A Shell Model Mass Formula for Exotic Light Nuclei

An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely： （a） charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; （b） the central charge and mass densities are larger than, and decrease towards, the ＂asymptotic＂ values that are the reference parameters for nuclear matter; and （c） after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the ＂skin effect＂ and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to： （a） to strong configuration mixing and new magic numbers, and （b） the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.

Relaxation-rate formula for the entropic lattice Boltzmann model

A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows.

Magic Formula轮胎模型参数辨识的一种混合优化方法

Magic Formula(MF)轮胎模型能够准确描述轮胎的侧偏特性,广泛应用于车辆动力学的研究。由于MF轮胎模型参数多,且高度非线性,从大量的试验数据中准确辨识这些参数相当困难。提出一种基于遗传算法和数值优化算法的混合优化方法,采用由粗到精的辨识过程,先利用遗传算法得出近似最优解,再利用数值优化算法辨识出精确的参数。利用辨识出的参数计算轮胎的侧偏特性,计算结果与试验数据吻合良好,表明该方法是辨识MF轮胎模型参数的有效手段。

基于Ackermann's formula的类反斜线回滞系统滑模控制

回滞现象广泛地存在于许多机械控制领域。由于回滞特性具有不可微性,从而使得对回滞系统的控制变得困难和复杂,同时由于回滞可能引起系统的振荡,甚至造成系统的不稳定,因此有必要对回滞系统的有效控制进行研究。考虑到回滞系统建模仍然是个研究的领域,针对类反斜线回滞系统进行研究。把类反斜线回滞模型分解为确定的线性部分和已知上界的不确定非线性部分,利用Ackermann's formula给出了类反斜线回滞系统的滑模控制律。仿真表明此滑模控制律是有效的,同时此滑模控制保证了整个系统的稳定性。

用Magic Formula对轮胎特性曲线的拟合与优化

轮胎特性是研究汽车动力学的基础 ,特别是轮胎的侧偏特性对汽车操纵稳定性有着非常重要的影响。在汽车操纵稳定性的仿真研究中 ,用试验的方法来获得轮胎特性已不能满足研究的需要 ,而有必要建立轮胎模型。作者介绍了采用MagicFormula建立轮胎模型的方法 ,包括试验曲线的样条化、优化目标函数的设计和拟合优化方法等 ,得到了MagicFormula轮胎模型中的各参数 ,为进一步对汽车操纵稳定性的仿真研究奠定了基础。

MagicFormula减振器数值模型的参数识别与虚拟调校

为研究减振器的调校和匹配,需要建立可以完整描述减振器的外特性曲线理论模型。介绍了一种新型减振器模型——Magic Formula减振器数值模型,同时给出了一种有效、精确地模型参数辨识方法。然后将模型参数化,嵌入到7自由度整车Simulink模型中,以整车的动力学性能为优化目标,联合Isight软件,使用多目标优化算法,在C级路面对减振器的阻尼特性进行虚拟调校。优化结果表明,调校后的减振器的阻尼特性能够较明显改善车辆的动力学性能。

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

Shear creep characteristics and constitutive model of limestone

The characters of limestone in weak interlayer of a high rocky slope in Xuzhou, China, are studied by shear static test and shear creep test. The results show that limestone specimens have attenuation creep properties and constant rate creep properties, almost have no accelerated creep properties. The exponential type empirical formula is selected to fit creep grading curves by polynomial regression analysis method, and the square sums of the fitting results residual are in the order of 10^(-7). Then grade creep curves at every shear loads are set up. Combining creep rate-time curve, the creep properties of limestone are analyzed. As the physical meaning of component model is clearer, the Poytin–Thomson model is set up. Through the least square method, the optimal parameters of Poytin–Thomson model are obtained,and the sums of squared residuals belong to 10^(-3)order of magnitude, which can meet the accuracy requirements of engineering calculation. So the Poytin–Thomson model can reflect the shear creep characteristics of limestone very well.

TYRE DYNAMICS MODELLING OF VEHICLE BASED ON SUPPORT VECTOR MACHINES

Various methods of tyre modelling are implemented from pure theoretical to empirical or semi-empirical models based on experimental results. A new way of representing tyre data obtained from measurements is presented via support vector machines （SVMs）. The feasibility of applying SVMs to steady-state tyre modelling is investigated by comparison with three-layer backpropagation （BP） neural network at pure slip and combined slip. The results indicate SVMs outperform the BP neural network in modelling the tyre characteristics with better generalization performance. The SVMsqyre is implemented in 8-DOF vehicle model for vehicle dynamics simulation by means of the PAC 2002 Magic Formula as reference. The SVMs-tyre can be a competitive and accurate method to model a tyre for vehicle dynamics simuLation.

Study on the Dynamics of an SIR Epidemic Model with Saturated Growth Rate

In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.

Comparison of Debris Flow Characteristics Obtained by Using Video Materials and Modeling

Velocity of debris flow is one of the most important characteristics for the protective construction design. Since debris flows are rare events, and observations are conducted only on stations in Russia, Ukraine, Italy, Switzerland, USA, China, Japan and New Zealand, the velocity is calculated rather than measured. Nowadays, a large number of videos with passing debris flows have appeared on the Internet. Scientists can use such video materials to obtain qualitative and quantitative characteristics of the debris flow. Therefore, the aim of our research is an attempt to measure the debris flow velocity using video materials and compare the obtained results with the calculated values using various methods. The debris flow that came down in Firgen, Austria on August 4, 2012 was chosen as the object of our study. The video was carried out from several angles, so it was possible to select a section of the channel, through which we could measure the debris flows waves velocity. In addition, we calculated the velocities of waves by formulas adopted in the regulatory documents and compared with the measured by video values. During the video analysis, debris flow velocities at different sites were observed: minimum—7.2 m/s and maximum—10 m/s. The calculated values varied from 4.5 m/s to 11.4 m/s. Moreover, we applied model of the transport-shear process of debris flow formation developed by Yu. B. Vinogradov. When we were comparing the obtained debris flow discharges with results from Austrian colleagues, we found out that the values were similar to each other. However, internal scatter in the model changed from 151 to 190 m3/s, while in the report of Austrian colleagues the discharges were from 80 to 250 m3/s.

Study of High-Tech Industry Integration Model of Base,Project,and Talent

The high-tech industry is highlighted for advanced techniques,substantial capital investment,and smart talents.But their effective combination can not be achieved in the development of high-tech industry,which impedes its industrialization.Meanwhile,an effective mechanism is needed to develop the high-tech industry healthily.The aim of this paper is to explore the integration model of base,project,and talent which is presented and served as a new road for high-tech industry development as well as prove this model rational.Some results of the model are appealing.Firstly,start-ups in the park have the higher success probabilities;secondly,higher expected return attracts talents to join into start-ups in park;thirdly,side payment is the inner incentive to initiate this high-tech industry integration model.

Preliminary Research on a Mesenchymal Stem Cell-model for Screening Traditional Chinese Medicines

The authors focused their attention on the establishment of a mesenchymal stem cell（MSC） model for screening traditional Chinese medicines（TCMs） so as to investigate the effects of Shuanglong Formula（SLF） components（Ginsenosides and salvianolic acids） and ingredients（ginsenoside Rb1 and salvianolic acid B） on cardiomyocyte differentiation from MSCs.The SLF components were analyzed and quantified by HPLC-TOF-MS.Cardiomyocyte differentiation was induced by culturing MSCs in the induction medium supplemented with SLF ingredients,SLF components,5-azacytidine（5-aza）,5-aza＋SLF ingredients and 5-aza＋SLF components,respectively,for up to 30 d,and evulated by the expression of Cardiac-specific myosin heavy chain（MHC） and troponin I（TnI） via immunofluoresent staining.Slow growth rate and changed morphology were observed during cardiomyocyte differentiation.After 20 d of induction,differentiating MSCs were positive for MHC and TnI staining.The effects of SLF components were better than those of SLF ingredients.Taken together,SLF can induce the differentiation of MSCs into cardiomyogenic cells in vitro,and MSCs can be used as a powerful tool for screening TCMs.

An Extension of the Black-Scholes and Margrabe Formulas to a Multiple Risk Economy

We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.

基于遗传算法的磨削力模型系数优化及验证

在磨削力模型求解问题中,目前大多使用分段计算法或列方程组直接计算各个待求系数,不仅计算量大且其精度也无法保证。另外,传统的回归模型容易陷入局部最优,难以描述非线性关系。为此,将遗传算法引入到非线性优化函数参数优化中,基于外圆横向磨削力模型、平面磨削力模型、外圆纵向磨削力模型等现有的模型数据,开展磨削力理论模型的系数优化方法研究。相关性分析结果表明:通过计算得到的3种模型磨削力的预测精度提高了14.69%~42.54%,且3种模型所预测的法向磨削力的平均误差分别为5.9%、9.13%、3.23%,切向力平均误差分别为6.78%、8.36%、3.69%。经对比知,优化后的模型拟合度较好,模型预测精度显著提高。遗传算法优化后的非线性优化函数GA-LSQ算法更适合磨削力模型的求解,可对磨削力的预测及实际加工生产中的参数优化提供参考。

融合多维度相似算法的中药复方个性化煎煮推荐研究

目的:为实现中药汤剂智能煎煮设备煎煮参数快速推荐,提出一种融合方剂多维度相似算法,借鉴古代经典名方的个性化煎煮推荐。方法:选取30首经典名方,给出算法推荐的煎煮参数值,比较与典籍记载对应的煎煮参数值之间的差异。针对中药复方的组成成分、剂量以及功用维度特性,分别采用Jaccard相似系数、夹角余弦相似度和潜在狄利克雷分布(LDA)主题模型相似度算法,计算实验方剂与煎煮数据库中方剂间的相似度,将各维度最为相似方剂的煎煮参数加权融合,获取30首经典名方的个性化煎煮参数。结果:加水量、武火及文火时长参数值之间的相对误差分别为5.3%、3.4%、7.1%。结论:2组煎煮参数值较为接近,较好地借鉴和传承经典名方煎煮工艺。

An Adaptive Time-Step Backward Differentiation Algorithm to Solve Stiff Ordinary Differential Equations: Application to Solve Activated Sludge Models

A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters.

Global Stability of A Stochastic Predator-prey Model with Stage-structure

In this paper, a stochastic predator-prey model with stage structure for predatorand ratio-dependent functional response is concerned. Sufficient conditions for the globalasymptotic stability of positive equilibrium are established. Some numerical simulations arecarried out to illustrate the theoretical results.

基于CEL法熔滴冲击基板的TPF/FSI数值模拟

航空发动机和燃气轮机的高温工作环境会对其热端金属部件造成不可逆损伤,热障涂层(thermal barrier coatings,TBCs)能够承受高温和高压的侵蚀性环境,从而保证金属部件使用的安全性及可靠性。以空心Y_(2)O_(3)-ZrO_(2)(yttrium-stabilized zirconia,YSZ)粒子在等离子焰流中的2种形态,即全熔熔滴和空心熔滴为研究对象对其冲击铺展过程进行了模拟。基于ABAQUS/EXPLICIT耦合欧拉-拉格朗日(coupled Eulerian-Lagrangian,CEL)有限元方法,首先针对ABAQUS缺少相变模型,导致使用CEL方法计算熔滴铺展形貌失真的问题,给出了适用的动力黏度随温度变化的经验公式。此外,考虑周围空气对熔滴铺展过程的影响,提出了“两相流(two phase flow,TPF)/流-固耦合(fluid-structure-interaction,FSI)”2.5D模型,对熔滴冲击基板凝固成型及空气卷入的过程进行了模拟,并揭示了2种熔滴铺展形貌存在较大差异的机理,对制备隔热性能更优的热障涂层具有指导意义。

A Full Asymptotic Series of European Call Option Prices in the SABR Model with Beta = 1

We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the SABR model (with β=1) of stochastic volatility, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al. (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term, by using the conditional density of the average volatility, and write it as a two-dimensional integral. For the correction part, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin, Peng, and Schellhorn (2016) with analytical calculations. The first approach, which we call “Dyson series on the return’s idiosyncratic noise” yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor’s (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion. The second approach, which we call “Dyson series on the common noise” necessitates the calculation of only a one-dimensional integral, but the formula is more complex. This research consisted of both analytical derivations and numerical calculations. The latter show that our formulae are in general more exact, yet more time-consuming to calculate, than the first order expansion of Hagan et al. (2002).