GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ（（φ（ρ））xxφ′（ρ））x with φ（ρ） = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] （α=1/2） to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.

Numerical Method for Solving Relativistic Hydrodynamic Equation Including Quark-Fragment Effect

In this paper, a numerical method is given to solve relativistic hydrodynamic equations with source terms by conservative finite difference scheme. In calculation, QGP (quark gluon plasma) phase transition is also considered. The numerical experiments have verified the effectiveness of the numerical method and some computational results are illustrated.

An alternating direction implicit （ADI） numerical model for two－dimensional hydrodynamic equations

A two-dimensional computational model is develope for the calulation of tides, storm surges and otherlong-period waves in coastal and shelf waters. The Partial differental equations are approximated by two sets of difference equations on a space-staggered grid system. Both sets are explicit with one set for water level and x-component velocity, and another for water level and y-component velocity. These two sets are used successively for stepby-step solution in time. An analytical investigation on the linearized sets of the difference equations indicates that thecomputational scheme is unconditionally stable. The model is of second order accuracy both in space and in time andconserves mass and momentum. Simulations of surface elevation caused by periodic forcing in one-opening rectangularbasin with flat topography and by steady wind stress in the basin with flat or slope topography show that the computed results are in excellent agreement with the corresponding analytic solutions. The steady-tate wind-induced setupin a ofed basin with discontinuous topography computed with the present model are also in excellent agreement withthe results from Leendertse's model. Finally, the model is applied to hindcast a storm surge in the South China Seaand reproduces the surge elevation satisfactorily.

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The stability condition and the Korteweg-de Vries （KdV） equation are derived to describe the density wave of pedestrian congestion by linear stability and nonlinear analysis. Through theoretical analysis, the soliton solution is obtained.

Effect of Ion Concentrations on the Characteristics of a Multi-Component Magnetized Plasma Sheath

A hydrodynamic approach is used to investigate a three-component magnetized plasma sheath which consists of electrons and two species of positive ions. Assuming a phase space of one-dimensional spatial coordinate system and three-dimensional velocity coordinate system, the effect of different concentrations of positive ion species on some characteristics of the plasma sheath such as the velocity and density distribution of positive ion species and the electrostatic potential of this region is investigated. The calculated results show that the increase in the density ratio of positive ion species causes a decrease in both the ion velocities and the electrostatic potential of the sheath region. Also, it is shown that in the sheath region of a magnetized plasma consisting of only one positive ion species the bumps of the net density of charged particles disappears much faster. In addition, three-dimensional velocity of each positive ion species in the sheath region is plotted for different concentrations of positive ion species.

Non-Local Theory of Bose-Einstein Condensate and Stopping of Light

The problem of an adequate description of the transport processes in Bose-Einstein condensates (CBE), including space-temporal evolution of CBE in a gravitational field is considered. The full nonlocal system for the CBE evolution is delivered including particular case and analytical solutions. We show (analytically) that a black hole can evolve in the Bose-Einstein condensate (CBE) regime. At the same time, there are modes in which black hole flickering occurs. Quantization of the black holes flickering is discovered. The corresponding nonlocal hydrodynamic equations indicated for fermions gas.

Dynamic Analysis of Propulsion Mechanism Directly Driven by Wave Energy for Marine Mobile Buoy

Marine mobile buoy（MMB） have many potential applications in the maritime industry and ocean science.Great progress has been made,however the technology in this area is far from maturity in theory and faced with many difficulties in application.A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB,especially with consideration of hydrodynamic force.The principle of wave-driven propulsion mechanism is briefly introduced.To set a theory foundation for study on the MMB,a dynamic model of the propulsion mechanism of the MMB is obtained.The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations.A simplified form of the motion equations is reached by omitting terms with high order small values.The relationship among the heave motion of the buoy,stiffness of the elastic components,and the forward speed can be obtained by using these simplified equations.The dynamic analysis show the following：The angle of displacement of foil is fairly small with the biggest value around 0.3 rad;The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy;The relationship among heaven motion,stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle,therefore,the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant.The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.