Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates (by R. Aghababaei and J.N. Reddy,Journal of Sound and Vibration 326 (2009) 277–289)”

This paper aims to prove the inaccuracy of the Navier solution presented by Aghababaei and Reddy [1] for the bending analysis of nanoplates based on the nonlocal theory of Eringen. According to the derived relations for bending of the nonlocal plate model, the main cause of this inaccuracy is attributed to an incorrect approximation of the Navier solution for a uniform transverse load. Of course, this problem does not inherently occur for the Navier solution in cases such as free vibration or the buckling of a nonlocal plate model in which the amount of transverse load is zero. In order to obtain further verification the results reported based on the Navier solution by Aghababaei and Reddy (2009, [1]) for the bending analysis of a nanoplate are compared with those computed by the differential quadrature (DQ) and finite difference (FD) methods. As shown, the results obtained by both the FD and DQ methods are consistently alike and unlike the solutions reported by Aghababaei and Reddy (2009, [1]) they are independent from small scale effect.     

Addendum to: “Geometrical and topological aspects of electrostatics on Riemannian manifolds” [J. Geom. Phys. 57 (8) (2007) 1679–1696]

In this note we discuss and solve several open problems posed in our recent paper “Geometrical and topological aspects of electrostatics on Riemannian manifolds”, also published in this journal. Some minor mistakes therein are corrected as well.     

Addendum to: “Ricci-flat holonomy: A classification” [J. Geom. Phys. 57 (6) 1457–1475]: The case of spin(10)

This note fills a hole in the author’s previous paper “Ricci-flat holonomy: A classification”, by dealing with irreducible holonomy algebras that are subalgebras or real forms of C⊕spin(10,C)$\mathbb{C}\oplus \mathfrak{s}\mathfrak{p}\mathfrak{i}\mathfrak{n}(10,\mathbb{C})$. These all turn out to be of Ricci type.     

Corrigendum to “Noether symmetries and conserved quantities for spaces with a section of zero curvature” [J. Geom. Phys. 61 (2011) 658–662]

In Feroze and Hussain (2011) it was proved that the number of new conserved quantities for spaces or spacetimes with an $m$-dimensional section of zero curvature is $m$. This result needs modification as it holds for the spaces having no proper homothetic vector (i.e. other than isometries).     

A response to ‘Comments on the effect of liquid layering on the thermal conductivity of nanofluids’, E. Doroodchi, T. M. Evans & B. Moghtaderi, 2009. J Nanopart Res 11(6):1501–1507

This article provides a response to a recent brief communication ‘Comments on the effect of liquid layering on the thermal conductivity of nanofluids’ by Doroodchi et al. in J Nanopart Res 11(6):1501–1507, 2009. It provides an opportunity for us to clarify the fundamental differences between the models of Yu and Choi (2003) and Leong et al. (2006) mentioned in the communication, followed by an explanation of the development of Leong et al.’s model. While we re-affirm that the model of Leong et al. (2006) was developed based on the right methodology, appropriate boundary conditions and mathematical basis and is therefore valid, there are at least three incorrect equations in Doroodchi et al.’s communication which raise serious doubts on their results calculated from the above models. Hence, the comments by Doroodchi et al. (2009) about the model of Leong et al. (2006) are not well-justified.     

Erratum to “Lower bounds for the eigenvalues of the basic Dirac operator on a Riemannian foliation” [J. Geom. Phys. 51 (2004) 166–182]

We correct some statements in the paper mentioned in the title.