Crossing the phantom divide in brane cosmology with curvature corrections and brane-bulk energy transfer

We consider the Randall-Sundrum brane-world model with bulk-brane energy transfer where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. It is remarkable that these curvature terms will not change the dynamics of the brane universe at low energy. Parameterizing the energy transfer and taking the dark radiation term into account, we find that the phantom divide of the equation of state of effective dark energy could be crossed, without the need of any new dark energy components. Fitting the two most reliable and robust SNIa datasets, the 182 Gold dataset and the Supernova Legacy Survey (SNLS), our model indeed has a small tendency of phantom divide crossing for the Gold dataset, but not for the SNLS dataset. Furthermore, combining the recent detection of the SDSS baryon acoustic oscillations peak (BAO) with lower matter density parameter prior, we find that the SNLS dataset also mildly favors phantom divide crossing.

Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of a dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasilocal gravitational energy found recently for f(R) gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the Friedmann-Robertson-Walker spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for f(R) gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.

Description of a radially polarized Laguerre-Gauss beam beyond the paraxial approximation

Fifth-order corrected expressions for the fields of a radially polarized Laguerre-Gauss (R-TEMn1) laser beams are derived based on perturbative Lax series expansion. When the order of Laguerre polynomial is equal to zero, the corresponding beam reduces to the lowest-order radially polarized beam (R-TEM01). Simulation results show that the accuracy of the fifth-order correction for R-TEMn1 depends not only on the diffraction angle of the beam as R-TEM01 does, but also on the order of the beam. (c) 2007 Optical Society of America.

Exact description of a cylindrically symmetrical complex-argument Laguerre-Gauss beam

Based on the perturbative series representation of a complex-source-point spherical wave an expression for cylindrically symmetrical complex-argument Laguerre-Gauss beams of radial order n is derived. This description acquires the accuracy up to any order of diffraction angle, and its first three corrected terms are in accordance with those given by Seshadri [Opt. Lett. 27, 1872 (2002)] based on the virtual source method. Numerical results show that on the beam axis the number of orders of nonvanishing nonparaxial corrections is equal to n. Meanwhile a higher radial mode number n leads to a smaller convergent domain of radius. (C) 2008 Optical Society of America.

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of particle phase is expanded into an infinite series by means of Grad's method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

风沙两相流中的跃移运动

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Ｂoltzmann方程；并以此将单相颗粒流理论中的广义平衡方程推广到气固两相流的情形。提出用Grad方法将粒子相速度分布函数展成无穷级数，并引入Gauss分布取代单相颗粒流中传统的Maxwell分布。在保留到3次项的情况下，建立了气体－颗粒两相湍流边界层三阶矩封闭理论的动力学方程组。并在风洞频闪摄影实验的基础上，对理论进行简化，得到便于工程应用的简化方程。

一个推广Virial定理的数学方法和应用

本文在提出广义Gauss定理的思路下,提出了广义Stokes定理和一个推广Virial定理的新方法,后者应用于天体磁流体力学和引力平衡问题时得到的结果有:(1)气体具有运动时的平衡系统的判据,(2)磁场对气团形态的影响。应用于实验室等离子体平衡问题时,其结果有:(1)包围在气体中孤立磁场的特性,(2)发现内包无力场必须外包一有力场,(3)无力场的形态,应用于Tokmak等离子体环时的结果有:(1)环的胖瘦对环表面磁压的影响,(2)两个外加磁场分量分别和气压、环的胖瘦,截面形态、环电流分布和逆磁或顺磁的平衡关系,搞清楚了外加磁场约束等离子体总体平衡的物理机制。

气流与化学激光中的碰撞和非均匀加宽效应——理论分析模型

本文把用于气流与化学激光性能计算的理论模型作了分析比较,包括常用的Lorentz-Gauss谱线形因子近似、本文提出的矩形谱线形因子近似以及文献[5]的理论。对气流化学激光的简化扩散混合模型,文中简要地导出了与上述诸理论相对应的具体结果。分析和计算表明:在碰撞与非均匀加宽同时起作用,特别是非均匀加宽占优势的情况下,两种谱线形因子近似以及文献[5]理论的结果三者之间存在显著的差异;矩形谱线形因子近似要比常用的Lorentz-Gauss谱线形因子近似精确,而矩形谱线形因子近似的计算量要比Lorentz-Gauss谱线形因子近似的计算量少。

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

计算流体力学