Generalized projective synchronization of two coupled complex networks of different sizes

We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach.     

Investigations into quantum correlation of coupled qubits in a squeezed vacuum reservoir

In this paper,we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in a squeezed vacuum reservoir.We compare and analyze the effects of squeezed parameters on quantum discord and quantum concurrence.The results show that in a squeezed vacuum reservoir,the quantum discord and quantum concurrence perform with completely opposite behaviors with the change of squeezed parameters.Quantum discord survives longer with the increase of squeezed amplitude parameter,but entanglement death is faster on the contrary.The results also indicate that the classical correlation of the system is smaller than quantum discord in a vacuum reservoir,while it is bigger than quantum discord in a squeezed vacuum reservoir.The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments,which indicates that the entanglement actually is easily affected by decoherence and quantum discord has a stronger ability to avoid decoherence in a squeezed vacuum reservoir.     

Resonant tunneling and enhanced Goos–Hänchen shift in a graphene double velocity barrier structure

Resonant transmission and Goos–Hänchen (GH) shift for Dirac fermion beams tunneling through graphene double velocity barrier structures (DVBs) are investigated theoretically. Analytical and numerical results demonstrate that strong resonant tunneling effect occurs in this structure and is highly dependent on the incident angle and the structure of velocity barriers. The resonant tunneling in graphene DVBs belongs to the Fabry–Pérot resonance and leads to oscillated conduction at wide energy range. It is also found that GH shifts in this structure can be enhanced by the resonant tunneling and multi-GH shift peaks with giant magnitudes can occur at these resonant energy positions. These special properties of GH shifts in graphene DVBs may have good application in lateral manipulation of electron beams and valley or spin beam splitter.     

Existence and stability of co-axial and meshed double-walled armchair silicon nanotubes

A systematic study of armchair double-walled Si nanotubes (DWNT) (n, n)@(m, m) (3≤n≤6; 7≤m≤12) using the finite cluster approximation is presented. The geometries of the tubes have been spin optimized with an all electron 3–21 G^⁎ basis set and the B3LYP functional. Analysis of the electronic structure properties of these tubes has also been performed with a larger basis set. The study indicates that the stabilities of the Si nanotubes are of the same order as those of single-walled Si nanotubes. It should be possible to experimentally synthesis both single-walled and double-walled Si nanotubes. The binding energy per atom or the cohesive energy of the nanotubes depends not only on the number of atoms but also on the coupling of the constituent single-walled nanotubes. Nanotubes with small interlayer separations, called meshed tubes, do not hold the coaxial cylindrical structure after optimization. The SiNTs (n, n)@(n+3, n+3) are found to have large formation energies and binding energies per atom. For example, (3, 3)@(6, 6), (4, 4)@(7, 7), (5, 5)@(8, 8), and (6, 6)@(9, 9) all have large binding energies per atom, around 3.7 eV/atom. All Si nanotubes are found to be semiconductors. However, the band gap, in general, is observed to decrease from single walled nanotubes to double walled nanotubes.     

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method’s new role.     

Comparative analysis of Monte Carlo methods via the example of calculating the complex dynamics of a lattice model for a chemical reaction

Complex oscillating dynamics of a microscopic model of a chemical reaction occurring on the surface of a catalyst is calculated using Monte Carlo methods. The five most common algorithms are used and complexity and efficiency of each of them are assessed. It is shown that the calculation time can vary by more than two orders of magnitude. The most efficient Monte Carlo algorithm is identified. Using it, mechanisms of the emergence of oscillations and waves at the microlevel in the lattice model containing millions of nodes are investigated.     

Comparative analysis of the machine repair Problem with imperfect coverage and service pressure condition

In this paper we analyze the warm-standby M/M/R machine repair problem with multiple imperfect coverage which involving the service pressure condition. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced with a coverage probability c by a standby if one is available. We use a recursive method to develop the steady-state analytic solutions which are used to calculate various system performance measures. The total expected profit function per unit time is derived to determine the joint optimal values at the maximum profit. We first utilize the direct search method to measure the various characteristics of the profit function followed by Quasi-Newton method to search the optimal solutions. Furthermore, the particle swarm optimization (PSO) algorithm is implemented to find the optimal combinations of parameters in the pursuit of maximum profit. Finally, a comparative analysis of the Quasi-Newton method with the PSO algorithm has demonstrated that the PSO algorithm provides a powerful tool to perform the optimization problem.     

Variational iteration method for the Burgers’ flow with fractional derivatives—New Lagrange multipliers

The flow through porous media can be better described by fractional models than the classical ones since they include inherently memory effects caused by obstacles in the structures. The variational iteration method was extended to find approximate solutions of fractional differential equations with the Caputo derivatives, but the Lagrange multipliers of the method were not identified explicitly. In this paper, the Lagrange multiplier is determined in a more accurate way and some new variational iteration formulae are presented.     

The derivations of some evolution algebras

In this work, we investigate the derivations of n-dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero. The spaces of derivations for evolution algebras with matrices of rank n ? 1 are described.     

A note on representations for the inverses of tridiagonal matrices

In this note, we propose an explicit representation with the nested sums for the entries of the inverses of general tridiagonal nonsingular matrices. Its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions, is considered. In addition, an analytical representation for the entries of the finite sections of the resolvent of Jacobi matrices, in terms of its related orthogonal polynomials, is observed.