abstract

Recently, even–even nuclei with quadrupole and octupole deformations have been studied, taking into account the triaxiality of their shape. This approach allows one to simultaneously describe the alternating-parity spectrum of different bands of these nuclei. In this case, the values of the parameters of quadrupole and octupole triaxiality go beyond the traditional characteristic values of separate consideration of these deformations: \(\gamma _{\rm eff}\) (\(0\leq \gamma _{\rm eff}\leq \frac {\pi }{6}\)) and \(\eta _{\rm eff}\) (\(0\leq \eta _{\rm eff}\leq \frac {\pi }{2}\)). To identify the reasons for these differences, we studied the behavior of low-lying energy levels of a rigid asymmetric rotator with alternating parity depending on the angular variable of the polar coordinates \(\varepsilon _0\) for fixed values of the triaxiality parameters \(\gamma _{\rm eff}\) and \(\eta _{\rm eff}\). We determined the region of experimentally observed energy levels with alternating parity corresponding to the given values of the triaxial parameters \(\gamma _{\rm eff}\) and \(\eta _{\rm eff}\) for different values of the angular parameter \(\varepsilon _0\).

abstract

Quantization of the kinetic energy of a nucleus with deformation in curvilinear coordinates in the presence of octupole vibrations of its surface is performed. The obtained Hamiltonian differs from the previously known expression for quadrupole vibrations only in the coefficients before the differentiation operators \(\partial /\partial \gamma \) and \(\partial /\partial \eta \). This is due to the difference in the components of the moment of inertia tensor of the nucleus for quadrupole and octupole modes. An exact expression for the full Hamiltonian of an even–even nucleus is determined, taking into account both quadrupole and octupole deformations, including seven dynamic variables. Some fields of application of the proposed Hamiltonian are discussed.

abstract

In this paper, we introduced two definitions of \(N\)-tuple compound synchronization (NCS) and \(N\)-tuple compound combination synchronization (NCCS) in (\(2N+2\)) and (\(3N+2\)) different chaotic models, respectively. The analytical formulas for the control functions are derived from two established theorems in order to perform these types of synchronization. These new types of synchronization are considered a generalization of various types disccussed in the literature. Numerous applications in engineering and physics may benefit from these new types of synchronization, e.g. , image encryption and electronic circuits. Using the active control technique for the choice \(N=5\), we study two examples of 5CS and 5CCS in 12 and 17 different chaotic models. The analytical forms of the control functions are used and good agreement is found. The Runge–Kutta method of order four is used in our numerical simulations. Other examples can be similarly studied. We designed an electronic circuit for the proposed \(N\)-tuple compound synchronization in 12 different chaotic models. Using MATLAB/Simulink, both numerical and simulation results show good agreement. For other drive models, similar circuit implementations can be created.