In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density...In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.展开更多
In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their...In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. The system is free to oscillate in the vertical plane. We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.展开更多
Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level de...Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schr?dinger equation, nonlinear terms appear in the neighborhood of the singular points.展开更多
文摘In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.
文摘In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. The system is free to oscillate in the vertical plane. We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.
文摘Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schr?dinger equation, nonlinear terms appear in the neighborhood of the singular points.
