The second-order dynamic phase transition and Lee--Yang zeros in Eggers urn model

A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calculated. By applying the Lee-Yang zeros method of equilibrium phase transitions, we study the distributions of the effective partition function zeros and obtain the same result for the model. Thus, the Lee-Yang theory can be applied to a more general non-equilibrium system.     

Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.     

A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations

In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.     

Periodic solutions and flip bifurcation in a linear impulsive system

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.     

Implementation of a Two-Atom √swap Gate in Cavity QED

We implement a two-atom √swap Bate via cavity QED. During the preparation, a cavity-assisted collision betweenatoms is required, and this does not need any auxiliary atom. The cavity is only virtually excited, thus our scheme is insensitive to the cavity field states and to the cavity decay. The scheme can be implemented by the present cavity QED techniques.     

Quantum Key Distribution Network Based on Differential Phase Shift

Using a series of quantum correlated photon pairs, we propose a theoretical scheme for any-to-any multi-user quantum key distribution network based on differential phase shift. The differential phase shift and the different detection time slots ensure the security of our scheme against eavesdropping. We discuss the security under the intercept-resend attack and the source replacement attack.     

Five-Dimensional Cosmological Model with Variable G and A

Einstein＇s field equations with C and A both varying with time are considered in the presence of a perfect fluid for five-dimensional cosmological model in a way which conserves the energy momentum tensor of the matter content. Several sets of explicit solutions in the five-dimensional Kaluza-Klein type cosmological models with variable G and A are obtained. The diminishment of extra dimension with the evolution of the universe for the five-dimensional model is exhibited. The physical properties of the models are examined.     

ON MEAN CURVATURES OF A PARALLEL CONVEX BODY

In this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in R^n. These mean curvature integrals are generalizations of the Santalo＇s results.     

A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.     

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.