Analysis of the stability and density waves for traffic flow

In this paper, the optimal velocity model of traffic is extended to take into account the relative velocity. The stability and density waves for traffic flow are investigated analytically with the perturbation method. The stability criterion is derived by the linear stability analysis. It is shown that the triangular shock wave, soliton wave and kink wave appear respectively in our model for density waves in the three regions: stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg－de Vries equation and modified Korteweg－de Vries equation. The analytical results are confirmed to be in good agreement with those of numerical simulation. All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.     

Travelling Waves for a Density Dependent Diffusion Nagumo Equation over the Real Line

We consider the density dependent diffusion Nagumo equation, where the diffusion coefficient is a simple power function. This equation is used in modelling electrical pulse propagation in nerve axons and in population genetics (amongst other areas). In the present paper, the δ-expansion method is applied to a travelling wave reduction of the problem, so that we may obtain globally valid perturbation solutions (in the sense that the perturbation solutions are valid over the entire infinite domain, not just locally; hence the results are a generalization of the local solutions considered recently in the literature). The resulting boundary value problem is solved on the real line subject to conditions at z →±∞. Whenever a perturbative method is applied, it is important to discuss the accuracy and convergence properties of the resulting perturbation expansions. We compare our results with those of two different numerical methods (designed for initial and boundary value problems, respectively) and deduce that the perturbation expansions agree with the numerical results after a reasonable number of iterations. Finally, we are able to discuss the influence of the wave speed c and the asymptotic concentration value α on the obtained solutions. Upon recasting the density dependent diffusion Nagumo equation as a two-dimensional dynamical system, we are also able to discuss the influence of the nonlinear density dependence (which is governed by a power-law parameter m) on oscillations of the travelling wave solutions.     

Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

In this paper, the analytical solutions of Schr¨odinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker–Planck equation known as the Klein–Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr¨odinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.     

Fractal dynamics and computational analysis of local fractional Poisson equations arising in electrostatics

In this paper, the local fractional natural decomposition method(LFNDM) is used for solving a local fractional Poisson equation. The local fractional Poisson equation plays a significant role in the study of a potential field due to a fixed electric charge or mass density distribution. Numerical examples with computer simulations are presented in this paper. The obtained results show that LFNDM is effective and convenient for application.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.     

Binding Energy Calculation of Electrons in Statistical Potentials for Arbitrary Temperature and Matter Density

Schroedinger‘s wave equation is solved in Thomas-Fermi potential including the self-interaction modification of elctrons for arbitrary matter density and temperature,In order to describe relativistic effects,the mass-velocity correction,the Darwin correction and the spin-orbit coupling terms are included in the wave equation.Calculations are presented for the Fe^26 and Rb^37 atoms at a few temperatures and matter densities.Comparisons of present results with other more accurate one^[9] are given in Table.The data obtained by the present method are not bad.     

Post-collision interactions and the polarization effect in （e, 2e） collisions of helium

A modified distorted-wave Born approximation (DWBA) method is used to calculate the triple differential cross sections (TDCSs) in a coplanar asymmetric geometry for the electron impact single ionization of a He (1s2) atom at intermediate and lower energies. The post-collision interaction and the polarization effect in (e, 2e) collisions of helium are considered in the calculations. The polarization potentials from the damping method and density functional theory (DFT) are compared. Theoretical results are compared with the recent experimental data.     

Time-Dependent Transport in Nanoscale Devices

A method for simulating ballistic time-dependent device transport, which solves the time-dependent Sehrǒdinger equation using the finite difference time domain （FDTD） method together with Poisson＇s equation, is described in detail. The effective mass Schrǒdinger equation is solved. The continuous energy spectrum of the system is discretized using adaptive mesh, resulting in energy levels that sample the density-of-states. By calculating time evolution of wavefunctions at sampled energies, time-dependent transport characteristics such as current and charge density distributions are obtained. Simulation results in a nanowire and a coaxially gated carbon nanotube field-effect transistor （CNTFET） are presented. Transient effects, e.g., finite rising time, are investigated in these devices.     

A new model analysis of the third harmonic voltage in inductive measurement for critical current density of superconducting films

The critical current density J c is one of the most important parameters of high temperature superconducting films in superconducting applications,such as superconducting filter and superconducting Josephson devices.This paper presents a new model to describe inhomogeneous current distribution throughout the thickness of superconducting films applying magnetic field by solving the differential equation derived from Maxwell equation and the second London equation.Using this model,it accurately calculates the inductive third-harmonic voltage when the film applying magnetic field with the inductive measurement for J c.The theoretic curve is consistent with the experimental results about measuring superconducting film,especially when the third-harmonic voltage just exceeds zero.The J c value of superconducting films determined by the inductive method is also compared with results measured by four-probe transport method.The agreements between inductive method and transport method are very good.     

Approximate analytic solutions for a generalized Hirota—Satsuma coupled KdV equation and a coupled mKdV equation

<正>This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries(KdV) equation and a coupled modified Korteweg-de Vries(mKdV) equation. This method provides a sequence of functions which converges to the exact solution of the problem and is based on the use of the Lagrange multiplier for the identification of optimal values of parameters in a functional.Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.     

Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrodinger Equation

The one-dimensional time-independent Schr6dinger equation is transformed into a Hamiltonian canonical equation by means of the Legendre transformation, then the symplectic schemes and a new shooting method extended to the eigenvalues of the Schr6dinger equation. The method is applied to the calculations of one-dimensional harmonic oscillator, an anharmonic oscillator and the hydrogen atom. The numerical results are in good agreement with the exact ones.     

Structures and Phase Transition of GaAs under Pressure

A first-principles plane wave method with the ultrasoft pseudopotential scheme in the frame of the density functional theory （DFT） is performed to calculate the lattice parameters a and c, the bulk modulus B0 and its pressure derivative B0 of the zinc-blende GaAs （ZB-GaAs）, rocksalt GaAs （RS-GaAs）, CsCl-GaAs, NiAs- GaAs and wurtzite GaAs （WZ-GaAs）. Our results are consistent with the available experimental data and other theoretical results. We also calculate the phase transition pressures among these different phases. The results are satisfactory.     

Structures and Equation of State of ε-Fe under High Pressure

The equation of state （EOS） and the axial ratio c/a of ε-Fe at high pressures are investigated by using the gen- eralized gradient approximation （GGA） within the plane-wave pseudopotential density functional theory （DFT）. The results show that at the lower pressure, the EOS of ferromagnetic ε-Fe is consistent with the experimental result. While at higher pressure, the EOS of the nonmagnetic ε-Fe is in good agreement with the experimental result. Meanwhile, we find an obvious increase of the axial ratio c/a with pressure, and there is only a small increase with increasing temperature at high pressure.     

Bulk Modulus and Electronic Band Structure of ZnGa2Xa （X=S,Se）： a First-Principles Study

First-principles local density functional calculations are presented for the compounds ZnGa2X4 （X = S, Se）. We investigate the bulk moduli and electronic band structures in a defect chalcopyrite structure. The lattice constants and internal parameters are optimized. The electronic structures are analysed with the help of total and partial density of states. The relation between the cohesive energy and the unit cell volume is obtained by fully relaxed structures. We derive the bulk modulus of ZnGa2Xa by fitting the Birch-Murnaghan＇s equation of state. The extended Cohen＇s empirical formula agrees well with our ab initio results.     

On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method

In this paper, we mainly study the time-space fractional strain wave equation in microstructured solids. He’s variational method, combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation. The main advantage of the variational method is that it can reduce the order of the differential equation, thus simplifying the equation, making the solving process more intuitive and avoiding the tedious solving process.Finally, the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method. The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics.     

Theoretical Study of Elastic Properties of Tungsten Disilicide1

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young＇s moduli of WSi2. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi2 are calculated as a function of pressure up to 35 GPa. The relationship between bulk modulus and temperature up to 1200 K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

Ground State Properties for Bose-Condensed Gas in Anisotropic Traps

Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross-Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 （1996） 2477] This new method is simple compared to other methods used to solve numerically the Gross-Pitaevskii equation, and one can obtain analytic and reliable results.     

First-Principles Study of Orthorhombic Perovskites MgSiO3 up to 120 GPa and Its Geophysical Implications

High-pressure behaviour of orthorhombic MgSiO3 perovskite crystal is simulated by using the density functional theory and plane-wave pseudopotentials approach up to 120 GPa pressure at zero temperature. The lattice constants and mass density of the MgSiO3 crystal as functions of pressure are computed, and the corresponding bulk modulus and bulk velocity are evaluated. Our theoretical results agree well with the high-pressure experimental data. A thermodynamic method is introduced to correct the temperature effect on the O-K first-principles results of bulk wave velocity, bulk modulus and mass density in lower mantle PIT range. Taking into account the temperature corrections, the corrected mass density, bulk modulus and bulk wave velocity of MgSiO3-perovskite are estimated from the first-principles results to be 2%, 4%, and 1% lower than the preliminary reference Earth model （PREM） profile, respectively, supporting the possibility of a pure perovskite lower mantle model.     

Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.     

Primary resonance of fractional-order Duffing–van der Pol oscillator by harmonic balance method

The dynamical properties of fractional-order Duffing–van der Pol oscillator are studied, and the amplitude–frequency response equation of primary resonance is obtained by the harmonic balance method. The stability condition for steady-state solution is obtained based on Lyapunov theory. The comparison of the approximate analytical results with the numerical results is fulfilled, and the approximations obtained are in good agreement with the numerical solutions. The bifurcations of primary resonance for system parameters are analyzed. The results show that the harmonic balance method is effective and convenient for solving this problem, and it provides a reference for the dynamical analysis of similar nonlinear systems.