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Corrigendum to “A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory” [Int. J. Non-linear Mech. 56 (2013) 61–70]
International Journal of Non-Linear Mechanics 82 (2016) 131
Contents lists available at ScienceDirect
International Journal of Non-Linear Mechanics journal homepage: www.elsevier.com/locate/nlm
Corrigendum
Corrigendum to “A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory” [Int. J. Non-linear Mech. 56 (2013) 61–70] D.J. Steigmann Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
art ic l e i nf o Article history: Received 28 February 2016 Accepted 2 March 2016 Available online 29 March 2016
I am grateful to Professors William Klug (UCLA) and Eliot Fried (OIST) for drawing my attention to an error in the text following Eq. (34). There it is stated, erroneously, that {g α}|ω = {aα}. This error implies that (35) should be replaced by
D|ω = δ, α ⊗ g α + (n·δ)−1η ⊗ n, wherein all terms are evaluated on ω. We resolve g α in the basis {a β , n} and use {g α }|ω = {a α } with δβα = g α·gβ = g α·aβ : thus,
g α = aα + (g α·n) n. Next, we resolve n in the basis {g i}. Recalling that g3 = δ and n ·g 3 = (n ·δ)−1, we obtain
n = (n·g i) g i = (n·g α) a α + (n·δ)−1δ. Accordingly,
n·g β = − (n·δ)−1δ β, where
δ β = a β · δ. Substitution into the second expression above then yields
g α = aα − (n·δ)−1δ αn. The correct expression for D|ω , replacing (35), is then given by substituting into the first expression above:
D|ω = ∇δ + (n·δ)−1(η − δ αδ, α ) ⊗ n, where
∇δ = δ, α ⊗ aα is the surface gradient of the director field, as in the paper. The error affects the algebraic detail in the considerations of Sections 4 and 5, particularly the passage from Eqs. (50)–(54) pertaining to the procedure for computing the areal energy density from the three-dimensional Frank energy for liquid crystals. The detailed changes are minor and thus best left to the interested reader.
DOI of original article: http://dx.doi.org/10.1016/j.ijnonlinmec.2013.02.006 http://dx.doi.org/10.1016/j.ijnonlinmec.2016.03.003 0020-7462/& 2016 Elsevier Ltd. All rights reserved.
Contents lists available at ScienceDirect
International Journal of Non-Linear Mechanics journal homepage: www.elsevier.com/locate/nlm
Corrigendum
Corrigendum to “A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory” [Int. J. Non-linear Mech. 56 (2013) 61–70] D.J. Steigmann Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
art ic l e i nf o Article history: Received 28 February 2016 Accepted 2 March 2016 Available online 29 March 2016
I am grateful to Professors William Klug (UCLA) and Eliot Fried (OIST) for drawing my attention to an error in the text following Eq. (34). There it is stated, erroneously, that {g α}|ω = {aα}. This error implies that (35) should be replaced by
D|ω = δ, α ⊗ g α + (n·δ)−1η ⊗ n, wherein all terms are evaluated on ω. We resolve g α in the basis {a β , n} and use {g α }|ω = {a α } with δβα = g α·gβ = g α·aβ : thus,
g α = aα + (g α·n) n. Next, we resolve n in the basis {g i}. Recalling that g3 = δ and n ·g 3 = (n ·δ)−1, we obtain
n = (n·g i) g i = (n·g α) a α + (n·δ)−1δ. Accordingly,
n·g β = − (n·δ)−1δ β, where
δ β = a β · δ. Substitution into the second expression above then yields
g α = aα − (n·δ)−1δ αn. The correct expression for D|ω , replacing (35), is then given by substituting into the first expression above:
D|ω = ∇δ + (n·δ)−1(η − δ αδ, α ) ⊗ n, where
∇δ = δ, α ⊗ aα is the surface gradient of the director field, as in the paper. The error affects the algebraic detail in the considerations of Sections 4 and 5, particularly the passage from Eqs. (50)–(54) pertaining to the procedure for computing the areal energy density from the three-dimensional Frank energy for liquid crystals. The detailed changes are minor and thus best left to the interested reader.
DOI of original article: http://dx.doi.org/10.1016/j.ijnonlinmec.2013.02.006 http://dx.doi.org/10.1016/j.ijnonlinmec.2016.03.003 0020-7462/& 2016 Elsevier Ltd. All rights reserved.