Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS) method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions, and can weaken or even eliminate the instability resulting from the stiffness problem, which occurs in the subsonic high-temperature region of the hypersonic flow field. In addition, when the full Jacobian of chemical source term is diagonalized, the stability of the FCI scheme relies heavily on the flow conditions. Especially in the case of high temperature and subsonic state, the CFL number satisfying the stability is very small. Moreover, we also consider the effect of the space step, and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step. Therefore, we propose an improved method on the grid distribution according to the flow conditions. Numerical tests validate sufficiently the foregoing analyses. Based on the improved grid, the CFL number can be quickly ramped up to large values for convergence acceleration.     

纳米氧化锆水悬浮液的稳定性

通过黏度、表面张力、密度及粒度测试等手段研究了球磨剂、球磨时间、pH值、添加剂等因素对纳米氧化锆水悬浮液稳定性的影响。结果表明:球磨时间2h,球磨剂与氧化锆质量比为3.5%,添加剂可用乙二醇,悬浮液pH值为10.0,氧化锆粒径小于15nm时,纳米氧化锆水悬浮液可稳定30天。     

Stability in a general coupled laser array

For the first time we have presented a method to investigate the stability of quiescent state in a coupled laser array. By introducing tiny perturbation, stability of quiescent state can be known by investigating eigenvalues of coefficient matrix of the corresponding linear differential equations. Only when real parts of the eigenvalues were all negative or zero, the corresponding quiescent state is stable. Two tapes of coupled laser array with loop and linear topological structure were studied respectively. It was found that there were innumerable quiescent states and they could be divided into several types based on phase relation. Some types were stable and others were unstable. Topological structure affects the stability of quiescent state in a coupled laser array.     

高聚合度钨磷多金属氧酸盐的电化学性质和热稳定性

用循环伏安、热重及示差扫描量热法研究了高聚合度钨磷多金属氧酸盐的电化学性质和热稳定性,实验表明,标题化合物H16{[P4W14Na3（H2O）7O58]2[Na4（H2O）13]2[P4W14Na2（H2O）2O56]}·24H2O因其高聚合度而改变了单个阴离子的氧化还原性质,并且该化合物是一种热稳定性高的微孔材料。     

AEGIS-K code for linear kinetic analysis of toroidally axisymmetric plasma stability

A linear kinetic stability code for tokamak plasmas: AEGIS-K (Adaptive EiGenfunction Independent Solutions-Kinetic), is described. The AEGIS-K code is based on the newly developed gyrokinetic theory [L.J. Zheng, M.T. Kotschenreuther, J.W. Van Dam, Phys. Plasmas 14 (2007) 072505]. The success in recovering the ideal magnetohydrodynamics (MHD) from this newly developed gyrokinetic theory in the proper limit leads the AEGIS-K code to be featured by being fully kinetic in essence but hybrid in appearance. The radial adaptive shooting scheme based on the method of the independent solution decomposition in the MHD AEGIS code [L.J. Zheng, M.T. Kotschenreuther, J. Comp. Phys. 211 (2006) 748] is extended to the kinetic calculation. A numerical method is developed to solve the gyrokinetic equation of lowest order for the response to the independent solutions of the electromagnetic perturbations, with the quasineutrality condition taken into account. A transform method is implemented to allow the pre-computed Z-function (i.e., the plasma dispersion function) to be used to reduce the integration dimension in the moment calculation and to assure the numerical accuracy in determining the wave–particle resonance effects. Periodic boundary condition along the whole banana orbit is introduced to treat the trapped particles, in contrast to the usual reflection symmetry conditions at the banana tips. Due to the adaptive feature, the AEGIS-K code is able to resolve the coupling between the kinetic resonances and the shear Alfvén continuum damping. Application of the AEGIS-K code to compute the resistive wall modes in ITER is discussed.     

Evaluation of critical exponents from raman intensities

Theory and experiment are compared for Raman intensities near continuous structural phase transitions. Situations in which the order parameter couples linearly to light or quadratically are considered. Both cases are easily analyzed for the soft modes in ferroelastic LnP₅O₁₄ (Ln = La, Pr, Nd, Tb). The trace polarizability tensor yields β = 0.49 ± 0.02; off-diagonal terms give γ’ = 1.16 ± 0.15 and γ = 1.07 ± 0.10. Mean field results are also obtained for barium sodium niobate near T (incommensurate) = 582 K and for tris-sarcosine calcium chloride near T _c = 128 K.     

Proton induced modification in Poly(ethylene terephthalate)

A systematic investigation of 62 r MeV proton irradiated Poly(ethylene terephthalate) (PET) has been carried out using Fourier Transformed Infrared Spectroscopy, thermogravimetric analysis, differential scanning calorimetry and X-ray diffraction spectroscopy. The experiments revealed a restoration of the crystalline matrix and simultaneous decrease in thermal stability in the irradiated polymer as a function of dose, indicating that PET underwent both degradation and cross-linking by proton irradiation.     

(CoO)_n(n≤6)合金团簇的结构和磁性理论研究

采用密度泛函理论中的广义梯度近似(DFT-GGA)对(CoO)_n(n≤6)合金团簇进行了系统的几何、电子结构和磁性质研究.研究结果表明(CoO)n(n≤6)团簇最稳定结构除(CoO)6团簇为三维立体结构外,其余团簇均呈二维平面结构,且(CoO)_n(n=1,2,3,4和6)结构均表现明显的钴氧分离特征,而(CoO)5团簇表现明显的Co—Co聚合和O—O分离特征.团簇的总磁矩在n=1,3,4时,以3μB为单元成倍增长,(CoO)5团簇显著降低,减小至1μB,(CoO)6团簇又有所增加,增大至6μB.(CoO)n(n≤6)团簇磁性变化的起因也从电荷转移、磁性耦合、电子差分密度和态密度进行了详细阐释.     

Inverse conductivity Problem with Internal Data

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This problem finds applications in multi-wave imaging, greedy methods to approximate parameter-dependent elliptic problems, and image treatment with partial differential equations. We first show that the inverse problem for smooth coefficients can be rewritten as a linear transport equation. Assuming that the coefficient is known near the boundary, we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin method. We propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization parameter. We finally provide numerical examples for the inversion assuming a lower regularity of the coefficient, and using synthetic data.     

On a Class of Quasilinear Elliptic Equations

We consider a class of quasilinear elliptic boundary problems, including the following Modified Nonlinear Schrödinger Equation as a special case: $$\begin{cases} ∆u+ \frac{1}{2} u∆(u^2)−V(x)u+|u|^{q−2}u=0 \ \ \ in \ Ω, \\u=0 \ \ \ \ \ \ \ ~ ~ ~ on \ ∂Ω, \end{cases}$$ where $Ω$ is the entire space $\mathbb{R}^N$ or $Ω ⊂ \mathbb{R}^N$ is a bounded domain with smooth boundary, $q∈(2,22^∗]$ with $2^∗=2N/(N−2)$ being the critical Sobolev exponent and $22^∗= 4N/(N−2).$ We review the general methods developed in the last twenty years or so for the studies of existence, multiplicity, nodal property of the solutions within this range of nonlinearity up to the new critical exponent $4N/(N−2),$ which is a unique feature for this class of problems. We also discuss some related and more general problems.