色散方程的一类具任意稳定性的显格式

本文对色散方程u_r=au_xxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。     

Effects of an electromagnetic field on intracellular calcium oscillations in a cell with external noise

Intracellular calcium ion concentration oscillation in a cell subjected to external noise and irradiated by an electromagnetic field is considered. The effects of the intensity E₀, the polar angle θ and the frequency omega of the external electric field on steady-state probability distribution and the mean Ca²⁺ concentration, respectively, are investigated by a numerical calculation method. The results indicate that (i) variation of ω cannot affect the intracellular calcium oscillation; (ii) the steady-state probability distribution presents a meaningful modification due to the variations of E₀ and θ, while variation of θ does not affect the steady-state probability distribution under the condition of a small E₀, and E₀ cannot affect the steady-state probability distribution either when θ = π/2; (iii) the mean Ca²⁺ concentration increases as E₀ increases when θ < π/2 and, as θ increases, it first increases and then decreases. However, it does not vary with E₀ increasing when θ = π/2, but it increases with θ increasing when E₀ is small.     

电网在三种边攻击方式下的级联失效

研究美国西部电网在三种边攻击方式下级联失效差异性.定义边ij的初始负载为(k_ik_j)^θ,k_i,k_j分别表示节点i和j的度,θ为一可调参数.三种边攻击方式分别为:最小负载边攻击方式(LL)、最大负载边攻击方式(HL)和容量比最小边攻击方式(SPC).通过分析电网的拓扑结构,研究三种攻击方式级联失效差异性.研究表明:HL和LL攻击方式下,受攻击边的范围不随θ而改变,HL的攻击效果随θ的增大而增强,LL的攻击效果随θ的增大而减弱.而SPC法选中的被攻击边随θ变化,当θ取值较小时,SPC攻击边是拓扑结构较特殊的一种最小负载边,随着θ的增大,SPC攻击边趋向于高负载边,因此θ较小时,SPC的攻击效果和LL接近,当θ较大时,SPC的攻击效果和HL接近.     

显微光谱研究半绝缘GaAs带边以上E0+Δ0光学性质

通过显微光致发光技术和显微拉曼(Raman)技术研究了半绝缘GaAs (SI-GaAs)晶体的带边附近的发光. 在光荧光谱中，观察到在高于GaAs带边0.348eV处有一个新的荧光峰. 结合Raman谱指认此发光峰来源于GaAs的E₀＋Δ₀能级的非平衡荧光发射. 同时, 通过研究E₀＋Δ₀能级的偏振、激发光强度依赖关系，以及温度依赖关系说明E₀＋Δ₀能级与带边E₀共享了共同的导带位置Γ₆，同时这也说明在GaAs中主要是导带的性质决定了材料的光学行为.同时，通过与n-GaAs和δ掺杂GaAs相比较，半绝缘GaAs晶体的E₀＋Δ₀能级的发光峰更能反映GaAs电子能级高临界点E₀＋Δ₀的能量位置和物理性质. 研究结果说明显微光致发光技术是研究半导体材料带边以上能级光学性质的一种非常有力的研究工具. 关键词： 半绝缘GaAs 显微光致发光 自旋轨道分裂     

相位角对容性耦合电非对称放电特性的影响

电非对称效应作为一种新兴技术,被广泛用于对离子能量和离子通量的独立调控.此外,在改善等离子体的径向均匀性方面,电非对称效应也发挥了重要作用.本文采用二维流体力学模型,并耦合麦克斯韦方程组,系统地研究了容性耦合氢等离子体中当放电由多谐波叠加驱动时,不同谐波阶数k下的电非对称效应,重点观察了相位角θ_n对自偏压以及等离子体径向均匀性的影响.模拟结果表明：在同一谐波阶数下,自偏压随相位角θ_n的变化趋势不尽相同,且当k增大（k>3）时,自偏压随最高频相位角θ_k的变化范围逐渐减小.此外,通过调节相位角θ_n,可以改变轴向功率密度和径向功率密度的相对关系,进而实现对等离子体径向均匀性的调节.研究结果对于利用电非对称效应优化等离子体工艺过程具有一定的指导意义.     

同位素效应对H+NH→N+H2反应的立体动力学性质的影响

基于翟红生和韩克利给出的势能面[Zhai H S, Han K L 2011 J. Chem. Phys. 135 104314], 运用准经典轨线方法对H+NH及其同位素取代反应的立体动力学性质进行了理论研究. 分别计算并讨论了碰撞能E_c=8和16 kcal/mol时反应的极化微分反应截面、两矢量k-j'相关分布函数P(θ_r)、 三矢量 k- k'- j'相关分布函数P(φ_r)、空间分布函数P(θ_r, φ_r). 结果表明, 对于上述的两个碰撞能, 由于同位素取代反应中质量因子的不同, 同位素效应对H+NH反应的立体动力学性质的影响很明显.     

镁基合金自由枝晶生长的相场模拟研究

利用定量相场模型, 以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程. 通过研究该合金体系数值模拟的收敛性, 获得了最优化值耦合参数λ = 5.5及网格宽度Δx/W₀ = 0.4, 并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Péclet数及稳定性常数σ^* 的影响. 结果表明, 由微观可解性理论得到的稳定性系数σ^* 与ε₆ 拟合值σ^*≅ ε₆ ^1.81905, 更接近理想值σ ^* (ε₆) ≅ε₆ ^1.75. 此外, 当过饱和度Ω < 0.6时, 稳定性系数σ ^* 不随ε₆ 的变化而变化, 而当Ω > 0.6时, 稳定性系数σ ^* 随着ε₆ 的增加而减小. 这反映了枝晶的生长由扩散控制向动力学控制的转变. 随着过饱和度的增加, 枝晶形貌由雪花状枝晶向圆状枝晶转变.     

高温超导体霍尔电阻和霍尔角在涡旋玻璃相变附近的普适标度律及统一霍尔电阻方程

发现了一个钉扎效应影响霍尔电阻ρ_xy和霍尔角θ_H的普适标度律. 同时,根据纵向电阻ρ_xx的扩展幂律形式和对霍尔电导σ_xy的微观分析,给出了一个对有一次或多次霍尔反号的高温超导体都适用的霍尔电阻方程. 关键词： 高温超导体 涡旋玻璃相变 普适标度律 霍尔电阻方程     

波浪破碎气体的卷入过程及相关统计量的估计

基于实验观测,导出了波浪破碎能量耗散ε_ed、气泡云卷入深度z_b、气体卷入速率Q(z)和湍流动能耗散率ε_T(z)的表达式,在此基础上建立了一种简单、实用的气泡粒径谱参数化模式N(a,z),揭示了波浪破碎气泡云卷入过程能量耗散、气泡破碎临界Hinze特征尺度和气泡粒径谱在不同海况下的变化. 研究表明：气泡云卷入过程能量耗 关键词： 波浪破碎能量耗散 气泡云卷入深度 气泡粒径谱     

BiTiO3电子结构及光学性质的第一性原理研究

采用基于第一性原理的赝势平面波方法, 对BiTiO₃的多种结构进行了计算. 计算结果表明, C1C1结构最为稳定, 对应晶格参数为a=b=5.606 Å, c=9.954 Å; α=β=105.1°, γ=61.2°. 进一步对C1C1结构的BiTiO₃的能带结构、电子性质和光学性质进行了研究, 发现BiTiO₃是间接带隙半导体, 其费米面附近的能带主要由Ti-3d和O-2p层的电子态构成. 通过介电函数、复折射率和反射率等的研究, 发现BiTiO₃的光学性质为近各向同性.     

A high-resolution,hybrid compact-WENO scheme with minimized dispersion and controllable dissipation

In this paper,a high-resolution,hybrid compact-WENO scheme is developed based on the minimized dispersion and controllable dissipation reconstruction technique.Firstly,a suffcient condition for a family of tri-diagonal compact schemes to have independent dispersion and dissipation is derived.Then,a specific 4th order compact scheme with low dispersion and adjustable dissipation is constructed and analyzed.Finally,the optimized compact scheme is blended with the WENO scheme to form the hybrid scheme.Moreover,the approximation dispersion relation approach is employed to optimize the spectral properties of the nonlinear scheme to yield the true wave propagation behavior of the finite difference scheme.Several test cases are carried out to verify the highresolution as well as the robust shock-capturing capabilities of the proposed scheme.     

Thermodynamics of quantum dissipative many-body systems

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits us to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.     

A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.     

Description of Finite-amplitude Standing Acoustic Waves Using Convection-diffusion Equations

This paper deals with problems of finite-amplitude standing waves in acoustical resonators of variable cross-section. Set of two one-dimensional partial differential equations in the third approximation, formulated in conservative form, is derived from the fundamental equations of gas dynamics. The model equations which takes into account external driving force, gas dynamic nonlinearities and thermoviscous dissipation are solved numerically in time domain using a central scheme developed for convection-diffusion equations integration. In this paper numerical results for closed air-filled acoustic resonators are presented.     

A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence

In this paper, a class of finite difference schemes which achieves low dispersion and controllable dissipation in smooth region and robust shock-capturing capabilities in the vicinity of discontinuities is presented. Firstly, a sufficient condition for semi-discrete finite difference schemes to have independent dispersion and dissipation is derived. This condition enables a novel approach to separately optimize the dissipation and dispersion properties of finite difference schemes and a class of schemes with minimized dispersion and controllable dissipation is thus obtained. Secondly, for the purpose of shock-capturing, one of these schemes is used as the linear part of the WENO scheme with symmetrical stencils to constructed an improved WENO scheme. At last, the improved WENO scheme is blended with its linear counterpart to form a new hybrid scheme for practical applications. The proposed scheme is accurate, flexible and robust. The accuracy and resolution of the proposed scheme are tested by the solutions of several benchmark test cases. The performance of this scheme is further demonstrated by its application in the direct numerical simulation of compressible turbulent channel flow between isothermal walls.     

The Lindblad and Redfield forms derived from the Born–Markov master equation without secular approximation and their applications

In this paper, we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems. The coefficients of the equations are re-evaluated according to the scheme in[(2019), Phys. Rev. A 99, 022118]. They are complex numbers rather than the real numbers obtained from traditional simplified methods. The dynamics of two models(one is an open threelevel quantum system model, and the other is the model of phycoerythrin 545(PE545) in a photosynthesis system) are studied. It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments, but a large distortion of the dynamics in others. These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.     

On nonlinear irreversible processes I

A functional integral expression of the two gate probability distribution function is obtained and the integral is performed in a “semiclassical” approximation. Based on this approximation, it is shown that the expression of the many gate probability distribution function in terms of two dissipation functions, which Onsager and Machlup presented before as the extension of Boltzmann's principle, is valid also for nonlinear processes with a slight modification of definition of the dissipation functions. Only the case that all the variables are even functions of time is treated for simplicity.     

Non-linear dynamics of a driven two-level tunnelling defect

With increasing external-field amplitude the dynamics of a driven two-level system shows a cross-over from the weak-coupling or linear-response behaviour to a non-linear regime which is characterised by the appearance of Rabi oscillations, a field-dependent dynamical susceptibility, saturation of energy dissipation and additional frequencies in the correlation function. The system any initial distribution will relax towards a stationary state with a time-dependent polarisation vector. These features are derived from the propagator of the two-level system which is calculated using a perturbative scheme with a well-defined small parameter; the roatating-wave approximation of the Bloch equations is avoided. the dynamical behaviour is discussed by means of correlation and response functions.     

摄动有限体积法重构近似高精度的意义

研讨有限体积(FV)方法重构近似高精度的作用问题.FV方法中积分近似采用中点规则为二阶精度时,重构近似高精度(精度高于二阶)的意义和作用是一个有争议的问题.利用数值摄动技术[1,2]构造了标量输运方程的积分近似为二阶精度、重构近似为任意阶精度的迎风型和中心型摄动有限体积(PFV)格式.迎风PFV格式无条件满足对流有界准则(CBC),中心型PFV格式为正型格式,两者均不会产生数值振荡解.利用PFV格式求解模型方程的数值结果表明:与一阶迎风和二阶中心格式相比,PFV格式精度高、对解的间断分辨率高、稳定性好、雷诺数的适用范围大,数值地"证实"重构近似高精度和PFV格式的实际意义和好处.     

解双曲型方程组的分离系数矩阵差分法

分离系数矩阵(SCM)差分方法是近年来发展的一种基于特征理论的数值方法,该方法将双曲型方程组系数矩阵,利用相似变换,按照特征值的正负构造成SCM方程,然后,合理地选择适合于SCM方法的二阶单向差分格式,能显示出流场中每点的特征值的方向和大小,也就是对于含正特征值的项用向后差分算子,并乘以正特征值,而含负特征值的项用向前差分算子,乘以负特征值,这比以往的差分计算具有合理的物理意义。本文参考文献[1]导得了三维非对称头部绕流的分离系数矩阵方法,不论内点或特殊点都是分离系数矩阵形式,除此之外,还将SCM方法推广于后身的超音速区域。通过计算表明,在头部区采用局部Δt步长,能加速非定常流的收敛,对于后身超音速区,该方法用较少的网格点,仍获得较高的精度。