International Journal of Modern Physics C

This paper introduces and analyzes new hyperchaotic complex Lorenz systems. These systems are 6-dimensional systems of real first order autonomous differential equations and their dynamics are very complicated and rich. In this study we extend the idea of adding state feedback control and introduce the complex periodic forces to generate hyperchaotic behaviors. The fractional Lyapunov dimension of the hyperchaotic attractors of these systems is calculated. Bifurcation analysis is used to demonstrate chaotic and hyperchaotic behaviors of our new systems. Dynamical systems where the main variables are complex appear in many important fields of physics and communications.

The dynamics of entropy exchange and correlation in u(2) algebraic model for two stretches of H₂O and SO₂ is studied in terms of the linear entropy with diagonal approximation, where various initial states are respectively taken to be the product of thermal states and squeezed states on each mode. It is shown that with a suitable parameter in initial states, the entropies in each stretch are positively correlated or anticorrelated, which depend on initial states and a molecule. The entropy correlation is also studied in terms of a correlation index. It is demonstrated that the correlation index and the sum of linear entropies in each stretch are identical in oscillation. The differences in the linear entropy in each stretch and the correlation index of the thermal states and the squeezed states between H₂O and SO₂ are noticed. These may be useful for quantum computing and quantum information processing based on two stretching modes in both molecules.

A controlled quantum dense coding protocol with GHZ-class state is proposed. In this case the sender (Alice) can send information to the receiver (Bob), whereas the supervisor (Cliff) can control the quantum channel between Alice and Bob via his local measurement. The amount of classical information is shown to be controlled by the supervisor through adjustments of the local measurement angles and depend on the coefficients of the original GHZ-class state. We also give two concrete methods for Alice to deal with one of Cliff's measurement result which is more complicated.

Site invasion percolation (IP) processes are combined with bond percolation model, to study the effects of size restriction on low capillary number immiscible displacement in heterogeneous nanoporous media. Both cases of compressible (NTIP) and incompressible defender fluid (TIP) are considered. It is found that in site IP the value of mass uptake increases with the size of invader particles, if the latter is not greater than a critical value. This occurs when the accessible porosity of the medium decreases as the size of fluid particles increases. We also investigate the effect of nanopore's concentration on the mass and the anisotropy of sample spanning cluster as well as the critical exponent of trap numbers.

An algorithm to share a secret among a set of users is introduced in this work. It is based on the use of linear cellular automata over the finite set 𝔽₂ and it is considered as a generalization of a previous work due to the authors dealing with an elementary cellular automata-based secret sharing scheme. The algorithm is shown to be secure, ideal, and perfect.

We propose quantitative definitions of network community and hierarchy in collaboration networks described by bipartite graphs, whose basic elements, named actors, take part in events, organizations or activities, named acts. We show, by examples, in some practical collaboration networks that the network acts, represented by certain complete subgraphs in the projected single-mode network, usually are highly interwoven. However, we can easily identify the communities by the definition and the algorithm presented in this paper. We also propose a novel statistical quantity, i.e., interweavement, which describes quantitatively how the acts are interwoven in a collaboration network.

We define an asset exchange model by adding the kickback rate to the trade, and discuss the Gini index with different kickback rates. It is found that for every kickback rate, the related Gini index tends to be steady; thus, the kickback rate — Gini index curve may be obtained. Furthermore, it is shown that the Gini index decreases when the kickback rate increases, so that the fair degree of social wealth distribution gets better. The Gini index reaches a minimum when the kickback rate is 0.58, and then it increases, as the accretion of the kickback rate destroys the fair degree of social wealth distribution. However, in all situations, the Gini index with kickback rate is less than the one without kickback. This means that the introduction of kickback rate is favorable to the raising of the fair degree of wealth distribution. We also define a moral index similar to the Gini index to weigh the differences of social moral level, and find that the differences of social moral level increase with time for the model with kickback rate.

In this paper, we have studied theoretically the effects of gold adsorption on the Al(001) surface, using ab initio pseudo-potential method in the framework of the density functional theory. Having found the hollow sites at the Al(001) surface as the most preferred adsorption sites, we have investigated the effects of the Au adsorption with different coverages (Θ =0.11, 0.25, 0.50, 0.75, 1.00 ML) on the geometry, adsorption energy, surface dipole moment, and the work function of the Al(001) surface. The results show that even though the work function of the Au substrate increases with the Au coverage, the surface dipole moment decreases with the changes in coverage from Θ =0.11 to 0.25 ML. We have explained this behavior by analyzing the electronic and ionic charge distributions. Furthermore, by studying the diffusion of Au atoms into the substrate, we have shown that at room temperature the diffusion rate of Au atoms into the substrate is negligible but increasing the temperature to about 200°C the Au atoms significantly diffuse into the substrate, in agreement with the experiment.

A finite-difference lattice Boltzmann (LB) algorithm is described on general body-fitted coordinate systems. An alternative treatment for the implicit collision term of the Boltzmann–Bhatnagar–Gross–Krook equation is used, which completely removes the implicitness of the numerical scheme through using the characteristic of collision invariants. LB simulations are carried out for a two-dimensional supersonic viscous flow past a circular cylinder and the natural convection heat transfer in a circular enclosure with an inner hexagonal cylinder for the first time. The pressure coefficient distribution along the surface of the circular cylinder and the Nusselt number in the natural convection obtained from the simulations agree well with previous experimental measurements and/or classical computational fluid dynamics simulations. Comparisons of detailed flow patterns with other studies are also satisfactory.

Combining a modified Independent Component Analysis (ICA) and a feedback cancellation of nonlinear terms, the approach of engineering control can efficiently govern a noisy chaotic system. The methodology is easy to comprehend and to implement, but previous knowledge of the system dynamics is needed.

A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic oscillator when x → 0. These models give rise to approximative equidistant energy levels of bound states and resonances as it is shown using numerical calculations based on an efficient method of generating functionals.

In the magnetic Eden model (MEM), particles have a spin and grow in contact with a thermal bath. Although Ising-like interactions affect the growth dynamics, deposited spins are frozen and not allowed to flip. This paper focuses on recent developments and future prospects, such as spontaneous switching phenomena, critical behavior associated with fractal, wetting, and order-disorder phase transitions, the equilibrium/nonequilibrium correspondence conjecture, as well as dynamical and critical features of the MEM defined on complex network substrates.