Discussion on the limit cycles of the Lev Ginzburg equation by M. Bellamy and R.E. Mickens,Journal of Sound and Vibration 308 (2007) 337–342

The authors M. Bellamy and R.E. Mickens in the article “Hopf bifurcation analysis of the Lev Ginzburg equation” published in Journal of Sound and Vibration 308 (2007) 337–342, claimed that this differential equation in the plane can exhibit a limit cycle. Here we prove that the Lev Ginzburg differential equation has no limit cycles.     

Reply to the comments of M.E. Golmakani and J. Rezatalab,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), Journal of Sound Vibration, 333 (2014) 3831–3835

Golmakani and Rezatalab [1] suggested in their paper that the deflection of a simply supported nonlocal elastic plate under uniform load is not affected by the small length scale terms. They based their proof on the use of Navier?s method using a sinusoidal-based deflection solution. This insensitivity of the deflection solution of a simply supported nonlocal elastic plate with respect to the small length terms of Eringen?s model is not correct, as already detailed in the literature (for example, see [2] for beam problems). In fact, the deflection of the nonlocal plate (in the Eringen sense) is larger than the one of the local case, as shown in many papers available in the literature. We prove in this reply to the authors that the Navier?s method has to be correctly applied for highlighting the specific sensitivity phenomenon of the deflection solution, as compared to exact analytical solution.     

Commentary on “Mechanical properties of monodomain side-chain nematic elastomers” by P. Martinoty,P. Stein,H. Finkelmann,H. Pleiner and H.R. Brand

We discuss the background to static and dynamic soft elasticity. The evidence in the static case and the symmetry basis for soft and semi-soft elasticity is well understood. By contrast the dynamic analogy is less clear. Lack of clean time scale separation clouds the interpretation of director relaxation keeping up, or not, with imposed strains. However, the reduction in modulus between geometries obtaining at low frequencies and being lost at high frequencies confirms that director reaction indeed determines dynamical semi-softness.Received: 13 April 2004, Published online: 17 August 2004PACS: 83.80.Va Elastomeric polymers - 61.30.-v Liquid crystals - 83.60.Bc Linear viscoelasticity     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.