapest, Hungary
P. VánMontavid Thermodynamic Research Group, Budapest, Hungary
A. BerezovskiCentre for Nonlinear Studies, Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21,12618 Tallinn, Estonia
C. PapenfussTechnical University of Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany
P. Ván et al.
On p. 8 Eq. (50) are written correctly as
�ψ i j + fi j = 0,
�β i j +gi j = 0. (1)
Further on the sign error appears on p. 11 in formula (69) for the entropy production of standard linearsolid, which should be replaced by
Tσ = (ti j − ρ∂εi jw
)εi j + ∂ψi jwρ f i j ≥ 0.
Finally, formula (86) on p. 13 of entropy production should be written as
Tσ = (ti j − ρ∂εi jw
)εi j − (
∂ψi jw − ∂k(∂∂kψi jw))ρ
�ψ i j − (
∂βi jw − ∂k(∂∂kβi jw))ρ
�β i j≥ 0. (2)
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