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.

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.

Multiresolution analysis over triangle meshes: method and data structure

A robust and efficient algorithm is presented to build multiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.

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.

NOx Absorption in Full Scale Plant Columns with Structured Packings

A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidation degree of NOx and outlet acid concentration, liquid acid temperature are simulated and tested. The gas phase reactions and equilibria, gas phase mass transfer, interracial equilibria, and liquid phase reactions are considered in the model. Absorption of nitrogen oxides is studied in packed with Mellapak 250Y columns in series in an industrial process of 20000 t oxalic acid per year. Favorable agreement is shown between the model predictions and the on-site observations.

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.

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.

Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks;an application to COVID-19

We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases.We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing.The model is fitted to data reported for the early spread of COVID-19 in South Korea,Brazil,and Venezuela.The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries.Using the fitted values,we estimate the effective reproduction number R_(e)and investigate its responses to varied control scenarios of contact tracing.Alongside the positivity of solutions,and a stability analysis of the disease-free equilibrium are provided.

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.

COMPUTER SYSTEM FOR GEOMETRIC MODELING OF GEOLOGIC BODIES AND APPLICATIONS

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Structural Analysis of Platforms with the Effect of Joint Flexibility

A modified space beam element is presented in this paper to consider the local joint flexibility of T, Y tubular joints subjected to axial forces and in-plane bending moments for analysis of platforms. Two numerical examples are shown to verify the efficiency and validity of the method presented here.

Model Simplification and Parameter Modification for Offshore Platforms Using Experiment Data

In this paper, a computation method has been developed so as to compare the finite element method (FEM) with the test results directly. The structure is divided into the 'master' and 'slave' degrees of freedom. The simplified model can be obtained with modal reduction. Then the design sensitivity analysis of the eigenvalues and eigenvectors has been carried out using the modal frequency and modal shape of the test. A two-story frame structure and a jacket model structure have been calculated. Meanwhile, the modified coefficient, the FEM computational and experimental values have been given. It has been shown that the FEM model modified using the test modal value is efficient.

Modeling of a Linear Scanning 3D Vision Coordinate Measurement System

This paper theoretically analyzes and researches the coordinate frames of a 3D vision scanning system, establishes the mathematic model of a system scanning process, derives the relationship between the general non-orthonormal sensor coordinate system and the machine coordinate system and the coordinate transformation matrix of the extrinsic calibration for the system.

Principle, Method of Object-Relation Hypermedia Data Model and Its Application in the Multimedia Spatial Data Management

In this paper, a new multimedia data model, namely object-relation hypermedia data model (O-RHDM) which is an advanced and effective multimedia data model is proposed and designed based on the extension and integration of non first normal form (NF2) multimedia data model. Its principle, mathematical description, algebra operation, organization method and store model are also discussed. And its specific application example, in the multimedia spatial data management is given combining with the Hainan multimedia touring information system.

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。

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。