Table of contents

This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantities for Nonholonomic Systems with Servoconstraints. The criterions of the Mei symmetry, the Noether symmetry, and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the results.

New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Bäcklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.

A new nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.

Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.

It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.

The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrödinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.

In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations u_xx = H(x)u_tt.

A new Lie algebra, which is far different form the known A_n-1, is established, for which the corresponding loop algebra is given. From this, two isospectral problems are revealed, whose compatibility condition reads a kind of zero curvature equation, which permits Lax integrable hierarchies of soliton equations. To aim at generating Hamiltonian structures of such soliton-equation hierarchies, a beautiful Killing–Cartan form, a generalized trace functional of matrices, is given, for which a generalized Tu formula (GTF) is obtained, while the trace identity proposed by Tu Guizhang [J. Math. Phys. 30 (1989) 330] is a special case of the GTF. The computing formula on the constant γ to be determined appearing in the GTF is worked out, which ensures the exact and simple computation on it. Finally, we take two examples to reveal the applications of the theory presented in the article. In details, the first example reveals a new Liouville-integrable hierarchy of soliton equations along with two potential functions and Hamiltonian structure. To obtain the second integrable hierarchy of soliton equations, a higher-dimensional loop algebra is first constructed. Thus, the second example shows another new Liouville integrable hierarchy with 5-potential component functions and bi-Hamiltonian structure. The approach presented in the paper may be extensively used to generate other new integrable soliton-equation hierarchies with multi-Hamiltonian structures.

With the help of an objective reduction approach (ORA), abundant exact solutions of (2+1)-dimensional higher-order Boussinesq system (including some hyperboloid function solutions, trigonometric function solutions, and a rational function solution) are obtained. It is shown that some novel soliton structures, like single linearity soliton structure, breath soliton structure, single linearity y-periodic solitary wave structure, libration dromion structure, and kink-like multisoliton structure with actual physical meaning exist in the (2+1)-dimensional higher-order Boussinesq system.

In this paper, we investigate entropy properties of the single-mode coherent optical field interacting with the two two-level atoms initially in one of the four Bell states. It is found that the different initial states of the two atoms lead to different evolutions of field entropy and the intensity of the field plays an important role for the evolution properties of field entropy.

In this paper, we propose a protocol that can produce perfect copy of an unknown d-dimensional equatorial quantum state with assistance from a state preparer. In this protocol, the maximally and non-maximally entangled bipartite d-dimensional of states are used as the quantum channels, respectively. The first stage of the protocol requires usual teleportation. In the second stage of the protocol, with the assistance of the preparer, the perfect copy of an original unknown state can be produced.

We present a scheme for teleporting atomic state through a dissipative quantum channel induced by spontaneous emission and investigate the destructive effect of the atomic decay on the success probability and the fidelity of teleportation associated to different channels. It is found that there exists an optimal channel to realize faithful teleportation.

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form Σ^d-1_{i = 0}p_iU_i, and the p_i's are complex numbers with module less or equal to 1 and constrained by |Σ_ip_i|≤1.

We show that the Susskind—Glogower phase state is a limiting case of a kind of SU(1,1) coherent states. By analogy, based on the bipartite entangled state representation (ESR) we demonstrate that an appropriate SU(1,1) coherent state composed of the two-mode unitary phase operator also leads to a new phase state in two-mode Fock space. is diagonalized in the ESR.

In this paper, we present a new macro model for traffic flow on a highway with ramps based on the existing models. We use the new model to study the effects of on-off-ramp on the main road traffic during the morning rush period and the evening rush period. Numerical tests show that, during the two rush periods, these effects are often different and related to the status of the main road traffic. If the main road traffic flow is uniform, then ramps always produce stop-and-go traffic when the main road density is between two critical values, and ramps have little effect on the main road traffic when the main road density is less than the smaller critical value or greater than the larger critical value. If a small perturbation appears on the main road, ramp may lead to stop-and-go traffic, or relieve or even eliminate the stop-and-go traffic, under different circumstances. These results are consistent with real traffic, which shows that the new model is reasonable.

In a recent paper [Commun. Theor. Phys. (Beijing, China) 49 (2008) 268], Huang et al. gave a general variable separation solution to the (2+1)-dimensional breaking soliton equation via a special Bäcklund transformation and the variable separation approach. In terms of the derived variable separation solution and by introducing Jacobi elliptic functions, they claimed that nonelastic types of interaction between Jacobi elliptic function waves are investigated both analytically and graphically. We show that some inappropriateness or errors exist in their paper, and say nothing of the conclusion that some nonelastic types of interaction between Jacobi elliptic function waves in the (2+1)-dimensional breaking soliton equation have been found.

In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg—Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.

A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle α between propagation directions of upper and lower layers can affect these waves.

The dynamical behavior in the cortical brain network of macaque is studied by modeling each cortical area with a subnetwork of interacting excitable neurons. We characterize the system by studying how to perform the transition, which is now topology-dependent, from the active state to that with no activity. This could be a naive model for the wakening and sleeping of a brain-like system, i.e., a multi-component system with two different dynamical behavior.

In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov—Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities (LMIs) is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.

We consider the minimal conformal model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its one-point and two-point correlation functions.

An improved Z^1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional formulae.

Properties of the triaxial superdeformed (TSD) bands of Hf isotopes are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. Quantitatively good results of the γ-ray energies, the dynamical moments of inertia, and the spin of the TSD bands in Hf isotopes are obtained. It shows that this approach is quite powerful in describing the properties of the triaxial superdeformation in Hf isotopes.

The second Born approximation (SBA) theory is applied to the study of electron-atom scattering in the presence of a CO₂ laser field.The absolute differential cross sections of e-Ar scattering are calculated with multiphoton exchange in two special scattering geometries G₁ (for small-angle scattering) and G₂. For geometry G₁, compared with the results of two different model potentials for electron elastic scattering by atoms, it is found that electron-atom polarization potential plays an important role in laser-assisted electron-atom scattering. Some calculational results in geometries G₂ are given. Our results are found to be better than other theoretical results as compared with the experimental data in geometries G₁ and G₂.

In this paper, a theoretical scheme is proposed to implement the Deutsch–Jozsa algorithm with SQUIDs (superconducting quantum-interference devices) in cavity via Raman transition. The scheme only requires a quantized cavity field and classical microwave pulses. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the cavity decay is suppressed.

In recent experiments [e.g., Nature Physics 2 (2006) 332], the enhanced light deflection in an atomic ensemble due to inhomogeneous fields is demonstrated by the electromagnetically induced transparency (EIT) based mechanism. In this paper, we explore a different mechanism for the similar phenomenon of the enhanced light deflection. This mechanism is based on the coherent population oscillation, which leads to the hole burning in the absorption spectrum. The medium causing the deflection of probe light is an ensemble of two-level atoms manipulated by a strong controlled field on the two photon resonances. In the large detuning condition, the response of the medium to the pump field and signal field is obtained with steady state approximation. And it is found that after the probe field travels across the medium, the signal ray bends due to the spatial-dependent profile of the control beam.

The system of mixture of single lane and double lane is studied by a cellular automata model, which is developed by us based on the Nagel and Schreckenberg's models. We justify that the model can reach a stable states quickly. The density distributions of the stable state is presented for several cases, which illustrate the manner of the congestion. The relationship between the outflow rate and the total number of vehicles and that between the outflow rate and the density just before the bottleneck are both given. Comparing with the relationship that occurring in the granular flow, we conclude that the transition from the free traffic flow to the congested traffic flow can also be attributed to the abrupt variation through unstable flow state, which can naturally explain the discontinuities and the complex time variation behavior observed in the traffic flow experiments.

In this paper, the dynamics behaviors on f₀-δ parameter surface is investigated for Gledzer–Ohkitani–Yamada model. We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase diagram on f₀-δ parameter surface, which is divided into periodic, quasi-periodic, and intermittent chaos areas. By means of varying Taylor-microscale Reynolds number, we calculate the extended self-similarity of velocity structure function.

We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry's linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two-dimensional monatomic β-FPU lattice.

By making use of the ϕ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the (2+1)-dimensional skyrmion excitations in ferromagnets. We also discuss the branch processes of these skyrmions and the generation and annihilation of skyrmion-antiskyrmion pairs.

Under the framework of Maxwell–Garnett (M-G) model, the optical and electrical properties of single-walled carbon naotube (SWCNT), double-walled carbon nanotube (DWCNT) and hydrogen-doped carbon nanotube (H-doped CNT) in terahertz (THz) region have been investigated. It has been found that as frequency increases the loss tangent and conductivity show a peak. The loss tangent and conductivity of SWCNT is larger than that of DWCNT and H-doped CNT. The loss tangent and conductivity increase with the increases of filling factor and the decreases of geometrical factor.

We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I(t)k or lose one monomer at a rate J(t)k, and with a probability P (t) an aggregate of any size is randomly removed. We then analytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I(t) — J(t) as well as the birth rate I(t). The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I(t) — J(t) ≥ P (t) or [J(t) + P (t) − I(t)]t ≃ 0 at t ≫ 1; otherwise, it will become extinct.

The structure aperiodicities can influence seriously the features of motion of soliton excited in the α-helix protein molecules with three channels. We study the influence of structure aperiodicities on the features of the soliton in the improved model by numerical simulation and Runge–Kulta method. The results obtained show that the new soliton is very robust against the structure aperiodicities including large disorder in the sequence of mass of the amino acids and fluctuations of spring constant, coupling constant, dipole-dipole interactional constant, ground state energy and chain-chain interaction. However, very strong structure aperiodicities can also destroy the stability of the soliton in the α-helix protein molecules.

We investigate the statistical nature of holographic gas, which may represent the quasi-particle excitations of a strongly correlated gravitational system. We find that the holographic entropy can be obtained by modifying degeneracy. We calculate thermodynamical quantities and investigate stability of the holographic gas. When applying to cosmology, we find that the holographic gas behaves as holographic dark energy, and the parameter c in holographic dark energy can be calculated from our model. Our model of holographic gas generally predicts c < 1, implying that the fate of our universe is phantom-like.

Based on the covariant anomaly cancellation method, which is believed to be more refined than the initial approach of Robinson and Wilczek, we discuss Hawking radiation from the plane symmetric black hole. The result shows that Hawking radiation from the non-spherical symmetric black holes also can be derived from the viewpoint of anomaly.

Considering the self-gravitation and energy conservation as well as charge conservation, we extend Medved and Vagenas's quantum tunneling method to the global monopole charged black hole, and give a correction to Hawking radiation of a charged particle.