Papers by Keyword: Time Scales

Abstract: In this paper,we consider the oscillation of second order linear dynamic equation on time scales, and obtain sufficient condition for oscillation of solutions.

Abstract: In this paper, we consider oscillation of solutions of the differential equations with variable coefficients on time scales, and obtain some sufficient conditions for oscillation of solutions.

Abstract: In this paper, we consider properties for solutions of the differential equations with variable delay on time scales, and obtain some sufficient conditions for properties of solutions.

Abstract: The mass transport in the presence of stress, electrical, mechanical and chemical potential gradients in multicomponent solid solution is analyzed. The method bases on the Darken concept and the calorimetric equation of state. We effectively coupled the conservation of the mass (continuity equations), energy, momentum and Gauss equations. The diffusion fluxes of the components are given by the Nernst-Planck formulae and take into account the electro-chemical and mechanical potentials. We simulate the deformation field during the diffusion caused by the gradients of the chemical potential of all elements in non-ideal Fe-Cu-Ni alloy. The simulations show that the model is compatible with experimental results, and can be effectively used for modelling the energy, momentum and mass transport problems in compressible multicomponent solid solutions. The numerical problems and methods of solution are presented.

Abstract: The Darken method is used to evaluate and compare different time scales in an ideal crystal lattice. The crystalline tungsten exemplifies presented approach. It is shown that in this metal and at 1273 K the time scales differ by nine orders of magnitude. Particular emphasis is given to the problem of deformation, the temperature and the mass diffusion time scales in tungsten quasicontinuum. The transport process in the nonuniform temperature and stress field is characterized by representative velocities. These velocities allow to quantify the time and length scales and can be used for the proper non-dimensialization and effective solution of the particular transport problems.