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1.
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.  相似文献   

2.
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.  相似文献   

3.
微液滴动力学特性的耗散粒子动力学模拟   总被引:1,自引:0,他引:1       下载免费PDF全文
常建忠  刘谋斌  刘汉涛 《物理学报》2008,57(7):3954-3961
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  相似文献   

4.
利用Ghost Fluid方法模拟激波与柱形界面相互作用   总被引:3,自引:0,他引:3  
利用Ghost Fluid方法(后面简称Ghos,方法)和γ-model方法,在同样的时空离散精度条件下,对激波与柱形界面相互作用的二维可压缩流场进行了直接模拟,并与实验结果相比较.从模拟结果看,在短时间内,Ghost方法和γ-model方法模拟的结果与实验结果基本相同,两种方法均正确地模拟出界面的位置、激波的强度和速度.但随着时间的发展,具有较大数值耗散的γ-model方法的计算结果与实验差别越来越大;而数值耗散较小的Ghos,方法能较为正确地模拟界面的运动.  相似文献   

5.
邢贵超  夏云杰 《物理学报》2018,67(7):70301-070301
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.  相似文献   

6.
黄轶凡  梁兆新 《物理学报》2023,(10):180-188
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.  相似文献   

7.
分子动力学模拟中的变截断半径算法   总被引:1,自引:0,他引:1  
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。  相似文献   

8.
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。  相似文献   

9.
软物质是指处于固体和理想流体之间的复杂态物质,主要包括聚合物、表面活性剂、液晶、胶体悬浮液、以及生物大分子等。软物质能够对外界微小的作用产生强烈的非线性响应,并展现出丰富的有序自组装相态。作为一种新颖的模拟技术,耗散粒子动力学方法非常适合在介观尺度上对软物质体系的复杂行为进行合理的描述。本文对耗散粒子动力学模拟方法的发展及一些应用进行了系统评述。耗散粒子动力学模拟方法体现了分子动力学与格子Boltzmann模型的优点,通过与其它理论模型(如Flory-Huggins理论、Smoothed particle hydrodynamics模型等)相结合,该方法能够在介观尺度上有效地研究聚合物熔体和溶液体系、生物膜及囊泡体系以及胶体悬浮液等体系的行为。这些研究结果,对新材料的研发、特殊材料的制备、以及材料加工条件的选择具有十分重要的科学意义和实际应用价值。  相似文献   

10.
在基于红外高光谱辐射数据进行大气遥感方面的研究中,准确模拟红外高光谱数据是很重要的一步。分析了红外高光谱辐射仪的测量原理,建立了基于Atmospheric Radiation Transfer Simulator(ARTS)的考虑仪器干涉图截断与离散化处理过程的正向模型。在该正向模型中,首先采用高光谱辐射传输模式ARTS模拟得到离散化理想光谱,通过逆傅里叶变换将理想光谱转化为干涉图,对干涉图加窗截断处理,模拟仪器响应函数对干涉图的影响,最后采用傅里叶变换得到仪器测量光谱。在这一过程中,窗口函数的选择取决于仪器的干涉图截断方式。未经过切趾处理的仪器,其对应的窗口函数为矩形窗口;经过切趾函数处理,可以减少干涉图截断造成的能量泄露现象。逆傅里叶变换与傅里叶变换过程中必须满足Nyquist采样定律。基于已建立的正向模型,模拟了Atmospheric Emitted Radiance Interferometer (AERI)在Southern Great Plains (SGP)站点的108组晴空辐射数据,并与AERI的实测结果进行比较分析,结果发现理想光谱与AERI实测光谱在吸收线上差异较大,最大残差达到35 mW·sr-1·m-2·(cm-1)-1(简称RU)以上,增加干涉图截断过程后,模拟光谱与实测光谱的最大残差减小到10 RU以内。截断过程的增加对模拟光谱的精度有明显提高,尤其在吸收线上,模拟光谱明显被平滑,模拟精度显著提高。进一步分析六种常用窗口函数截断处理的结果与AERI实测数据的残差,结果发现,模拟过程中选择窗口函数为矩形窗口时,模拟光谱与AERI实测数据残差最小,基本可以约束在5 RU以内,确定了AERI的干涉图截断方式可以近似看作矩形截断。另外,在理想光谱转换为干涉图的过程中,理想光谱分辨率的选择决定了干涉图信息的采样率以及ARTS的计算效率,因此综合考虑模型计算精度和模型计算效率,确定最佳的理想光谱分辨率对于提高模型计算效能是非常必要的;基于此,本文模拟了不同理想光谱分辨率下的仪器测量光谱,对比分析了模拟光谱与AERI实测光谱的残差分布,并讨论了光谱分辨率对模型计算耗时的影响。结果表明,对于AERI,在对应的正向模型中设置理想光谱分辨率为0.241 1 cm-1时,可在保证模型准确度的前提下,最大化模型计算效率。  相似文献   

11.
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.  相似文献   

12.
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.  相似文献   

13.
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.  相似文献   

14.
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.  相似文献   

15.
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.  相似文献   

16.
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.  相似文献   

17.
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.  相似文献   

18.
A finite-difference scheme arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation is used for the numerical solution of the improved Boussinesq equation (IBq). The resulting linear scheme, which is analyzed for local truncation error and stability, is tested numerically and conclusions with corresponding results known in the bibliography are derived.  相似文献   

19.
A single-parameter family of self-adjoint compact difference (SACD) schemes is developed for discretizing the Laplacian operator in self-adjoint form. Developed implicit scheme is formally second-order accurate (with respect to truncation error) with a free parameter, α which helps control the numerical properties in the spectral plane. The SACD scheme is analyzed in the spectral plane for its resolution properties for both periodic and non-periodic problems using the matrix spectral analysis [T.K. Sengupta, G. Ganeriwal, S. De, Analysis of central and upwind schemes, J. Comput. Phys. 192 (2) (2003) 677–694]. The major objective here is to identify the advantages of the new scheme over the traditional explicit second order CD2 scheme, in discretizing the Laplacian operator in self-adjoint form. This appears in Navier–Stokes equation and in other transport equations and boundary value problems (bvp) expressed in orthogonal co-ordinate systems, either in physical or in transformed plane. We also compare the developed method with the higher order compact schemes for non-uniform grids. To demonstrate the accuracy of SACD scheme we have tested it for: (i) bi-directional wave propagation problem, given by the second order wave equation and (ii) an elliptic bvp, as in the Stommel ocean model for the stream function. These examples help infer the properties of SACD scheme when solving different types of partial differential equations. Most importantly the effects of grid-stretching and choice of value of the free parameter (α) are investigated here. We also compare the present implicit compact method with explicit compact method known as the higher order compact (HOC) method.Also, the practical applications of the SACD scheme are explored by solving the Navier–Stokes equation for the cases of: (a) a flow inside a lid-driven cavity and (b) the receptivity and instability of an external adverse pressure gradient flow over a flat plate. In the former, unsteadiness of the flow is captured and in the latter, the receptivity of the flow is studied in causing flow instability by triggering Tollmien–Schlichting waves. The new scheme shows a marked improvement over the explicit scheme for low Reynolds number steady flow in lid driven cavity. Whereas for the flow in the same geometry at higher Reynolds numbers, efficacy of the scheme is established by showing the formation of a triangular vortex and secondary vortical structures. Presented scheme is perfectly capable of expressing the diffusion operator accurately as shown via the capturing of instability waves inside the shear layer.  相似文献   

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