费米型级联运动方程的绝热截断方案

研究开放量子系统的量子耗散动力学对于理解许多新奇量子现象背后的机制和实现量子器件的精确量子态控制具有重要意义. 级联运动方程方法已成为研究这类量子耗散动力学最常用的数值方法之一. 然而，在处理强电子关联系统时，准确描述强关联效应需要高的级联截断层数. 这导致级联运动方程方法需要耗费大量物理内存和计算时间. 为了解决该问题，将具有最快耗散速率的耗散模式与其他较慢的耗散模式分离，提出了一种级联运动方程的绝热截断方案. 在单杂质安德森模型上进行的数值测试表明，与传统的方案相比，该截断方案显著地降低了级联运动方程收敛需要的截断层数. 此外，该截断方案缓解了长时间耗散动力学中的数值不稳定性.     

重离子碰撞两体关联输运理论V.等级截断

讨论了两体关联输运理论在不同的等级截断下对中能重离子碰撞动力学过程的描述. 不同的等级截断对动力学过程尤其是耗散过程的描述是不同的.     

微液滴动力学特性的耗散粒子动力学模拟

对传统的耗散粒子动力学方法进行了改进.改进的耗散粒子动力学方法采用了包含远程吸引力和近距排斥力的保守力势函数,从而使得用耗散粒子动力学方法模拟多相流动成为可能.应用改进的耗散粒子动力学方法,对微尺度下液滴的形成及液滴在微重力下的大幅度振荡变形进行了数值模拟.计算结果表明,改进的耗散粒子动力学(DPD)方法能够有效地描述微尺度下液滴的动力学特性,对研究复杂流体多相流动有着重要的意义. 关键词： 多相流 微液滴 耗散粒子动力学(DPD)方法 保守力势函数     

与热库耦合的光学腔内三原子间的纠缠动力学

研究了与热库耦合的光学腔中三个相互作用的二能级原子间的纠缠动力学.采用拉普拉斯变换和下限共生等方法,通过数值计算,分析了原子间三体纠缠的演化以及腔场与热库间的两体纠缠演化,讨论了各耦合参数对系统纠缠演化的影响.研究结果表明:原子间纠缠在短时间内随着原子间耦合强度的增加而增加,随原子与腔场耦合强度的增加而减小,在长时极限下趋于一稳定值;体系的非马尔科夫性由原子与腔场的耦合强度以及热库的谱宽度共同决定,当热库与腔场为强耦合时,原子与腔场组成的系统遵循非马尔科夫动力学,此时随着热库谱宽的增加,原子系统由非马尔科夫性变为马尔科夫性,随着谱宽的继续增加,原子与腔场组成的系统遵循马尔科夫动力学,原子系统又表现出非马尔科夫性;调整腔场与热库的失谐可以有效抑制热库耗散对纠缠衰减的影响.     

激子极化激元凝聚体中的二维亮孤子

在非保守非线性系统中,产生孤子的基本物理机理是系统的动能与非线性、以及增益与耗散达到双动力学平衡.如何在该系统中产生稳定的自由高维孤子是目前孤子理论具有挑战性的前沿课题.本文提出了一种在激子极化激元玻色-爱因斯坦凝聚体中实现二维自由亮孤子理论方案,即通过时间周期调制相互作用以及增益与耗散双平衡的物理机理产生稳定的二维自由空间亮孤子.为此,首先通过拉格朗日量变分法得到了二维亮孤子参数的动力学方程,得到其动力学稳定的参数空间.其次,数值模拟广义增益耗散Gross-Pitaveskii方程的含时演化,验证了二维亮孤子的稳定性.最后,加入高斯噪声模拟真实实验环境,发现在实验可观测的时间范围内,二维亮孤子是稳定的.本文的实验方案打开了在非保守系统中研究高维自由空间亮孤子的大门.     

分子动力学模拟中的变截断半径算法

在分子动力学模拟中,人们往往根据所研究的对象选取一个固定的截断半径,而不同的作者所推荐的有效截断半径值甚为分散。这一方面影响了模拟结果的精度,同时也造成了截断半径选取的困难。本文提出了一种变截断半径的新算法,可根据对象所处的状态灵活地改变截断半径。文中以两相平衡系的非均匀各向异性区的模拟为例,采用所提出的方法得到了更接近实验的结果,同时也节约了计算时间。     

偏心圆环中对流换热的耗散粒子动力学研究

能量守恒的耗散粒子动力学(eDPD)对复杂流动问题的模拟有着先天的优势。本文将eDPD方法应用于偏心圆环中气体的对流换热问题的模拟。首先模拟了因圆环旋转引起的强迫对流换热问题。然后,引入Boussinesq假设,模拟了自然对流换热问题。最后,模拟了混合对流问题。得到了温度场和流场等数据,并将结果和有限体积法模拟得到的结果或实验数据进行了比较。结果表明,DPD能有效地模拟复杂形状内的对流换热问题,并且精度很高。     

带凹槽的微通道中液滴运动数值模拟

运用改进的耗散粒子动力学方法模拟了液滴在由凹槽所构成的粗糙表面微通道内的运动行为.改进的耗散粒子动力学方法采用新近提出的一种短程排斥、长程吸引相互作用势能函数,从而可以模拟带有自由面的流体,如液滴等.模拟了新势能函数下液滴与固体壁面的静态接触角,并用2次多项式拟合了"接触角-a_wf/a_f"变化曲线.研究了液滴在带凹槽的微通道中运动时,微通道壁面浸润性、外场力、液滴温度对液滴流动特性的影响.研究表明壁面浸润性和外场力对液滴流动特性的影响较大,液滴温度对液滴流动特性的影响较小.研究结果对运用耗散粒子动力学方法模拟并分析微流体在复杂微通道的流动有一定的参考价值.     

耗散粒子动力学对颗粒沉降问题的研究

给出了一种耗散粒子动力学方法模拟流体流动的理论及数值模型,包括控制方程组、边界条件、数值计算方法.使用耗散粒子动力学方法编程计算了颗粒在重力作用下的沉降运动,观察到颗粒的质量和所受重力对颗粒运动轨迹的影响,且颗粒质量越小,所受重力越小,颗粒运动所表现出的随机性越强烈.从而验证了所采用的数学模型、计算方法在流动数值模拟中的可行性及潜在优势.     

介观尺度通道内多相流动的耗散粒子动力学模拟

采用四次方光滑函数构造了包含远程吸引近距排斥的保守力势函数, 应用该势函数, 采用耗散粒子动力学方法, 对十字型微通道内的多相流动进行了计算. 计算结果表明, 该势函数能有效模拟十字型微通道内的流动过程及模式. 关键词： 多相流 耗散粒子动力学 保守力势函数     

三维定常问题的高阶紧致差分格式向非定常问题的推广

将已经建立的求解三维定常对流扩散方程的高阶紧致差分格式直接推广到三维非定常对流扩散方程的数值求解,时间导数项利用二阶向后欧拉差分公式,所得到的高阶隐式紧致差分格式时间为二阶精度,空间为四阶精度,并且是无条件稳定的.数值实验结果验证了本文方法的精确性和稳健性.     

Numerical experiments on the efficiency of local grid refinement based on truncation error estimates

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested.     

A nonstandard numerical method for the modified KdV equation

A linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg–de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.     

Compact finite difference method for the fractional diffusion equation

High-order compact finite difference scheme for solving one-dimensional fractional diffusion equation is considered in this paper. After approximating the second-order derivative with respect to space by the compact finite difference, we use the Grünwald–Letnikov discretization of the Riemann–Liouville derivative to obtain a fully discrete implicit scheme. We analyze the local truncation error and discuss the stability using the Fourier method, then we prove that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.     

用高分辨差分格式解SNS方程

本文从Sweby的显式TVD格式^[2,3]出发,构造发一个推进方向一阶精度、侧向二阶精度的隐式TVD差分格式,并用于解可压缩流定常简化Naviev-Stokes(SNS)方程。对不出现流向分离的平板边界层和激波—边界层相互干扰两个问题的数值计算表明,方法可以有效捕捉流场中的间断。     

High-Precision Direct Method for the Radiative Transfer Problems

It is the main aim of this paper to investigate the numerical methods of the radiative transfer equation.Using the five-point formula to approximate the differential part and the Simpson formula to substitute for integral part respectively, a new high-precision numerical scheme, which has 4-order local truncation error, is obtained. Subsequently,a numerical example for radiative transfer equation is carried out, and the calculation results show that the new numerical scheme is more accurate.     

New band structures in 107Ag

High spin states in ¹⁰⁷Ag are studied via the ¹⁰⁰Mo(¹¹B, 4n)¹⁰⁷Ag reaction at an incident beam energy of 60 MeV. Prompt γ-γ coincidence and DCO ratios are measured by the detector arrays in CIAE. The level scheme has been updated and a new negative band belonging to ¹⁰⁷Ag is identified. The new negative side band has been constructed and its configuration is tentatively assigned to πg_9/2 νh_11/2(g_7/2/d_5/2).     

Numerical simulation of the soliton solutions for a complex modified Korteweg—de Vries equation by a finite difference method

In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.     

Comparison of the iterated equation of motion approach and the density matrix formalism for the quantum Rabi model

The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results.