The linear friction welding process of α+β titanium alloys VT6 and VT8M-1 has been studied and in particular the investigation of microstructure in the weld zone. The results of this investigation were used for development of a numerical model of LFW equilibrium stage using the ANSYS Mechanical software. The set of parameters used in this model allowed to reach a quantitative agreement with experiments

We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane Couette or Poiseuille flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external electric and/or magnetic field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semianalytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analyzed.

Stability of some unsteady three-dimensional flows (exact solutions of the viscous incompressible Navier–Stokes equations in cylindrical coordinates) is studied via separation of variables in the linearized equations for the flow perturbations. The flows in an expanding rotating porous cylinder and in a gap between two coaxial rotating cylinders are considered. Converting the stability equations to the new variables allows perturbation forms (counterparts of normal modes of the steady state parallel flow stability problem) such that the linear stability problems are exactly reduced to eigenvalue problems of ordinary differential equations. The eigenvalue problems are solved numerically with the help of the spectral collocation method based on Chebyshev polynomials. The results showing dependence of the stability threshold on the parameters of the problems and a spatial structure of the unstable perturbation modes are presented. For some classes of perturbations, exact analytical solutions of the eigenvalue problems are available. A combination of analytical and numerical solutions can provide useful testing for numerical methods used in the hydrodynamic stability studies. It may also provide a basis for a well-grounded discussion of some problematic points of (numerical) stability analysis. In particular, in the present paper, a problem of formulation of the boundary conditions for perturbations at the axis r=0 is discussed on the basis of the solutions obtained.

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