On the possibility of surface transversal wave guidance in an elastic subsurface layer of cubic crystal systems with periodic material inhomogeneities

In the paper, the possibility of surface transversal waves existence on an elastic surface layer with artificially induced periodic inhomogeneities has been described. Such kind of waves, unlike well-known surface modes sustained close to the surface boundary by an elastic layer as well as constant or periodic electrical short, have potential to transfer higher energy with higher velocity. Such parameters are very important for applications of sensors. In the work, some outline of the theory, chosen qualitative aspects of such wave propagation on regular crystal surfaces as well as the results of preliminary experimental tests were presented.

Convergence of equilibria for bending-torsion models of rods with inhomogeneities

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show that, as $h\searrow 0$, stationary points of the energy , for a rod $\Omega _h\subset {\open R}^3$ with cross-sectional diameter h, subconverge to stationary points of the Γ-limit of , provided that the bending energy of the sequence scales appropriately. This generalizes earlier results for homogeneous materials to the case of materials with (not necessarily periodic) inhomogeneities.

Solitary waves in an inhomogeneous chain of α-helical proteins

The dynamics of Davydov's model of α-helical proteins is considered by including the influence of inhomogeneities in the monomer units. Using the D2 ansatz for the exciton–phonon quantum state, the model Hamiltonian is transformed into a pair of classical lattice equations, which is further reduced in the continuum limit to a sole perturbed nonlinear Schrödinger (NLS) equation. The results of the perturbation theory of this equation show that the inhomogeneities in the localized form do not affect the velocity and amplitude of the solitary waves during propagation. We employ also the sine–cosine functions method to construct the exact solitary wave solutions in the presence of a variety of nonlinear inhomogeneities such as biquadratic, exponential and periodic inhomogeneities and it reveals that the coherent energy transport in the α-helical proteins is very much influenced by these nonlinear inhomogeneities.