Three-dimensional elastic problems of three-dimensional quasicrystals

An analytic solution of initial boundary value problem for 3D quasicrystals in half space

“…Following the idea suggested in [34][35][36], the solution method of the problem for elastodynamic model of quasicrystals, the model based on Bak's arguments, with polynomial data is established. In Section 2, basic equations of elastodynamic theory of quasicrystals and formulation of the problem are introduced.…”

Complex potential theory for the plane elasticity problem of decagonal quasicrystals and its application

“…Wang et al [15] investigated the arc-shaped crack problem of decagonal quasicrystals. The three-dimensional initial value problem for three-dimensional quasicrystals was considered in reference [16]. Two-dimensional problems of one-dimensional quasicrystals elasticity were turned into the boundary value problems of holomorphic vector functions in a given region by means of the generalized Stroh formalism [17].…”

A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

“…The problem has been reduced to the sequence of the initial value problems for the system of second-order hyperbolic equations with two independent variables x 3 and t. The obtained initial value problems have been solved by d'Alembert formula. PS method has been successfully generalized for the solution of the initial boundary value problem in anisotropic half space (Yakhno and Akmaz, 2007) and for the solution of the initial value problem of elastodynamics for 3D quasicrystals (Akmaz, 2009). The modified PS method has been applied in Altunkaynak (2009, 2010) for the system of crystal optics.…”