International Journal of Modern Physics B

The aim of this survey paper is to illustrate the perspectives on the theories of the single- and multi-pulse global bifurcations and chaotic dynamics of high-dimensional nonlinear systems and applications to several engineering problems in the past two decades. Two main methods for studying the Shilnikov type multi-pulse homoclinic and heteroclinic orbits in high-dimensional nonlinear systems, which are the energy-phase method and generalized Melnikov method, are briefly demonstrated in the theoretical frame. In addition, the theory of normal form and an improved adjoint operator method for high-dimensional nonlinear systems is also applied to describe a reducing procedure to high-dimensional nonlinear systems. The aforementioned methods are utilized to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of the cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end. How to employ these methods to analyze the Shilnikov type multi-pulse homoclinic and heteroclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications is demonstrated through this example.

The speed of quantum computation is investigated through the time evolution of the speed of the orthogonality. The external field components for classical treatment besides the detuning and the coupling parameters for quantum treatment play important roles on the computational speed. It has been shown that the number of photons has no significant effect on the speed of computation. However, it is very sensitive to the variation in both detuning and the interaction coupling parameters.

A unidirectional coupling method to successfully suppress spiral waves in excitable media is proposed. It is shown that this control method has high control efficiency and is robust. It adapts to control of spiral waves for catalytic CO oxidation on platinum as well as for the FHN model. The power law n ~ c^-k of control time steps n versus the coupling strength c for different models has been obtained.

Glow curves of natural thermoluminescence (NTL) of colorless microcline (triclinic form of KAlSi₃O₈ feldspar) have been subjected to the rigorous Computerized Glow Curve Deconvolution (CGCD) in the framework of kinetic formalism and Various Heating Rates (VHR) methods to compare the spectroscopy of traps. It is observed that trapping parameters obtained by the two methods are coincident, which is well-supported by the standard error analyses, i.e., Figure of Merit (FOM) and Chi-square test. Further analysis shows that the value of Urbach's constant (U_m) is no more constant in the present case for the whole temperature range, but has certain values for a certain temperature zone.

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

A spin-2 system consisting of two layers of Bethe lattices each with a branching ratio of q Ising spins was analyzed by the use of the exact recursion relations in a pairwise approach. The upper layer interacting with nearest-neighbor (NN) bilinear interaction J₁ is laid over the top of the lower layer interacting with bilinear NN interaction J₂, and the two layers are tied together via the bilinear interaction between the vertically aligned adjacent NN spins denoted as J₃. The study of the ground state phase diagrams on the (J₂/|J₃|, J₁/|J₃|) plane with J₃>0 and J₃<0 and on the (J₂/J₁, J₃/q J₁) plane with J₁>0 has yielded five distinct ground state configurations. The temperature dependent phase diagrams are obtained for the case with intralayer coupling constants of the two layers with ferromagnetic type J₁ and J₂>0, and the interlayer coupling constant of the layers with either ferromagnetic J₃>0 or antiferromagnetic type J₃<0 on the (kT/J₁, J₃/J₁) planes for given values of the J₂/J₁ for various values of the coordination numbers. As a result, we have found that the model presents both second- and first-order phase transitions, therefore, tricritical points.

A penalty finite element method for the incompressible viscous Navier–Stokes equations is incorporated in an arbitrary Lagrangian–Eulerian formulation to model a flow in the fluid–structure interaction (FSI) with moving meshes. The formulation is derived based on the classical Ritz–Galerkin framework for forming a coupled formulation on the finite element method. In such a way, the pressure-constrained equation is incorporated in the momentum equations of the system with FSI. An improving spring smooth and remeshing technique is used to successively accommodate fluid meshes as the oscillation of a solid boundary in simulation. To demonstrate the performance of the proposed approach, the simulations of the flow with an elastic beam in water, that is oscillating in a large amplitude are presented. The simulations show that the methodology suggested in this paper has a good numerical stability and reliability, and the results are highly agreeable with the published reference.

Al₂O₃ films were deposited by reactive magnetron sputtering. As measured with Raman spectroscopy, the atomic force microscopy (AFM), nanohardness and spectrophotometer, respectively. Raman microscopy was then employed to follow their characteristics of optical and acoustic phonon modes. At the optimal sputtering time of 30 minutes, defect-induced first and second order Raman spectra were observed in the 100–900 cm^-1 band, which was related to coating composition. However, at the thickness at 250, 300, 450 and 500 nm crystals of the order of nano size of α- Al₂O₃ phase were achieved, which could be clearly identified by the presence of Raman peaks at 388, 417 cm^-1 and 521 cm^-1 assigned to Si substrate. The average nano grain size is measured by atomic force microscopy (AFM). It was found that the hardness was strongly dependent on the roughness of the films, the maximum of which was achieved at 20.01 GPa. The optical band gap of Al₂O₃ films was found to be in the range of 5.55 eV. All these results were analyzed and presented as a function of the deposition parameters and composition, and crystalline phases excited in the films.

We consider wave packet propagation in mesoscopic quantum systems. A number of approaches are compared to look at the general solution of a time-dependent Schrödinger equation and the validity of the Ehrenfest theorem. Detailed calculations are presented to illustrate the results of a charged particle motion in the time-dependent systems, and show that the Ehrenfest theorem is not directly applicable in topologically nontrivial systems.

In this work, the heat capacity in dimensionally quantized semiconductor thin films with Kane's dispersion law is investigated. Under certain conditions, quantum size effect occurs, depending on the thickness of the thin film, the concentration of conductive electrons, and the non-parabolicity parameters. In thin films having non-parabolic energy spectrum in degenerate electron gas, the film thickness depends on the subband number and the concentration. Therefore, heat capacity takes the form of the saw toothwise and changes as non-monotonous.

Two quantum broadcasting multi-signature schemes are presented: one is used to sign classical digital messages and the other to sign quantum messages. The quantum one-way function is used to realize signature and verification in the digital multi-signature scheme, while quantum teleportation is used in the quantum multi-signature scheme. The proposed schemes support infinite amounts of signatories and provide a novel and experimentally feasible method to construct multi-signature quantum signature systems within current technology.

We investigate the thermodynamic properties of a trapped Bose gas of Rb atoms interacting through a repulsive potential at low but finite temperature (k_BT < μ < T_c) by Quantum Monte Carlo method based upon the generalization of Feynman-Kac method^1-3 applicable to many-body systems at T=0 to finite temperatures. In this paper, we report temperature variation of condensation fraction, chemical potential, density profile, total energy of the system, release energy, frequency shifts and moment of inertia within the realistic potential model (Morse type) for the first time by diffusion Monte Carlo technique. The most remarkable success was in achieving the same trend in the temperature variation of frequency shifts as was observed in JILA⁴ for both m=2 and m=0 modes. For other things, we agree with the work of Giorgini et al.,⁵ Pitaevskii et al.⁶ and Krauth.⁷

The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot–Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot–Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.