Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet’s boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.     

Derivation of the multisymplectic Crank–Nicolson scheme for the nonlinear Schrödinger equation

The Crank–Nicolson scheme as well as its modified schemes is widely used in numerical simulations for the nonlinear Schrödinger equation. In this paper, we prove the multisymplecticity and symplecticity of this scheme. Firstly, we reconstruct the scheme by the concatenating method and present the corresponding discrete multisymplectic conservation law. Based on the discrete variational principle, we derive a new variational integrator which is equivalent to the Crank–Nicolson scheme. Therefore, we prove the multisymplecticity again from the Lagrangian framework. Symplecticity comes from the proper discrete Hamiltonian structure and symplectic integration in time. We also analyze this scheme on stability and convergence including the discrete mass conservation law. Numerical experiments are presented to verify the efficiency and invariant-preserving property of this scheme. Comparisons with the multisymplectic Preissmann scheme are made to show the superiority of this scheme.     

GPELab,a Matlab toolbox to solve Gross–Pitaevskii equations I: Computation of stationary solutions

This paper presents GPELab (Gross–Pitaevskii Equation Laboratory), an advanced easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics situations related to Bose–Einstein condensation. The model equation that GPELab solves is the Gross–Pitaevskii equation. The aim of this first part is to present the physical problems and the robust and accurate numerical schemes that are implemented for computing stationary solutions, to show a few computational examples and to explain how the basic GPELab functions work. Problems that can be solved include: 1d, 2d and 3d situations, general potentials, large classes of local and nonlocal nonlinearities, multi-components problems, and fast rotating gases. The toolbox is developed in such a way that other physics applications that require the numerical solution of general Schrödinger-type equations can be considered.     

Stochastic defect diffusion model for relaxation effects in crystalline polyethylene

It is suggested that some relaxation processes observed in crystalline polyethylene are consequences of the diffusive motion of a particular defect called a point dislocation or twist dispiration loop along the polyethylene stems in lamellar crystals. The motion of the defect, characterized by a diffusion coefficient and a mobility, is described by solutions of the Smoluchowski diffusion equation with boundary conditions that constrain the defect to move along routes that produce experimentally observable results. The fact that passage of the defect causes both a 180° rotation of the chain and moves an extra CH₂ group in the direction of the chain axis is important to the interpretation of the data according to this model. The diffusion coefficient for a defect is estimated to be around 2 × 10^?9 cm² s^?1 at 70°C. This value is shown to be reasonable both from the viewpoint of detailed computer modelling of defect motion and contemporary ideas about scaling.     

回转窑煤粉浓度的测量方法

回转窑水泥厂一次风煤粉浓度测定的准确性对整个窑的标定与生产管理都有着相当重要的作用,而我们在测定中常因一次风的压力与温度影响造成较大的测量误差,根据行业中常用的测量方法提出个人的一些看法。     

Dynamics of fluid circulation in coupled free and heterogeneous porous domains

Fluid flow in coupled free and porous domain, particularly when the porous medium is heterogeneous, is encountered in many hydro-environmental conditions, e.g., leakage from underground pipe, combined groundwater lake-subsurface interactions. One of the most difficult problems in the study of coupled flow behaviour has been the development of a universally applicable modelling scheme for combining the flow regimes. This is because the free/porous interfacial properties (e.g., shear-stress; velocity slip) that govern the coupled flow behaviour are difficult to determine experimentally under hydro-environmental conditions. On the other hand, the implications of various forms of heterogeneity in the porous media properties can be very different on the fluid-flow behaviour. Difficulties may also arise in direct coupling of the model equations that govern the fluid flow in the individual regions (e.g., Navier-Stokes for free-flow region and the Darcy's equation for the porous flow region). Consequently, models of coupled free and porous flow for hydro-environmental conditions are not very well developed at the moment. While there are some indications that fluids in coupled free and porous domains may circulate (i.e., development of flow cells), there is a lack of appropriate 3D analysis on how heterogeneities in porous media may affect such flow patterns. In this paper, we aim to analyse how porous media heterogeneity affects the dynamics of flow circulation in the porous side of a coupled free and porous domain. For this purpose, we analyse flow patterns in several model domains made up of two porous layers with differing permeabilities. The governing model equations are discretised and solved using the standard finite volume method on a staggered cell-centred mesh. The temporal discretisation is done using the explicit method. An in-house graphical user interface (GUI) has been created specifically to aid in the visualisation of otherwise complex flow patterns. The GUI contains many post-processing options and provides a comprehensive tool for the analysis of hydrodynamics and contaminant motion (not discussed in this paper) in coupled free and porous flow domains. This GUI is described in this paper briefly. The effects of altering the aspect ratio (i.e., multi-scale) of the domain on the coupled flow pattern have also been discussed.     

Variance-penalized Markov decision processes: dynamic programming and reinforcement learning techniques

In control systems theory, the Markov decision process (MDP) is a widely used optimization model involving selection of the optimal action in each state visited by a discrete-event system driven by Markov chains. The classical MDP model is suitable for an agent/decision-maker interested in maximizing expected revenues, but does not account for minimizing variability in the revenues. An MDP model in which the agent can maximize the revenues while simultaneously controlling the variance in the revenues is proposed. This work is rooted in machine learning/neural network concepts, where updating is based on system feedback and step sizes. First, a Bellman equation for the problem is proposed. Thereafter, convergent dynamic programming and reinforcement learning techniques for solving the MDP are provided along with encouraging numerical results on a small MDP and a preventive maintenance problem.     

CO2混合物热物性在CCS研究中的作用:实验数据、理论模型和典型应用

二氧化碳捕集与封存（CCS）各工艺过程的设计、运行都依赖于对CO₂及其混合物热物理性质的深入理解。同时，CCS的规模化发展和商业化进程，对CO₂混合物及其热物性的准确性提出了更高的要求。本文从实验数据、理论模型和典型应用3个方面综述了CO₂及其混合物热物性的发展现状，并尝试对发展趋势进行归纳。在实验研究方面，CO₂混合体系的研究进展视组分不同，差异较大，其中CO₂-N₂、CO₂-CH₄、CO₂-H₂O和CO₂-H₂二元体系已形成较完善的物性数据库，而CO₂-NH₃、CO₂-NO _x 和CO₂-CO体系的物性数据还比较欠缺；在物性估算方面，面向CCS的物性估算模型研究自2008年开始活跃，基于不同理论构架，目前已逐步形成面向CCS的多元化的物性估算体系。物性研究在CCS中的应用主要体现在物性是支撑CCS过程研究的基础，其不准确性在过程模拟或计算中会被“放大”，从而影响过程评估的准确性，本文从物性在循环构建和能效分析中的作用以及CO₂水合物的形成3个方面入手做了说明。文章最后对面向CCS的物性研究趋势进行了梳理，对分子模拟技术、通用性强的物性估算模型和物性在过程设计和循环分析中的角色进行了展望。     

乙醇－氯仿－苯三元体系等温汽液平衡

用改进的Ｒｏｓｅ釜结合等温等压控制装置，测定了乙醇－氯仿－苯三元体系在５５℃及６０℃的等温汽液平衡数据，并用Ｗｉｌｓｏｎ方程由二元参数推算了三元体系的数据，取得了满意的结果。     

Comparing the revised NIOSH lifting equation to the psychophysical,biomechanical and physiological criteria used in its development

The purpose of this study was to perform a systematic and comprehensive comparison between the recommended weights of lift (RWL) from the revised NIOSH lifting equation, and the specific biomechanical, psychophysical and physiological criteria that were stated to be used in the equation's development. A composite acceptable load (CAL) table was developed for the 216 conditions presented in the female lifting table of Snook and Ciriello (1991). Each CAL value was calculated to correspond to the most conservative load of the three design criteria. The RWLs caused lumbar compression forces close to the biomechanical limit of 3400 N for lifts below knuckle height, but resulted in compression forces that are much lower at higher lifting heights. At moderate lifting frequencies, the average RWL would be acceptable to more than 95% of female workers according to the psychophysical criterion. At the highest frequencies, the RWL was found to be an average of 63% of the CAL values based on the integration of the psychophysical and physiological criteria. It is recommended that ergonomists acknowledge the very conservative nature of the revised NIOSH lifting equation when using it to evaluate occupational lifting tasks.