High-level Stark Effect and Spectrum of Spherical Nanometer System

In the electric field and layer-to-layer interaction energy, the law of split-level of high-level Stark effect of spherical nanometer system is explored as well as the frequency of spectrum, intensity and size effect of coefficient of spontaneous radiation. Taking three layers CdS/HgS spherical nanometer system as an example, the influence of the electric field and layer-to- layer interaction energy is explored on Stark effect and spectrum. The results show that in the Stark effect system, the energy level is split based on 1, 3, ..., （2n-1）, when it is in the electric field only, similar to the hydrogen atoms; and in the electric field and layer-to-layer interaction, it is split based on 1, 4, ~ -., n2; with the quantum transition, the frequency of the spectrum decreases with the increasing size of the system; apart from a few spectral lines, the intensity of most spectral lines will decreased as the size increases; while the coefficient of spontaneous radiation will increase with the increasing size; the electric field will cause the changes of spectrum frequency; its spectrum frequency shift is proportional to the square of the electric field intensity; apart from a few spectral lines, the frequency shift of spectral lines that is caused by the electric field and layer-to-layer interaction will decrease as the size increases; the interaction will make the level of electronic energy level lower slightly （the order of magnitude is between 10-7-10-9 eV）, the slightly increased spectrum intensity and the slightly increased value of coefficient of spontaneous radiation, but it will not influence the frequency of spectrum, intensity, and the trend that coefficient of spontaneous radiation changes with the size; when the size is smaller, the layer-to-layer interaction effect will be significant.

Nonequilibrium Statistical Physics Subject to the Anomalous Langevin Equation in Liouville Space

Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics. This equation reflects that the law of motion of particles obeying reversible, deterministic laws in dynamics becomes irreversible and stochastic in thermodynamics. From this the fundamental equations of nonequilibrium thermodynamics, the principle of entropy increase and the theorem of minimum entropy production have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation etc. have been derived rigorously from the kinetic kinetic equation which is reduced from the anomalous Langevin equation in Liouville space. All these are unified and self consistent. But it is difficult to prove that entropy production density σ can never be negative everywhere for all the isolated inhomogeneous systems far from equilibrium.

Numerical simulation of pollutant diffusion and decay process after a water pollution incident in the Three Gorges Reservoir

We established a hydrodynamic model to simulate the pollutant transport and decay process in the case of a pollution incident in the sections of the Yangtze and the Jialing passing through the city area of Chongqing. The Boussinesq assumptions and the Navier-Stokes equations of incompressible fluid were applied to setting up the pollutant diffusion equations and the equations for the decay process. E. colt was taken as the example pollutant, and chloride dosage, light, temperature and ultraviolet intensity were considered in the equations for bacterial decay process. The calculated values of the fluid velocities in the two rivers agree well with corresponding measured results, indicating an ideal accuracy of the model. In simulation, the concentration of E. colt in water was assumed to be zero before the accident. The and 1.75 m/s for the Yangtze flow, and the downriver boundary was upriver boundary velocity was -1.35 m/s for the Jialing flow water depth set at 0. Simulation results show that the bacteria are transported downstream along the riverbank. A long and narrow pollutant belt develops at 12 h after the start of the accident ascribed to the quick longitudinal transfer. After the pollution sources are cut off, the pollutant concentration decreases slowly, mostly by advection and diffusion, suggesting inadequate self-purification ability of the rivers and the necessity of effective decontaminating measures in the case of a pollution incident, The model can be a useful tool for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water body of the Three Gorges Reservoir.

Turbulence Model Investigations on the Boundary Layer Flow with Adverse Pressure Gradients

In this paper, a numerical study of flow in the turbulence boundary layer with adverse and pressure gradients （APGs） is conducted by using Reynolds-averaged Navier-Stokes （RANS） equations. This research chooses six typical turbulence models, which are critical to the computing precision, and to evaluating the issue of APGs. Local frictional resistance coefficient is compared between numerical and experimental results. The same comparisons of dimensionless averaged velocity profiles are also performed. It is found that results generated by Wilcox （2006） k-co are most close to the experimental data. Meanwhile, turbulent quantities such as turbulent kinetic energy and Reynolds-stress are also studied.

Effect of Bed Vicinity on Vortex Shedding and Force Coefficients of Fluid Flow on an Offshore Pipeline

The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×10^4.Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.

Recent Advances to Change the Standards in Designing Hulls in Waves, a Validation Using an Efficient SWENSE Level-Set Approach

This paper presents recent naval applications of the SWENSE （Spectral Wave Explicit Navier-Stokes Equations） approach implemented for the first time with high order fully unstructured schemes and an efficient level-set method to capture free surface flows around realistic hull geometries. Numerical simulations in waves and/or viscous flows still lead generally to very large CPU times because of grid requirements to ensure a good propagation of incident waves in the meshed part of the fluid domain that makes unreachable any hull design optimization process in an industrial context. Furthermore, even if the SWENSE method clearly shows promising results in an academic context in both regular and irregular waves, the most recent publications still highlight several issues that remain unresolved up to now, e.g. poor scalability, diffusive wake pattern, non-versatile structured mesh approaches and only very few validation test cases are carried out on Wigley or DTMB 5415 hulls. In order to overcome those numerical difficulties and get an in-depth validation of the method on several cases in realistic wave conditions, a two and a half years＇ research project has been achieved involving several steps, starting by a set of dedicated model test experiments later used as reference for the validation of the method. The CFD commercial code ANANASTM used and developed in this research program is presented and validated in detail. The use of high order schemes on unstructured grids in combination with these SWENSE method and level-set approach offer to the maritime industry an innovative and state of the art method to achieve unequaled accuracy, low computation time and some unique advantages such as, amongst others, the end of the numerical wave propagation problems. The results of the validation were pleasing and can be considered as acceptable in general, with some challenges remaining to the solyed. Results obtained indicate that an optimization processes in waves in realistic conditions is now affordable in an industrial context.

Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations

The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous （inviscid） regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes- Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient v →0.

GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS

The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.

Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

Ignition of Hydrocarbon-Air Supersonic Flow by Volumetric Ionization

The paper describes the results of the electron-beam initiation of the combustion in the mixtures of hydrogen,natural gas or kerosene vapors with air.Electron beam characteristics were studied in closed volume with immobile gas.The researches included definition of an integrated current of an electronic beam,distribution of a current density and an estimation of average energy of electrons.Possibility of fuel mixtures ignition by means of this approach in the combustor at high velocity at the entrance was demonstrated.Experiments were carried out at Mach numbers of 4 and 5.Process of ignition and combustion under electron beam action was researched.It was revealed that ignition of mixture occurs after completion of electron gun operation.Data obtained have confirmed effectiveness of electron beam application for ignition of hydrogen and natural gas.The numerical simulation of the combustion of mixture in channel was carried out by means of ANSYS CFD 12.0 instrumentation on the basis of Reynolds averaged Navier-Stokes equation using SST/k-ωturbulence model.For combustion modeling,a detailed kinetic scheme with 38 reactions of 8 species was implemented taking into account finite rate chemistry.Computations have shown that the developed model allow to predict ignition of a mixture and flame propagation even at low flow temperatures.

Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.

Incompressible limit and stability of all-time solutions to 3-D full Navier-Stokes equations for perfect gases

This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.

REMARKS ON THE EXISTENCE OF WEAK SOLUTIONS TO 2-D INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for initial vorticity in LP form. Moreover,the uniqueness is to be proved here.