广义含时谐振子的精确解和Berry相因数

本文利用Lewis-Riesenfeld的量子理论,求出广义含时谐振子的精确解。研究了此精确解的绝热渐近极限,并求出广义谐振子在量子绝热情形的Berry相因数。进而利用此精确解构造了广义含时谐振子的相干态,并得到相应的经典Hannay角。     

含时受迫谐振子传播子的精确解

在薛定谔绘景中,运用李代数方法,给出谐振子湮灭算符和产生算符的含时么正线性变换公式,结合含时量子系统的演化方程,得到含时受迫谐振子传播子的精确表达式。     

受迫振子的对称性与守恒量

讨论受迫振子体系的对称性和守恒量,导出了其含时位势的具体形式,给出了相应的对称变换算符,并讨论了线谐振子体系的含时守恒量.     

含时耦合谐振子体系的动力学演化

利用含时量子变换理论,给出含时双模耦合谐振子的严格解.并根据这一结果,对于给定的初态为Fock态和相干态情形,讨论了其动力学演化.     

依赖于速度的量子受迫非简谐振子的演化

运用积分算子和迭代方法求得了依赖于速度的量子受迫非简谐振子的精确解。给出了非简谐振子坐标和动量算符的时间演化。这些算符被表示成适当泛函的拉普拉斯变换及随后的逆拉普拉斯交换的形式。 关键词：     

RLC介观电路中的量子涨落

从线性谐振子哈氏量出发,通过正则变换,得到了受迫阻尼谐振子哈氏量,还讨论了在压缩态下的电荷和电流的量子涨落。     

线性谐振子的非定态波函数

引入初坐标算符和初动量算符为线性谐振子的力学量完全集，求解薛定谔方程，可得到线性谐振子的两类非定态波函数．     

非平衡功与自由能差的关系

以一个受迫谐振子为对象证明了Jarzynski等式,即两平衡态的自由能差可以用它们之间非平衡功的指数平均来表示,这里两个态的转换是在有限时间完成的.当外部驱动力是一个周期信号时,发现外界对系统所做的广义功存在一个共振现象.     

线性谐振子的非定态波函数

引入初坐标算符和初动量算符为线性谐振子的力学量完全集，求解薛定谔方程，可得到线性谐振子的两类非定态波函数。     

用算符分解方法计算非同调谐振子几何相位及其推广

将几何相位理论应用于非同调谐振子(isotonic oscillator缩写为IO)这类量子系统,运用算符分解方法计算了系统在二态体系的Aharonov-Anandan相位,推广至三态及多态体系,并讨论了AA相位更普遍的计算公式和变化规律.     

A modified transfer matrix method for the study of the bending vibration band structure in phononic crystal Euler beams

We introduce a modified transfer matrix (MTM) method for the calculation of the bending vibration band structure of one-dimensional phononic crystal (PC) Euler beams. A particular combination of hyperbolic functions and triangular functions is introduced to transform the state parameters of the transfer matrix (TM) method into four initial parameters, which have the explicit meanings of the displacement, rotation angle, bending moment and shear force at one beam end. The method is used to calculate the band structures of two PC Euler beams constructed from aluminum–Lucite and 100 kinds of materials. The effectiveness and high efficiency of the MTM method are demonstrated by the results. Several advantages make it a proper choice for the calculation of the bending vibration band structure of PC Euler beams.     

Evaluation of numerical strategies for large eddy simulation of particulate two-phase recirculating flows

Predicting particle dispersion in recirculating two-phase flows is a key issue for reacting flows and a potential application of large eddy simulation (LES) methods. In this study, Euler/Euler and Euler/Lagrange LES approaches are compared in the bluff body configuration from Borée et al. [J. Borée, T. Ishima, I. Flour, The effect of mass loading and inter-particle collisions on the development of the polydispersed two-phase flow downstream of a confined bluff body, J. Fluid Mech. 443 (2001) 129–165] where glass beads are injected into a complex recirculating flow. These tests are performed for non-reacting, non-evaporating sprays but are mandatory validations before computing realistic combustion chambers. Two different codes (one explicit and compressible and the other implicit and incompressible) are also tested on the same configuration. Results show that the gas flow is well predicted by both codes. The dispersed phase is also well predicted by both codes but the Lagrangian approach predicts root-mean-square values more accurately than the Eulerian approach. The effects of mesh, solvers and numerical schemes are discussed for each method.     

Relativistic Hydrodynamics and Essentially Non-oscillatory Shock Capturing Schemes

Numerical solutions of relativistic hydrodynamic equations are obtained with essentially non-oscillatory (ENO) finite differencing schemes. The method is explicit, conservative, consistent with the entropy condition, and high order accurate in space and time. The present implementation is applicable to the most general, three-dimensional problems with an arbitrary equation of state. Numerical experiments, including computations of multi-dimensional flows, demonstrate that the method delivers sharp, non-oscillatory shock transitions without sacrificing high resolution of the smooth regions. This extends results already established for the Euler gas dynamics to the relativistic regime, suggesting the usefulness of ENO schemes for modelling relativistic nuclear collisions.     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.     

使用非定常无反射边界条件模拟上游尾迹/叶片排干扰问题

本文采用显式时间推进方法求解二维Euler方程计算了上游尾迹与下游叶片排相互干扰而形成的复杂流场。根据Giles提出的理论编制了无反射边界条件非定常计算程序，取得了满意的效果。进口上游尾迹的特性白尾迹模型给定．预测到了尾迹在叶栅流道内的切割，迁移及剪切等重要的非定常现象。     

Directed Motion of a Molecular Motor Based Qn the Four－State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps between arbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probability distribution as a function of the time and position for any initial distribution with all the transients included. Next, the transient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecular motor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kinetic behaviors of a molecular motor under external load F.     

On the stability and performance of discrete event methods for simulating continuous systems

This paper establishes a link between the stability of a first order, explicit discrete event integration scheme and the stability criteria for the explicit Euler method. The paper begins by constructing a time-varying linear system with bounded inputs that is equivalent to the first order discrete event integration scheme. The stability of the discrete event system is shown to result from the fact that it automatically adjusts its time advance to lie below the limit set by the explicit Euler stability criteria. Moreover, because it is not necessary to update all integrators at this rate, a significant performance advantage is possible. Our results confirm and explain previously reported studies where it is demonstrated that a reduced number of updates can provide a significant performance advantage compared to fixed step methods. These results also throw some light on stability requirements for discrete event simulation of spatially extended systems.     

3D Euler equations and ideal MHD mapped to regular systems: Probing the finite-time blowup hypothesis

We prove by an explicit construction that solutions to incompressible 3D Euler equations defined in the periodic cube Ω=[0,L]³ can be mapped bijectively to a new system of equations whose solutions are globally regular. We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding regular solution of the new system. In the hypothetical case of Euler finite-time singularity, we provide an explicit formula for the blowup time in terms of the regular solution of the new system. The new system is amenable to being integrated numerically using similar methods as in Euler equations. We propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite-time singularity problem of Euler equations, based on the conservation of quantities directly related to energy and circulation. The method of mapping to a regular system can be extended to any fluid equation that admits a Beale-Kato-Majda type of theorem, e.g. 3D Navier-Stokes, 2D and 3D magnetohydrodynamics, and 1D inviscid Burgers. We discuss briefly the case of 2D ideal magnetohydrodynamics. In order to illustrate the usefulness of the mapping, we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1D inviscid Burgers equation.     

Classification of Equilibrium Solutions of the Cometary Flow Equation and Explicit Solutions of the Euler Equations for Monatomic Ideal Gases

The set of smooth equilibrium solutions of a kinetic model for cometary flows is split into equivalence classes according to similarity transformations. For each equivalence class in the two- and three-dimensional cases a normal form is computed. Each such equilibrium solution gives rise to an explicit solution of the compressible Euler equations for monatomic gases. The set of these solutions is discussed with special emphasis on solutions containing vacuum regions.     

Explicit multi-symplectic method for the Zakharov—Kuznetsov equation

We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.