Well-Posedness and a Finite Difference Approximation for a Mathematical Model of HPV-Induced Cervical Cancer

We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential equations and a nonlinear first-order ordinary differential equation. The scheme is analyzed and used to provide an existence-uniqueness result. Numerical simulations are performed in order to demonstrate the first-order rate of convergence. A sensitivity analysis was done in order to compare the effects of two drug types, those that increase the death rate of HPV-infected cells, and those that increase the death rate of the precancerous cell population. The model predicts that treatments that affect the precancerous cell population by directly increasing the corresponding death rate are far more effective than those that increase the death rate of HPV-infected cells.

Stage-structured models for interacting wild and sterile mosquitoes

Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.

ANALYTIC STUDY ON POTENTIAL INSTABILITY AND SPIRAL STRUCTURE OF RAIN CLUSTERS

This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinates and acquire its analytic solution.Second,we discuss the potential instability of non-axisymmetrical rain clusters.Finally,we conclude that spiral structures can exist in rain clusters.Our analysis indicates that potential instability occurs when humid stratification coefficient is less than zero.Unstable growth rate increases with the increase of the absolute value for humid stratification coefficient.The simpler the vertical structure of perturbation,the thicker the inversion layer;additionally,the smaller the radius of the rain clusters,the larger the unstable growth rate.Simulation results agree well with those from observation and forecast.The spiral structure simulated by our model is similar to a radar echo,suggesting that rain clusters with spiral structures can occur in the atmosphere.In addition,they are generally close to the model solution in this work.

SECOND ORDER STEADY DRIFT FORCES ON OFFSHORE STRUCTURES

In this paper, the second order steady drift forces on the ships and other floating offshore structures are calculated by the far field method. The amplitudes of diffracted waves and radiated waves at infinity are obtained by the two-dimensional source distribution and strip-theory method. For the twin hull structure, the hydrodynamic interaction between the two hulls is taken into account. The drift forces on cross sections of Lewis type as well as on the semi-submersibles are computed. The theoretical results obtained by the present method agree fairly well with experimental results.

ON SOME PROBLEMS IN DYNAMIC COMPUTATION FOR THIN-WALLED STRUCTURES

This article discusses the problems of the dynamic computation for thin-walled structures such as thin plates and thin shells under impact load to find the dynamic factor mainly. In calculation we take into account the effect of the mass of the striking object and the system of thin-walled structures to be struck and transform the distributed mass of thin-walled structures into only one concentrated 'equivalent mass' by the method of reduced mass. Accordingly we derive the dynamic factor for the system of thin-walled structures under impact load.

Recovery Behavior of the Propagating Buckle on Elastic Structures

Based on the beam system model used by Chater, Hutchinson and Neale (1982), the recovery behavior of propagating buckle on elastic structures is first found out from the computational results. As the representative of some elastic structures, the Chater-Hutchinson-Neale model indicates that once the buckle meets arrestors, unlike the case in submarine pipelines, it will be reflected back to continue its propagation in a negative phase or a negative direction. The pressure which maintains the negative propagation, however, is as same as that required for the positive propagation. This fact has been examined in the experiment of the bulge propagation on a long elastic latex tube. The present discovery greatly supports the hypothesis that the buckle propagation corresponds to the coexisting phase of structures.

Latent Structure Linear Regression

A short review is given of standard regression analysis. It is shown that the results presented by program packages are not always reliable. Here is presented a general framework for linear regression that includes most linear regression methods based on linear algebra. The H-principle of mathematical modelling is presented. It uses the analogy between the modelling task and measurement situation in quantum mechanics. The principle states that the modelling task should be carried out in steps where at each step an optimal balance should be determined between the value of the objective function, the fit, and the associated precision. H-methods are different methods to carry out the modelling task based on recommendations of the H-principle. They have been applied to different types of data. In general, they provide better predictions than linear regression methods in the literature.

水下控制模块安装工具结构设计与对接精度分析

水下控制模块是水下生产系统的关键部件,针对水下控制模块在水下如何精准、高效、安全地实现回收和再安装工作的问题,本文设计了一种水下控制模块安装工具。对此安装工具进行了机械结构的设计,将安装工具各部分结构在工作过程中的作用进行了介绍。针对安装工具能够顺利完成水下控制模块的安装,基于安装工具各部分结构对接精度关系分析,通过数学建模与仿真分析,得到影响水下控制模块安装精度的原因,设计合理的安装精度参数。将仿真分析得到的数据与设计参数相比较,可证明水下控制模块的结构设计能满足水下控制模块的对接定位精度要求。结果表明:各精度参数满足水下控制模块安装工具设计要求,在此设计参数下安装工具能够完成水下控制模块的精确安装。

Some studies on mathematical models for general elastic multi-structures

The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem.

西南地区典型河道型水库水温结构及水动力机制研究

大型河道型水库在发挥水电效益的同时,其特有的水温分层对水环境的影响不容忽视。现有研究多偏重于水温垂向差异及时空演变规律研究,对于其形成过程的水动力影响研究尚不够深入。本研究利用数学模型模拟分析西南地区典型河道型水库—乌东德水库水温结构变化过程,发现水动力条件是水温结构形成的决定性因素,主温跃层的形成和演变取决于温差异重流导致的水动力机制。2—3月来水下潜于水库底部,二者界面形成主温跃层,并不断向库区下游发展;4—6月来流形成中间流,其上和其下分别形成两个温跃层;7月入库水流为上浮流,其下形成主温跃层;坝前局部区域水体主温跃层因取水孔口动力抽吸作用等温线出现局部收缩。

基于理论力学的旋耕机核心结构布局研究

针对现有的旋耕机作业效率和作业水平较低、作业效果无法达到农民要求的问题,基于理论力学对旋耕机的核心结构布局进行了设计与分析。旋耕机的主要组成包括机架、传动系统、电源和动力装置、旋耕刀和工作部件、避障系统、耕深调节装置及悬挂装置。为了保证旋耕机在作业过程中的动力匹配,通过建立旋耕机各部件的功耗数学模型,以优化旋耕机的结构和运动参数,提升旋耕机的作业性能。为了验证旋耕机的性能,对其进行机械作业性能测试,结果表明:旋耕机的作业效果良好,最终确定的旋耕机的基本性能参数合理。

采用解析和数值方法分析浮动式矩形浮箱的波浪诱导载荷研究

A three-dimensional mathematical hydrodynamic model associated with surface wave radiation by a floating rectangular box-type structure due to heave,sway,and roll motions in finite water depth is investigated based on small amplitude water wave theory and linear structural response.The analytical expressions for the radiation potentials,wave forces,and hydrodynamic coefficients are presented based on matched eigenfunction expansion method(MEFEM).The correctness of the analytical results of wave forces is compared with the construction of a numerical model using the open-source boundary element method code NEMOH.In addition,the present result is compared with the existing published experimental results available in the literature.The effects of the different design parameters on the floating box-type rectangular structure are studied by analyzing the vertical wave force,horizontal wave force,torque,added mass,and damping coefficients due to the heave,sway,and roll motions,and the comparison analysis between the forces is also analyzed in detail.Further,the effect of reflection and transmission coefficients by varying the structural width and drafts are analyzed.

轴扭耦合冲击器结构设计与室内试验

为提高PDC钻头切削齿在硬地层中的吃入深度、消除扭转振动带来的危害,在自激换向式扭冲总成结构的基础上,增设水力脉冲式轴冲总成,利用扭冲总成拨叉带动轴冲总成动盘阀同步旋转,使过流面积发生周期性变化,产生水力脉冲轴冲载荷,与扭冲载荷一起形成轴扭耦合冲击,设计出一种结构简单、冲击频率相同的新型轴扭耦合冲击器。同时,基于能量转换与守恒定律,建立了冲击器性能参数数学模型,并开展了轴扭耦合冲击器性能参数室内试验。试验结果表明,该轴扭耦合冲击器的压降、轴冲载荷与流量平方呈正比,扭冲载荷、冲击频率与流量呈线性增大关系,最大相对误差仅7.91%,验证了该数学模型的准确性。研究结果可为同类冲击钻井工具的开发提供理论指导。

高中数学在线视频学习行为影响因素研究——基于结构方程模型的机制路径

探究高中数学在线视频学习行为的影响因素,可以为相关学习平台提供优化建议,提升学习高中数学用户的学习效果。基于D&M与TAM模型、“SOR-KAP”融合模型构建了以高中数学在线视频学习行为为结果变量的理论框架,并运用结构方程模型对模型进行检验、分析。结果显示:在线视频平台的信息质量、系统质量和服务质量作为外界刺激会对包括感知有用性、易用性和高中数学在线视频学习态度、意愿在内的用户认知有机体产生正外部性,并最终影响用户学习行为;在线视频平台的信息质量、系统质量、服务质量、感知有用性、感知易用性以及在线视频学习态度、意愿作为影响因素并非简单地线性影响高中数学在线视频学习行为,而是要通过复杂的机制路径协同作用促进高中数学在线视频学习行为。文章据此构建了高中数学在线视频学习行为影响因素模型,并基于问卷调研,采用结构方程模型验证了该模型的科学性。

卸压增透下底板定向拦截钻孔瓦斯抽采模拟研究

杜儿坪矿68311工作面在回采时下邻近层瓦斯涌入量较多,为此采用在底板打定向拦截钻孔并进行瓦斯抽采的方法。为体现工作面回采对底板造成的卸压增透以及合理设计瓦斯抽采参数,首先使用FLAC3D模拟工作面回采不同距离下的底板有效应力变化,将其转换为渗透率变化并导入至COMSOL中,再通过建立流-固耦合数学模型完成不同抽采参数下的瓦斯抽采模拟。研究结果表明:工作面回采距离越大,卸压增透效果越好;钻孔层位由6 m降低至2 m,瓦斯抽采有效半径提高15.10%;钻孔直径由φ60 mm增加至φ120 mm,瓦斯抽采有效半径增加15.03%。

基于无线传感技术的多层砌体结构抗震自动化监测

自动化监测多层砌体结构抗震能力能够最大程度降低地震带来的损失,然而砌体结构的承受负荷和下沉量难以准确监测。为了解决上述问题,提升多层砌体结构抗震自动化监测效果,对基于无线传感技术的多层砌体结构抗震自动化监测模型进行设计。首先分析二维状态的砌块等效体积单元的应力-应变关系,进而判断得到的砌体受压应力-应变关系,确定监测点,再通过无线传感分析建立监测数学模型,利用信息采集对数据进行控制,实现抗震自动监测。实验结果表明,设计模型在受力超过临界值后,能够精准地判断出多层砌体结构所受荷载,监测的下沉量准确率在99.8%以上,具有一定的应用价值。

数学模型在服装结构设计中的建立与应用

服装结构设计中数学模型发挥着关键作用,设计师可以通过数学模型,明确服装整体效果及具体尺寸、形状、面料要求,从而对设计方案进行有效的调整和改善。不仅如此,在数据分析与优化方面,数学模型也贡献突出,可减少不必要的资源浪费,提升服装生产效率。基于此,本文聚焦现代服装结构设计,探讨了服装结构设计中运用数学模型的重要性,阐述了现代服装结构设计中所采用的多种数学模型,并指出数学模型的具体应用方向,文章旨在提高整体服装设计的水平,更好地满足消费者的审美需求。

Mathematical modeling of fuel cells fed with an electrically rechargeable liquid fuel

Lately,utilizing a novel electrically rechargeable liquid fuel(e-fuel),a fuel cell has been designed and fabricated,which is demonstrated to achieve a much better performance than alcoholic liquid fuel cells do.However,its current performance,which thus hampers its wide application,demands further improvement to meet up with industrial requirement.Therefore,to attain a better performance for this system,an in-depth understanding of the complex physical and chemical processes within this fuel cell is essential.To this end,in this work,a two-dimensional transient model has been developed to gain an extensive knowledge of a passive e-fuel cell and analyze the major factors limiting its performance.The effects of various structural parameters and operating conditions are studied to identify the underlying performance-limiting factors,where deficient mass transport is found to be one of the major causes.The increment of anode porosity and thickness are found to be effective methods of improving the cell performance.This study therefore provides insights on achieving further per-formance advancement of the fuel cell in the future.

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.

A Multiple Model Approach to Modeling Based on LPF Algorithm

Input-output data fitting methods are often used for unknown-structure nonlinear system modeling. Based on model-on-demand tactics, a multiple model approach to modeling for nonlinear systems is presented. The basic idea is to find out, from vast historical system input-output data sets, some data sets matching with the current working point, then to develop a local model using Local Polynomial Fitting (LPF) algorithm. With the change of working points, multiple local models are built, which realize the exact modeling for the global system. By comparing to other methods, the simulation results show good performance for its simple, effective and reliable estimation.