Table of contents

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps between arbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probability distribution as a function of the time and position for any initial distribution with all the transients included. Next, the transient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecular motor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kinetic behaviors of a molecular motor under external load F.

The homogeneous balance method is a method for solving general partial differential equations (PDEs). In this paper we solve a kind of initial problems of the PDEs by using the special Bäcklund transformations of the initial problem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initial problems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.

A novel dynamics equation of elastic rotation shaft possessing twin side based on the theory of relativity is built in this paper. The equation is established in different coordinate systems, which can provide the foundation theoretically and methods for the similarity engineering and the similarity calibration of instruments used for measuring, observing, and controlling.

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2+1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2+1)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach, a general variable separation solution of this system is derived. Besides the stable localized coherent soliton excitations like dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractal behaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.

This article discusses the complete separability and partial separability of the pure states of the quantum network of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variables in three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled state representations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained, which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.

This paper generalizes the quantum clock synchronization protocol of Josza, et al., [Richard Jozsa, et al., Phys. Rev. Lett. 85 (2000) 2010] to synchronize space and time simultaneously.

We study particles in a vortex state driven to a core state with lower energy and zero angular momentum by the trap potential asymmetries. We find that at $T=0$ when the role of the thermal gas can be ignored, there will be coexisting condensates. We also calculate the fluctuation of the number difference and argue that in certain range of the parameters the state of the whole system is the macroscopic quantum self-trapping in the Josephson tunnelling regime.

In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is applied to some nonlinear evolution equations to derive their multi-order solutions.

Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties of high security, fast encryption (decryption) speed, and robustness against noise disturbances in communication channel. The overall features of this spatiotemporal-chaos-based cryptosystem are better than chaotic cryptosystems known so far, and also than currently used conventional cryptosystems, such as the Advanced Encryption Standard (AES).

A general type of localized excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess quite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the real natural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universal formula is valid for some quite universal (2+1)-dimensional physical models. The "universal" formula is also extended to a more general form with many more independent arbitrary functions.

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in $D=2$ and $D=3$ Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some special first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in $D=3\enspace GN$ model a first order phase transition does occur in the case of zero temperature and finite chemical potential.

We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. The corresponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are given.

Based on the effective Hamiltonian with the generalized factorization approach, we calculate the branching ratios and CP asymmetries of B → VV decays in the Topcolor-assisted Technicolor (TC2) model. Within the considered parameter space we find that: (a) for the penguin-dominated $B\rightarrow K^{*+}\phi$ and $K^{*0}\phi$ decays, the new physics enhancements to the branching ratios are around 40%; (b) the measured branching ratios of $B\rightarrow K^{*+}\phi$ and $K^{*0}\phi$ decays prefer the range of $3\lesssim N_c^{\text {eff}}\lesssim 5$; (c) the SM and TC2 model predictions for the branching ratio $\mathcal{B}(B^+\rightarrow\rho^+\rho^0)$ are only about half of the Belle's measurement; and (d) for most B → VV decays, the new physics corrections on their CP asymmetries are generally small or moderate in magnitude and insensitive to the variation of $m_\widetilde{\pi}$ and $N_c^{\text{eff}}$.

In the minimal supersymmetric standard model (MSSM) with CP violating phases, this paper discusses the production of the lightest neutral Higgs boson in association with tau sleptons at future high-energy $e^+e^-$ linear colliders. In parameter space of the constrained MSSM, the production cross section of $e^+e^-\rightarrow h^0\widetilde{\tau}_1^+\widetilde{\tau}_1^-$ can be very substantial at high energies. This process would provide a production mechanism for probing couplings of neutral Higgs bosons to tau sleptons as well as some soft supersymmetric breaking parameters at next linear colliders.

Effect of conversion process (Ξ^-P → ΛΛ) on Ξ^--hypernucleus is studied for $_\Xi-{^{12}}Be$. It is found that the conversion process has a certain extent effect on properties of low-lying states of the Ξ^--hypernuclei.

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approximation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional very rough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximation at microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation and integral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancement on the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.

After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.

An efficient scheme is proposed for the generation of atomic Schrödinger cat states in an optical cavity. In the scheme N three-level atoms are loaded in the optical cavity. Raman coupling of two ground states is achieved via a laser field and the cavity mode. The cavity mode is always in the vacuum state and the atoms have no probability of being populated in the excited state. Thus, the scheme is insensitive to both the cavity decay and spontaneous emission.

Applying the approximate Fokker-Planck equation we derived, we obtain the analytic expression of the stationary laser intensity distribution $P_{st}(I)$ by studying the single-mode laser cubic model subject to colored cross-correlation additive and multiplicative noise, each of which is colored. Based on it, we discuss the effects on the stationary laser intensity distribution $P_{st}(I)$ by cross-correlation between noises and "color" of noises (non-Markovian effect) when the laser system is above the threshold. In detail, we analyze two cases: One is that the three correlation-times (i.e. the self-correlation and cross-correlation times of the additive and multiplicative noise) are chosen to be the same value $(\tau_1=\tau_2=\tau_3=0)$. For this case, the effect of noise cross-correlation is investigated emphatically, and we detect that only when $\lambda\neq0$ can the noise-induced transition occur in the $P_{st}(I)$ curve, and only when $\tau\neq0$ and $\lambda\neq0$, can the "reentrant noise-induced transition" occur. The other case is that the three correlation times are not the same value, $\tau_1\neq\tau_2\neq\tau_3$. For this case, we find that the noise-induced transition occurring in the $P_{st}(I)$ curve is entirely different when the values of $\tau_1,\enspace\tau_2,$ and $\tau_3$ are changed respectively. In particular, when $\tau_2$ (self-correlation time of additive noise) is changing, the ratio of the two maximums of the $P_{st}(I)$ curve R exhibits an interesting phenomenon, "reentrant noise-induced transition", which demonstrates the effect of noise "color" (non-Markovian effect).

The energy spectra of low-lying states of an exciton in a single and a vertically coupled quantum dots are studied under the influence of a perpendicularly applied magnetic field. Calculations are made by using the method of numerical diagonalization of the Hamiltonian within the effective-mass approximation. We also calculated the binding energy of the ground and the excited states of an exciton in a single quantum dot and that in a vertically coupled quantum dot as a function of the dot radius for different values of the distance and the magnetic field strength.

The methods for the few-body system are introduced to investigate the states of the barrier Li quantum dots (QDs) in an arbitrary strength of magnetic field. The configuration, which consists of a positive ion located on the $z$-axis at a distance d from the two-dimensional QD plane (the $x-y$ plane) and three electrons in the dot plane bound by the positive ion, is called a barrier Li center. The system, which consists of three electrons in the dot plane bound by the ion, is called a barrier Li QD. The dependence of energy of the state of the barrier Li QD on an external magnetic field B and the distance d is obtained. The angular momentum L of the ground states is found to jump not only with the variation of B but also with d.

We study the steady state properties of a logistic growth model in the presence of Gaussian white noise. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution function and its extrema have been investigated. It is found that the fluctuation of the tumor birth rate reduces the population of the cells while the fluctuation of predation rate can prevent the population of tumor cells from going into extinction. Noise in the system can induce the phase transition.

We study the kinetics of an irreversible aggregation model with removal term. We solve the mean-field rate equation to obtain the general solution of the cluster-mass distribution for the case with arbitrary time-dependent removal probability $P(t)$. In particular, we analyze the scaling properties of the cluster distribution in the case with $P(t) = u(t + t_0)^v$ and find that the cluster-mass distribution always obeys a scaling law. We also investigate the kinetic behavior of another simple system, in which the removal probability of a cluster is proportional to its mass, and the results indicate that for this system the scaling description of the cluster-mass distribution breaks down completely.

Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528.