In the present research, vibrational behavior of anisotropic protein microtubules (MTs) immersed in cytosol via Cooper–Naghdi shell model is investigated. MTs are hollow cylindrical structures in the eukaryotic cytoskeleton which surrounded by filament network. The temperature effect on vibration frequency is also taken into account by assuming temperature-dependent material properties for MTs....

We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, th...

We investigate linear stability of solitary waves of a Hamiltonian system. Unlike weakly nonlinear water wave models, the physical system considered here is nonlinearly dispersive, and contains nonlinearity in its highest derivative term. This results in more detailed asymptotic analysis of the eigenvalue problem in presence of a large parameter. Combining the technique of singular perturbation...

U. Introduction In Doyle and Bricksen [1956. p. 77] it is observed that the Cauchy stress tensor 0 can be derived by varying the internal energy e with respect to the Riemannian metric on space: oab =Zpae/agab. Their formula has gone virtually unnoticed in the elasticity literature. In this lecture we shall explain some of the reasons why this formula is, in fact, of fundamental significance. S...