Optimal convergence rates for three-dimensional turbulent flow equations

In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6）.

Estimating Crash Rate of Freeway Segments Using Simultaneous Equation Model

This study develops crash rate prediction models based on the premise that crash frequencies observed from adjacent paired non-weaving and weaving freeway segments are spatially correlated and therefore requires a simultaneous equation modeling approach. Simultaneous equation models for paired freeway non-weaving segments and weaving segments along with combined three freeway segments upstream and downstream were developed to investigate the relationship of crash rate with freeway characteristics. The endogenous variables have significant coefficients which indicate that unobserved variables exist on these contiguous segments, resulting in different crash rates. AADT is a variable that can show the interaction between the traffic and crashes on these contiguous segments. The results corroborate such an interaction. By comparing the simultaneous equation model and the multiple linear regression model, it is shown that more model parameters in the simultaneous models are significant than those from linear regression model. This demonstrates the existence of the correlation between the interchange and between-interchange segments. It is crucial that some variables like segment length can be identified significant in the simultaneous model, which provides a way to quantify the safety impact of freeway development.

Application of differential equations in mathematical modeling

This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.

Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

Modeling of the Dyeing Uptake Rate for Direct Dyestuff on Cotton in Batch Dyeing Process Based on Grey System Theory

The grey system theory, with the characteristics of fewer modeling data and higher accuracy, was employed to model the batch dyeing process for the purpose of accurate online control. The GM（1, 1） and GM （0, N） models of the grey system theory were discussed for their feasibilities of modding for batch dyeing process. The combination of direct dyestuff Fast Red F3B on cotton was chosen as a representative of the common dyeing method for describing the modeling process. Firstly, the GM（ 1, 1 ） model and the GM（1, 1） combined with GM（0, N） model were employed to model the equilibrium percentage of dyeing uptake rate. Secondly, an integrated dyeing uptake rate model with three factors （ temperature, salt concentration, and pH） was established based on the adsorption rate equation. Experimental results show that this model has higher accuracy and beetler generalization ability, which can predict the results of batch dyeing process. Due to the application of grey system theory, the model has a lot of advantages, such as being easy to determine the parameter value and small amount of calculation. So it can also be suitable for the same type of combination of dyestuff-fahric by changing the parameters value only.

Control Model of the HIV/AIDS Epidemic Based on Kinetic Equation

The corresponding dynamics equation model of HIV/AIDS was given based on the popular situation of HIV/AIDS in recent years. We studied the stability of the equilibrium point, discussed the threshold of epidemic, and carried on the numerical simulation based on the different persuade rate P, the different disease mortality α and the different infection rate β. The HIV/AIDS epidemic disease can pop in city at R0 > 1. We suggested that more persuade should be increased in addition to strengthening routine work according to the characteristics of R0 in the prevented and the controlled work of HIV/AIDS, which could more effectively reduce the number of HIV/AIDS patients. It provided the theoretical guidance, the beneficial reference on the prevented and the controlled work of HIV/AIDS.

A Two-Step Growth Curve: Approach to the von Bertalanffy and Gompertz Equations

Many curves have been proposed and debated to model individual growth of marine invertebrates. Broadly, they fall into two classes, first order (e.g. von Bertalanffy) and sigmoidal (e.g. Gompertz). We provide an innovative approach which demonstrates that the growth curves are not mutually exclusive but that either may arise from a simple three-stage growth model with two steps (k1 and k2) depending on the ratio of the growth parameters . The new approach predicts sigmoidal growth when is close to 1, but if either growth from stage A to stage B or B to C is fast relative to the other, the slower of the two steps becomes the growth limiting step and the model reduces to first order growth. The resulting curves indicate that there is a substantial difference in the estimated size at time t during the period of active growth. This novel two-step rate model generates a growth surface that allows for changes in the rate parameters over time as reflected in the new parameter n(t) = k1(t) - k2(t). The added degree of freedom brings about individual growth trajectories across the growth surface that is not easily mapped using conventional growth modeling techniques. This two (or more) stage growth model yields a growth surface that allows for a wide range of growth trajectories, accommodating staged growth, growth lags, as well as indeterminate growth and can help resolve debates as to which growth curves should be used to model animal growth. This flexibility can improve estimates of growth parameters used in population models influencing model outcomes and ultimately management decisions.=

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

基于综合贡献率的舰船装备体系寿命评估

为了更科学地预测装备寿命,提升装备的作战效益,从装备对体系的“综合贡献率”视角出发,探究了舰船装备“体系寿命”的评估方法。首先,基于作战环理论和非线性结构方程模型,引入二次交互项,构建舰船装备体系作战能力的指标体系,建立了体系作战效能的评估模型;然后,运用阈值法建立了舰船装备体系的复杂网络模型,基于拓扑特征统计值,构建了舰船装备体系网络结构特征的指标体系,将层次分析法与熵权法相结合来计算指标权重;最后,提出了舰船装备体系综合贡献率、体系寿命的定义和数学模型,并以航母编队体系对抗为算例,通过实验仿真数据,验证了模型和方法的可行性和有效性。

基于动态损伤速率的岩石损伤本构模型

【目的】本构模型是描述岩体变形破坏特性、表征其力学行为最有效的方法,针对岩石受荷过程中损伤速率变化建立动态损伤演化方程及本构模型成为岩体力学重要内容。【方法】为进一步深入研究荷载作用下岩石变形破坏全过程,将受荷岩石抽象为损伤和未损伤2部分,且未损伤部分承担有效应力,损伤部分承担残余应力,基于动态损伤速率的演化特征,建立动态损伤演化方程及本构模型,通过红砂岩常规三轴压缩试验结果验证模型的合理性。【结果和结论】结果表明:模型理论曲线可较好地反映岩石受荷损伤破坏的力学行为,其动态损伤演化依次经过损伤不变、损伤加快扩展、损伤缓慢增加和完全损伤4个阶段,分别对应理论曲线的压密-弹性变形、塑性变形、峰后软化和残余变形阶段;随着围压的增加,岩石动态损伤累积速率减缓,说明围压可抑制损伤扩展,表现为岩石抗压强度的增加和塑性特性的渐次增强;最大损伤速率较为接近峰值点,并在其右侧应力下降阶段,且对应的损伤变量在不同围压下基本一致;模型参数f增加,岩石强度及塑性变形增加;模型参数m减小,岩石强度增加,但对岩石损伤变形影响较小。通过建立的演化方程及本构模型,探讨了最大损伤速率点的特征及模型参数对岩石强度和损伤变形的影响,对岩石力学的发展有重要的参考价值。

考虑材料应变率效应的冲击响应模型相似律研究

目的研究考虑材料应变率效应的冲击响应模型相似律,获得一个能够综合材料弹塑性和应变率效应的精确相似解,支撑工程领域的模型试验。方法根据BuckinghamП定理,综合考虑材料的弹性、应变硬化和应变率效应,进一步推导了工程结构在冲击响应的模型相似律表达式。在此基础上,提出改变结构质量和冲击器速度来满足模型相似律的方法。结果相比最近冲击模型相似律的研究中存在近似相似、迭代求解的缺陷,该方法是一个显式、完全精确的相似解,并且能够同时考虑材料的弹性、应变硬化和应变率效应。采用圆板撞击的有限元数值模型进行了验证。结论推导出的模型相似律能够准确地预测原型的动态冲击的响应。相比而言,使用以往的相似方法具有明显的误差。

基于特征矩阵分区等值和自适应插值切换的有源配电网多速率并行仿真方法

现代有源配电网呈现复杂多变、多时间尺度的特征,采用单一仿真速率难以同时兼顾计算效率与精度,对此该文提出基于特征矩阵分区等值和自适应插值切换的有源配电网多速率并行仿真方法。首先,构建系统状态空间矩阵,并基于状态矩阵特征值的量级将系统拆分为多个动态特性差异的子系统,通过将系统的状态矩阵进行分块等效,实现子区域在小步长时刻的独立仿真解算与在大步长时刻的等效补偿,在保证仿真精度的基础上大幅降低了系统仿真规模;然后,针对各区域间数据交互不同步问题,通过倍率步长相量法分析线性插值误差产生原理及主要影响因素,并提出基于二阶泰勒展开式的多步自适应插值仿真算法,可以根据系统频率与仿真步长需求调节相关插值参数,显著降低插值误差;最后,采用改进型IEEE 123节点配电网算例,通过分区等值/插值计算与仿真结果的对比,验证了所提多速率并行仿真方法的可行性与有效性。

A Semiparametric Additive-multiplicative Rates Model for the Weighted Composite Endpoint of Recurrent and Terminal Events

Recurrent event data are commonly encountered in many scientific fields,including biomedical studies,clinical trials and epidemiological surveys,and many statistical methods have been proposed for their analysis.In this paper,we consider to use a weighted composite endpoint of recurrent and terminal events,which is weighted by the severity of each event,to assess the overall effects of covariates on the two types of events.A flexible additive-multiplicative model incorporating both multiplicative and additive effects on the rate function is proposed to analyze such weighted composite event process,and more importantly,the dependence structure among the recurrent and terminal events is left unspecified.For the estimation,we construct the unbiased estimating equations by virtue of the inverse probability weighting technique,and the resulting estimators are shown to be consistent and asymptotically normal under some mild regularity conditions.We evaluate the finite-sample performance of the proposed method via simulation studies and apply the proposed method to a set of real data arising from a bladder cancer study.

重庆万盛雷电活动特征研究

利用重庆万盛国家气象观测站1978~2012年人工观测的雷暴资料和重庆市闪电监测网2008~2020年系统监测的万盛闪电定位资料,采用线性回归趋势方程、气候倾向率、Mann-Kendall突变检验、Morlet小波分析等方法对雷暴日和雷电日进行统计和差异性分析,得到万盛的雷电活动时间分布特征。

Nonaffine Network Structural Model for Molten Low-Density Polyethylene and High-Density Polyethylene in Oscillatory Shear

We propose molten polymer's entanglement network deformation to be nonaffine and use transient network structural theory with the revised Liu's kinetics rate equation and the revised upper convected Maxwell constitutive equation to establish a nonaffine network structural constitutive model for studying the rheological behavior of molten Low Density Polyethylene (LDPE) and High Density Polyethylene (HDPE) in oscillatory shear. As a result, when the strain amplitude or frequency increases, the shear stress amplitude increases. At the same time, the accuracy of the nonaffine network model is higher than that of affine network model. It is clear that there is a small amount of nonaffine network deformation for LDPE melts which have long chain branches, and there is a larger amount of nonaffine network deformation in oscillatory shear for HDPE melts which has no long chain branches. So we had better consider the network deformation nonaffine when we establish the constitutive equations of polymer melts in oscillatory shear.

Quantum-dot Semiconductor Optical Amplifiers in State Space Model

A state space model(SSM) is derived for quantum-dot semiconductor optical amplifiers(QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA′s static and dynamic characteristics with high accuracy.

Towards Kinetic Modeling of Global Metabolic Networks： Methylobacterium extorquens AM1 Growth as Validation

Here we report a systematic method for constructing a large scale kinetic metabolic model and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium. Its central metabolic network includes formaldehyde metabolism, serine cycle, citric acid cycle, pentose phosphate pathway, gluconeogensis, PHB synthesis and acetyl-CoA conversion pathway, respiration and energy metabolism. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. Our method consists of the following major steps: 1) using a generic enzymatic rate equation to reduce the number of enzymatic parameters to a minimum set while still preserving their characteristics; 2) using a set of steady state fluxes and metabolite concentrations in the physiological range as the expected output steady state fluxes and metabolite concentrations for the kinetic model to restrict the parametric space of enzymatic reactions; 3) choosing enzyme constants K's and K'eqs optimized for reactions under physiological concentrations, if their experimental values are unknown; 4) for models which do not cover the entire metabolic network of the organisms, designing a dynamical exchange for the coupling between the metabolism represented in the model and the rest not included.

Modelling of passively Q-switched lasers with intracavity Raman conversion

We present a model of passively Q-switched Raman lasers by utilizing the rate equations. The intracavity fun-damental photon density, Raman photon density and the initial population-inversion density of the gain medium are assumed to be of Gaussian spatial distributions. These rate equations are normalized by introducing some synthetic parameters and solved numerically, and a group of general curves are generated. Prom these curves we can understand the dependence of the Raman laser pulse characteristics on the parameters about the pumping, the gain medium, the Raman medium and the resonator. An illustrative calculation for a passively Q-switched Nd^3＋：GdVO4 self-Raman laser is presented to demonstrate the usage of the curves and related formulas.

A new general rheological model for rheological lubrication

Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresummarized. The constitutive eqUation is proposetl for a new general theobocal model. The general medel feaaressimple structure and wide coverage, and can take the Place of many edsting thcofogical ed. The whel has suc-cessfully been used for Elastohydrodynamic lubrication calculation.

An equivalent circuit model for terahertz quantum cascade lasers:Modeling and experiments

Terahertz quantum cascade lasers（THz QCLs） emitted at 4.4 THz are fabricated and characterized. An equivalent circuit model is established based on the five-level rate equations to describe their characteristics. In order to illustrate the capability of the model, the steady and dynamic performances of the fabricated THz QCLs are simulated by the model.Compared to the sophisticated numerical methods, the presented model has advantages of fast calculation and good compatibility with circuit simulation for system-level designs and optimizations. The validity of the model is verified by the experimental and numerical results.