THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

THE LARGE TIME BEHAVIOR OF SPECTRAL APPROXIMATION FOR A CLASS OF PSEUDOPARABOLIC VISCOUS DIFFUSION EQUATION

The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.

Large Time Behavior of a Weak Solution for Non-Newtonian Flow

This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvaiue of the Stokes operator.

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum

We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that there is a global strong solution and is unique for the 2D Cauchy problem with the initial density which can allow vacuum conditions and even have compact support. Besides, the large time decay rates of the gradients of velocity, temperature and pressure can also be obtained which are also the same as those of the homogeneous case.

LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS

In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable ＂pressure＂ functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.

GLOBAL EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTION TO REACTING FLOW MODEL WITH BOUNDARY EFFECT

The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH FADING MEMORY

We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approach- ing to predetermined diffusion waves, Pointwise estimates on the convergence details are obtained.

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.

LARGE TIME BEHAVIOR OF SOLUTION TO NONLINEAR DIRAC EQUATION IN 1+1 DIMENSIONS

This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R^(1+1). It is shown that the solution will tend to travelling wave solution when time tends to infinity.

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations of Korteweg Type

In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.

Effect of ageing time on corrosion behavior of Mg-10Gd-4.8Y-0.6Zr extruded-alloy

The corrosion behaviors of Mg-10Gd-4.8Y-0.6Zr extruded-alloys with various ageing time were investigated by immersion test and electrochemical measurements.The results show that the corrosion rate of the experimental alloy decreases with the increase of ageing time from 0 to 108 h.The corrosion resistance of the experimental alloy was found to increase with the increase of the size of the precipitate phases.The open circuit potential of the experimental alloy increases with the increase of the ageing time.The potentiodynamic polarization curves show that the cathodic over-potential increases with the increase of ageing time,leading to a decrease in the current density of anodic current plateau with the increase of ageing time.

Large Eddy Simulations of Mixing Time in a Stirred Tank

Large eddy simulations (LES) of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with Sma-gorinsky-Lilly subgrid scale model. The impeller rotation was modeled using the sliding mesh technique. Better agree-ment of power demand and mixing time was obtained between the experimental and the LES prediction than that by the traditional Reynolds-averaged Navier-Stokes (RANS) approach. The curve of tracer response predicted by LES was in good agreement with the experimental. The results show that LES is a reliable tool to investigate the unsteady and quasi-periodic behavior of the turbulent flow in stirred tanks.

Time Domain Simulation of Transient Responses of Very Large Floating Structures Under Unsteady External Loads

A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is developed directly in time domain and the hydrodynamic problem is formulated based on linear, inviscid and slightly compressible fluid theory and the structural response is analyzed on the thin plate assumption. The time domain finite element procedure herein is validated by comparing numerical results with available experimental data. Finally, the transient elastic response of a pontoon-type VLFS under the landing of an airplane is computed by the proposed time domain FEM. The time histories of the applied force and the position and velocity of an airplane during landing are modeled with data from a Boeing 747-400 jumbo jet.

THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

We use Hopf-Lax formula to study local regularity of solution to Hamilton- Jacobi （HJ） equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T 〉 0, which depends only on the Hamiltonian and initial datum, for t 〉 T the solution of the IVP （1.1） is smooth except for ~ smooth n-dimensional hypersurface, across which Du（x, t） is discontinuous. And we show that the hypersurface 1 tends asymptotically to a given hypersurface with rate t-1/4.

Modeling and simulation of solvent behavior and temperature distribution within long stick propellants with large web thickness undergoing drying

Drying is a complicated physical process which involves simultaneous heat and mass transfer in the removal of solvents inside propellants.Inappropriate drying techniques may result in the formation of a hard skin layer near the surface to block the free access of most solvent through for long stick propellants with large web thickness,which lead to lower drying efficiency and worse drying quality.This study aims to gain a comprehensive understanding of drying process and clarify the mechanism of the blocked layer near the propellant surface.A new three-dimensional coupled heat and mass transfer(3D-CHMT)model was successfully developed under transient conditions.The drying experiment results show that the 3DCHMT model could be applied to describe the drying process well since the relative error of the content of solvent between simulation and experiment values is only 5.5%.The solvent behavior simulation demonstrates that the mass transfer process can be divided into super-fast(SF)and subsequent minorfast(MF)stages,and the SF stage is vital to the prevention of the blocked layer against the free access for solvent molecules inside propellant grains.The effective solvent diffusion coefficient(Deff)of the propellant surface initially increases from 3.4×10^(-6)to 5.3×10^(-6)m^(2)/s as the temperature increases,and then decreases to 4.1×10^(-8)m^(2)/s at 60-100 min.The value of Deffof surface between 0-1.4 mm has a unique trend of change compared with other regions,and it is much lower than that of the internal at100 min under simulation conditions.Meanwhile,the temperature of the propellant surface increases rapidly at the SF stage(0-100 min)and then very slowly thereafter.Both the evolution of Deffand temperature distribution demonstrate that the blocked layer near the propellant surface has been formed in the time period of approximately 0-100 min and its thickness is about 1.4 mm.To mitigate the formation of blocked layer and improve its drying quality of finial propellant products effectively,it should be initially dried at lower drying temperature(30-40℃)in 0-100 min and then dried at higher drying temperature(50-60℃)to reduce drying time for later drying process in double base gun propellants.The present results can provide theoretical guidance for drying process and optimization of drying parameters for long stick propellants with large web thickness.

Experimental investigation on behaviors of bolt-supported rock strata surrounding an entry in large dip coal seam

In order to investigate the behaviors and stability of rock strata surrounding an entry with bolt supporting in large dip coal seams (LDCSs) dipping from 25° to 45°, a self-developed rotatable experimental frame for similar material simulation test was used to build the model with the dip of 30°, based on analyses of geological and technological conditions in Huainan mine area, Anhui, China. The strata behaviors, such as extracting- and mining-induced stresses development, deformation and failure modes, were synthetically integrated during working face advancing. Results show that the development characteristics of mining-induced stress and deformation are asymmetrical in the roadway. The strata behaviors are totally different in different sections of the roadway. Because of asymmetrically geometrical structure influenced by increasing dip, strata dislocating, rock falling and breaking occur in roof. Then, squeezing, collapsing and caving of coal happen in upper- and lower-rib due to shearing action caused by asymmetrical roof bending and dislocating. Owing to the absence of supporting, floor heaving is very violent and usually the zone of floor heaving develops from the lower-rib to upper-rib. Engineering practices show that, due to the asymmetrical characteristics of rock pressure and roadway configuration, it is more difficult to implement bolt supporting system to control rock stability of roadways in LDCSs. The upper-rib and roof of entries are the key sections. Consequently, it is reliable to use asymmetrical bolt-mesh-cable supporting system to control rock stability of roadways based on the asymmetrical characteristics of roadway configuration and strata behaviors.

Time Domain Calculation of Connector Loads of a Very Large Floating Structure

Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures （VLFSs） and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet-Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0° This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS

Structural first failure times under non-Gaussian stochastic behavior

An analytical moment-based method for calculating structuralfirst failure times under non-Gaussian stochastic behavior is proposed. In the method, a power series that constants can be obtained from response moments （skewness, kurtosis, etc.） is used firstly to map a non-Gaussian structural response into a standard Gaussian process, then mean up-crossing rates, mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated, and finally, the formula for calculating first failure times is established on the assur^ption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussian model.

Effect of sex,temperature,time and flock size on the diving behavior of the wintering Scaly-sided Merganser(Mergus squamatus)

Background: The foraging and diving behavior of waterfowl are affected by a number of important factors. Hence, learning more about these major factors is of great concern in order to protect endangered species. In this study, we verified the effect of sex, temperature, time and flock size on the diving behavior of the Scaly-sided Merganser(Mergus squamatus).Methods: The study was conducted by means of focal animal sampling in the Wuyuan section of the Poyang Lake watershed in Jiangxi Province, China from December 2015 to March 2016. We used one-way ANOVA and LSD tests to investigate the differences among these factors. Pearson correlations were used to test the relation between pause duration and the previous or subsequent dive duration. The relations between these factors and dive/pause duration are illustrated using Spearman correlations.Results: Mean dive duration and mean time on the pause of males were significantly higher than those of females. With an increase in temperature, dive duration significantly increased. Along with the passage of time of year and daytime, dive duration significantly increased, while dive duration decreased significantly with the increase in flock size.Conclusions: Sex, temperature, time and flock size have an effect on the diving behavior of the wintering Scalysided Merganser. The difference of diving behavior between males and females is related to differences in body mass. The difference of diving behavior among various temperatures and time periods may be related to a low minimum rate of oxygen consumption, while the difference among various flock sizes may be caused by rising intraspecific competition.

A phenomenological model for plastic flow behavior of rotating band material with a large temperature range

The plastic flow behavior of the rotating band material is investigated in this paper. The rotating band material is processed from H96 brass alloy, which is hardened to a much higher yield strength compared to the annealed one. The dynamically uniaxial compression behavior of the material is tested using the split Hopkinson pressure bar(SHPB) with temperature and strain rate ranging from 297 to 1073 K and500 to 3000 s^(-1), respectively, and a phenomenological plastic flow stress model is developed to describe the mechanical behavior of the material. The material is found to present noticeable temperature sensitivity and weak strain-rate sensitivity. The construction of the plastic flow stress model has two steps. Firstly, three univariate stress functions, taking plastic strain, plastic strain rate and temperature as independent variable, respectively, are proposed by fixing the other two variables. Then, as the three univariate functions describe the special cases of flow stress behavior under various conditions, the principle of stress compatibility is adopted to obtain the complete flow stress function. The numerical results show that the proposed plastic flow stress model is more suitable for the rotating band material than the existing well-known models.