Fractional differential models for anomalous diffusion

In this study, we investigate three kinds of fractional differential models (distributed-order model, variable-order model and random-order model) for characterization of anomalous diffusion. The characteristics, physical advantages and potential applications of each model are highlighted. The numerical simulations also validate our analytical and comparison results. Furthermore, a generalized distributed-variable-order model and a more generalized distributed-variable-random-order model are proposed to combine the advantages of distributed-order model, variable-order model and random-order model.     

最优速度模型与元胞自动机模型的比较研究

用解析分析与数值仿真的手段研究了一种典型的车辆跟驰模型(OV模型)与元胞自动机模型(NS模型)之间的区别与联系.首先通过对模型规则的分析,证明了确定NS模型是OV模型的一种离散形式.随后针对两模型更复杂的具体形式,通过数值仿真的手段进行了模型的密度-流量关系与模型在开放边界下的动态特性的研究.实验结果表明,从现象来看,OV模型与NS模型具有非常近似的性质,但两种模型的机制不相同,并且各自具有不能相互替代的优势.为交通流模型的使用和改进提供了参考.     

The phase diagram of the 2D Ising model with anisotropic next-nearest-neighbor and four-spin interactions

In the present paper, the two-dimensional Ising model with anisotropic nearest-neighbor, next-nearest-neighbor and four-spin interactions has been studied. The ground states and energy of the model have been obtained. The model is equivalent to an eight-vertex model on its dual lattice. In some special cases, the model can be solved exactly as a zero-field eight-vertex model or a free-fermion model. Explicit phase diagrams are obtained exactly.     

Reducing slab track vibration into bridge using elastic materials in high speed railway

In this paper, the problem of vibration transmission from slab track structures into bridge is studied by theoretical analysis. A vehicle-track-bridge coupling system dynamics model is established based on a multibody dynamics theory and a finite element method. The system model consists of vehicle model, track-bridge model and wheel/rail interaction model. The vehicle model is established based on the multibody dynamics theory, and the tack-bridge model is established by the finite element method. The vehicle model and track-bridge model are coupled through wheel/rail interaction model, and the track irregularities are included. The system dynamic responses are calculated, and the effectiveness of elastic materials in vibration reducing is discussed. The results demonstrate that elastic materials like slab mat layer inserted between slab track and bridge can reduce vibration transmitted from track into the bridge. Some suggestions for the design and application of slab mat are provided in the end of the paper.     

An asymmetric full velocity difference car-following model

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.     

基于MC-UVE、GA算法及因子分析对葡萄酒酒精度近红外定量模型的优化研究

对葡萄酒酒精度偏最小二乘（Partial least squares,PLS）回归模型进行优化研究。使用近红外光谱仪采集葡萄酒样本的光谱数据,用于建立酒精度定量模型,实现在线快速检测。通过蒙特卡罗无信息变量消除（Monte Carlo uninformative variable elimination,MC-UVE）和遗传算法（Genetic algorithm,GA）进行变量选择,基于被选择的变量分别进行PLS和因子分析（Factor analysis,FA）,建立回归模型。结果表明,MC-UVE-GA-FAR模型预测集相关系数（R²）为0.946,预测均方根误差（Root mean square error of prediction,RMSEP）为0.215,效果优于MC-UVE-GA-PLS模型。与基于全范围光谱所建PLS回归模型相比,模型效果有所提升,而且模型所选变量个数仅为6,极大地简化了模型。MC-UVE和GA算法与FA分析结合可以实现模型的优化。     

The non-uniform level density effect on exciton state densities

The equidistant spacing model has been widely used in the exciton model. To test the accuracy, we used the harmonic oscillator potential and the Fermi gas spacing model to account the non-uniform level effect based on the method of exact Pauli exclusion principle correction. The results indicate that the non-uniform effects increase with the increasing of excitation energies. The harmonic oscillator potential overestimated the non-uniform effects. The Fermi gas spacing model is more realistic which gives small correction to the equidistant spacing model. So that the equidistant spacing model used in the exciton model is a good approximation.     

Modelling dynamic behaviour and noise generation in gear pumps: Procedure and validation

The paper presents a methodology for noise and vibration analysis of gear pumps and its application to an external gear pump for automotive applications. The methodology addresses the use of a combined numerical model and experimental analyses. The combined model includes a lumped-parameter model, a finite-element model and a boundary-element model. The lumped-parameter (LP) model regards the interior parts of the pump (bearing blocks and gears loaded by the pressure distribution and the driving torque), the finite element (FE) model regards the external parts of the pump (casing and end plates), while the boundary element (BE) model enables the estimation of the emitted noise in operational conditions. Based on experimental evidences, attention has been devoted to the modelling of the pump lubricant oil: the fluid–structure interaction between the oil and pump casing was taken into account. In the case of gear pumps all these important effects have to be considered in the same model in order to take their interactions into account. The model has been assessed using experiments: the experimental accelerations and acoustic pressure measured in operational conditions have been compared with the simulated data coming from the combined LP/FE/BE model. The combined model can be considered a very useful tool for design optimisation.     

旋流燃烧NO生成的USM湍流反应模型

用统一二阶矩(USM)湍流反应模型对不同旋流数下甲烷-空气旋流燃烧NO生成进行了数值模拟,并和EBU-Arrhenius(E-A)燃烧模型对燃烧的模拟结果和简化PDF湍流反应模型对NO生成的模拟结果以及相应的实验结果进行对比。结果表明,USM模型显著地优于E-A模型和简化PDF模型。E-A模型不能合理地模拟有限反应动力学,而简化PDF模型用两个单变量PDF的乘积代替联合PDF,大大地低估了NO湍流反应率。USM模型预报结果和实验结果符合最好。     

Weizsäcker-Skyrme核质量模型的统计误差研究

基于最大值近似估算的方法,系统地研究了Weizsäcker-Skyrme（WS4）核质量模型的参数不确定性,并计算了WS4核质量模型理论预言值的统计误差。WS4核质量模型的理论预言值与实验值的偏差基本都小于模型的统计误差,表明采用最大值近似估算法对WS4核质量模型理论预言的统计误差的分析是简捷而有效的。进一步研究了WS4核质量模型理论计算中最敏感的参数,结果表明,对称能系数相关的两个参数c_sym和κ对中子滴线附近的原子核质量有重要影响。此外还对WS4模型与WS*模型的参数不确定性及统计误差进行了对比研究,WS4模型中各模型参数的不确定性比WS*模型中相应模型参数的不确定性降低了10%~ 50%。The statistical uncertainties of 15 model parameters in the Weizsäcker-Skyrme(WS4) mass model are investigated with an efficient approach, and the propagated errors in the predicted masses are estimated. The discrepancies between the predicted masses and the experimental data are almost all smaller than the model errors. The most sensitive model parameter which causes the largest statistical error is analyzed for all bound nuclei. We find that the two coefficients of symmetry energy term significantly influence the mass predictions of extremely neutron-rich nuclei. In addition, the parameter uncertainties and statistical errors of the WS4 mass model and the WS* mass model are compared. The uncertainties of model parameter in the WS4 mass model is reduced by 10% ~ 50% compared with the WS* mass model.     

Automatic fringe analysis of the induced anisotropy of bent optical fibres

A new theoretical model considering the refraction of the incident light beam by the fibre is suggested to determine the refractive index profile of bent optical fibres. This new model (slabs model) considering the cross section of the bent optical fibre consists of large number of slabs. The slabs model bases on the refraction of the incident beam by the fibre. The refractive index profile of the optical fibre cladding before bending obtained using the automated Fizeau interferometer with the aid of suggested model is compared with other models such as, the homogenous model and the multilayer model to verify the ability of this slab model. The refractive index profile of the bent optical fibre cladding is investigated using this suggested model. In addition, the new model is used to obtain the induced birefringence and the guiding parameters. The bending radius is recommended to be greater than 7.1 mm for the used optical fibre. The consideration of the refraction increases the accuracy of the results.     

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.     

基于无导数优化方法的数值模式误差估计

初始场误差和模式误差是制约数值预报准确率的两个关键因素,本文主要考虑利用历史观测资料实现时空演变的模式误差的估计问题.通过把模式误差综合考虑成为准确模式中的未知项,把历史资料看作是带有未知项的准确模式的特解,构造了求解时空演变的模式误差项的反问题及其最优控制问题.给出了一个解决最优控制问题的无导数优化方法,该方法的优点是不需要建立原数值模式的切线性模式与伴随模式,它只需在增加一个外强迫项的基础上运行原数值模式即可实现模式误差项的最优估计.关于Burgers方程的算例表明,无论模式的初始状态是否准确已知,无导数优化方法都能有效解决时空演变的模式误差的最优估计问题,它为实际业务模式利用历史数据提取模式误差信息并显著地改进预报效果提供了一种方便可行的数值方法与理论依据.     

A dual model strategy to transfer multivariate calibration models for near-infrared spectral analysis

A dual-model method is proposed for correcting the calibration model. In the method, a primary calibration model is built using the spectra of a primary instrument and a correction model is established to describe the ratios between the predicted results from the spectra of different instruments. The prediction for the spectra of secondary instrument can be achieved by correcting the prediction of the primary model. A mathematical proof is described for the existence of the correction model, and the model is investigated using a near-infrared spectroscopic dataset of plant leaf samples measured on two instruments. The results show that a precise correction model is obtained and the model can be used to correct the predictions of the primary model. The correlation coefficients between the predicted and the reference ratios are above 0.9, and the prediction error after the correction is at the same level of the primary model.     

包含液相扩散方程简化的锂离子电池电化学模型

锂离子电池的电化学模型对于电池特性分析和电池管理具有重要意义,但是准二维(P2D)模型复杂度太高,为了在保证模型精度的基础上尽量降低复杂度,本文提出了一种包含液相简化的P2D (LSP2D)模型,该模型首先基于电化学平均动力学将电池端电压化简成为仅耦合固相Li+浓度c_s和液相Li+浓度c_e的方程,然后进一步对表达c_s和c_e演化规律的偏微分方程进行抛物线近似化简,使得最终的模型由多项式组成.COMSOL仿真表明在放电倍率为1C时该模型与单粒子(SP)模型的估算精度和速度相当,但在放电倍率为3C时,该模型的估算时间比P2D模型减少了99.73%,与SP模型相当,估算精度相比SP模型有大幅度提升.     

两种气液两相流模型的应用和比较

本文应用MUSIG模型[1]和均一直径模型对某溶液堆台架模型堆芯内气液流动传热进行了数值模拟.在MUSIG模型中堆芯内离散相气泡被分为5组不同直径的气泡,用于分析堆芯内气泡的流动变化和大小分布,采用Luo and Svendsen[2]和Prince and Blanch[3]模型描述不同直径气泡组间的破裂和聚合.在均一直径模型中,堆芯内的气体被考虑为同一直径的组分,并且不考虑其破裂与聚合现象.计算得到采用两个模型的模拟结果并且对其进行了对比研究.结果显示应用MUSIG模型的计算结果与台架实验结果吻合更好.     

用视密度加权平均二阶矩模型模拟旋流两相流动

本文用视密度加权平均代替时平均,建立了视密度加权平均的统一二阶矩两相湍流模型方程组（ＭＵＳＭ）,其中用体积分数代替了数密度,用颗粒驰豫时间作为封闭两相脉动速度关联方程耗散项的时间尺度,并引入了颗粒视在的气体速度脉动的输运方程。用ＭＵＳＭ模型模拟了旋流数为０．４７的气粒两相流动。并和实验结果及时间平均的ＵＳＭ模型的模拟结果进行了对照,两种模型均能较好地预报的两相的轴向和切向速度,轴向和切向脉动速度。此外,ＭＵＳＭ模型可以减少所用方程数,节省计算量。因此视密度加权平均的统一二阶矩两相湍流模型是一种对时间平均的统一二阶矩模型的改进,今后可以进一步扩大应用。     

相变过程的格子Boltzmann方法模拟

应用Shan提出的伪势多相模型替代R-K着色模型,建立一种新的描述气液相变过程的格子Boltzmann理论模型,模拟蒸发(高密度转化为低密度)过程.改进了计算效率,且得到较好的计算结果.同时应用该模型从孔隙尺度模拟了多孔介质中的相变现象,验证了该模型模拟复杂相变问题的可行性.     

Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

Ta及Nanbu库仑碰撞模型数值对比研究

深入研究库仑碰撞,对两种库仑碰撞模型-Ta模型与Nanbu模型在理论上进行了对比分析,详细阐述了两种模型中散射角大小的区别.在已有的采用Ta模型的全三维粒子模拟/蒙特长罗(PIC/MCC)算法基础上,采用Nanbu模型对电子间库仑碰撞计算模块重新进行了算法设计.分别应用Ta模型、Nanbu模型和无库仑碰撞的全三维PIC/MCC算法对国外热门负氢离子源JAEA 10A中的电子能量沉积进行了模拟分析.模拟结果与实验结果的对比分析发现:1)库仑碰撞使电子能量分布更接近于麦克斯韦分布;2)相对于传统的Ta模型,Nanbu模型的散射角考虑了多体碰撞的累加效果从而具有更高的期望值,按其模拟得到的电子温度具有更高的精度.这些为国内外学者设计相关算法指明了方向.