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An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm

MATHEMATICAL BIOSCIENCES AND ENGINEERING 2020年第5期17卷 5752-5801页

作者： Wacker, Benjamin Schlueter, Jan Max Planck Inst Dynam & Self Org Next Generat Mobil Grp Dept Dynam Complex Fluids Fassberg 17 D-37077 Gottingen Germany Georg August Univ Gottingen Fac Phys Inst Dynam Complex Syst Friedrich Hund Pl 1 D-37077 Gottingen Germany

Since age and sex play an important role in transmission of diseases, we propose a SIR (susceptible-infectious-recovered) model for short-term predictions where the population is divided into subgroups based on both factors without taking into account vital dynamics. After stating our model and its underlining assumptions, we analyze its qualitative behavior thoroughly. We prove global existence and uniqueness, non-negativity, boundedness and certain monotonicity properties of the solution. Furthermore, we develop an explicit-implicit numerical solution algorithm and show that all properties of the continuous solution transfer to its time-discrete version. Finally, we provide one numerical example to illustrate our theoretical findings.

关键词： age structure existence and uniqueness nonlinear ordinary differential equations numerical algorithm sex structure SIR model

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Analysis of seepage evolution law of rock mass based on the numerical algorithm considering strength weakening water absorption

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ARABIAN JOURNAL OF GEOSCIENCES 2018年第13期11卷 1页

作者： Guo, Ying Jiang, Xinliang Song, Zhifei Tianjin Univ Sch Civil Engn 92 Weijin Rd Tianjin 110032 Peoples R China Shenyang Univ Sch Civil Engn 21 Wanghua South St Shenyang 110044 Liaoning Peoples R China North China Univ Technol Sch Civil Engn 5 Jinyuanzhuang Rd Beijing 100144 Peoples R China

Conventional numerical methods for modeling water seepage hardly provide a realistic description for the associated degradation of rock material and the permeability evolution mechanism. A numerical algorithm was utilized to investigate the rock seepage evolution process and the course of deformation failure. A theoretical model for depicting the weakening of rocks modulus and strength caused by water absorption in rock substrate was developed, and the mathematical relationships are presented in this paper. The softening process of a siltstone specimen due to water absorption was simulated under low- and high-fluid pressures as the boundary condition based on the theoretical model. Moreover, uniaxial compression test was performed for the specimen under different time of water absorption. The results indicated that the higher the fluid pressure, the quicker that the rock specimen reached saturation. It was observed that at the beginning of a seepage process, the openings are mainly filled by free water, but as time proceeds, there is a transition from absorption of free water in openings to water absorption by rock substrate. Fluid pressure, as the boundary condition, has a controlling effect on seepage rate but barely has any effect on the rate of water absorption in rock substrate. As the time of water absorption increases, rock strength (cohesion and angle of internal friction) decreases gradually until reaching the residual value. The numerical estimation of the changes in water content of rock substrate over time agrees with the theoretical explanations, which indicates high precision of the developed numerical method.

关键词： Rock mass Seepage evolution Strength weakening numerical algorithm

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A fast numerical algorithm for a basic dual integral equation of the flapping wing in a flow of non-viscous incompressible fluid

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 344卷 457-472页

作者： Popuzin, V. V. Sumbatyan, M. A. Tarasov, A. E. Southern Fed Univ Inst Math Mech & Comp Sci Milchakova St 8a Rostov Na Donu 344090 Russia

The present paper proposes a new approach to the classical problem of the harmonic oscillations of a thin wing in a flow of non-viscous incompressible fluid. The problem is reduced to a dual integral equation, permitting application of numerical methods. The numerical experiments are performed by using some advanced fast non-stationary iterative methods, with the help of the two-dimensional Fast Fourier Transform. There is given a brief survey on the iterative methods, to evaluate the most efficient algorithms in application to the considered problem of the flapping wing theory. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Flapping wing Dual integral equation numerical algorithm Toeplitz blocks Conjugate gradients Bi-conjugate gradients

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An efficient numerical algorithm in the classical 3d theory of thin lifting surface in a flow of non-viscous incompressible fluid

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MECHANICS RESEARCH COMMUNICATIONS 2018年 89卷 18-22页

作者： Sumbatyan, M. A. Bondarchuk, A. A. Mescheryakov, K. I. Southern Fed Univ Milchakova St 8a Rostov Na Donu Russia

The work is devoted to a new semi-analytical method, to treat the classical dual integral equation of the lifting surface theory. The method operates with the initial form of the integral equation, and no preliminary ... 详细信息

关键词： Lifting surface theory Two-dimensional integral equation numerical algorithm

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Finite-time stability analysis of a class of nonlinear time-varying systems: a numerical algorithm

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2018年第10期49卷 2224-2242页

作者： Chen, Zhihua Xie, Yongchun Beijing Inst Control Engn Beijing Peoples R China Sci & Technol Space Intelligent Control Lab Beijing Peoples R China Tianjin Key Lab Micrograv & Hypograv Environm Sim Tianjin Peoples R China

The paper investigates the finite-time stability (FTS) analysis of a very general class of nonlinear time-varying systems. The FTS of the considered system, whose vector field consists of a nonlinear part which can be sublinear or superlinear, and a linear part which can be time-varying, has not been fully studied before. By estimating the bound of the norm of the considered system's states with the generalised Gronwall-Bellman inequality, a sufficient criterion is established to guarantee the FTS of the considered system. To facilitate checking the criterion in practice, a novel numerical algorithm is proposed by numerically solving certain differential equations. Therefore, the FTS of the considered class of nonlinear time-varying systems can be easily analysed by the numerical algorithm. Further considering the numerical errors in the practical numerical computation, we strictly prove the credibility and programmability of the numerical algorithm in theory. Finally, three numerical examples are provided to illustrate the effectiveness the proposed results.

关键词： Finite-time stability nonlinear system time-varying system generalised Gronwall-Bellman inequality numerical algorithm

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Enhancements of the numerical simulation algorithm for natural gas networks based on node potential analysis 21st

Enhancements of the numerical simulation algorithm for natur...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Ruediger, Jens Tech Univ Appl Sci Wildau Hsch Ring 1 D-15745 Wildau Germany

A reliable energy supply for the economy of every country is a matter of national importance. Powerful simulation tools for natural gas networks are essential for operators of gas networks. In this paper, enhancement algorithms of previous developed node potential analysis algorithm are presented. These enhancement algorithms are used for a reasonable setting of initial values in the numerical gas net simulation algorithm. The setting of the initial values has a significant influence on the convergence behavior of the numerical simulation. The presented enhancement algorithms are explained and simulation results are evaluated. Copyright (C) 2020 The Authors.

关键词： energy supply gas net pipelines natural gas simulation numerical algorithm

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On the uniform finite-time stability of continuous linear time-varying systems: A numerical algorithm 37

On the uniform finite-time stability of continuous linear ti...

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37th Chinese Control Conference (CCC)

作者： Chen, Zhihua Xie, Yongchun Beijing Inst Control Engn Beijing 100190 Peoples R China Sci & Technol Space Intelligent Control Lab Beijing 100190 Peoples R China Tianjin Key Lab Micrograv & Hypograv Environm Sim Tianjin 300301 Peoples R China

ISBN: (纸本)9789881563958

The paper deals with the uniform finite-time stability (UFTS) of continuous linear time-varying (LTV) systems. Firstly, a necessary and sufficient condition for the UFTS of continuous LTV systems is devised with the idea of computing the envelope of all the trajectories of the considered system. Then, a corollary is obtained under the perspective of numerical computation. Further, based on the obtained corollary, a novel numerical algorithm is designed by utilizing the Lipschitz continuity of certain functions. With the proposed algorithm, only limited numerical computation is needed when analyzing the UFTS of continuous LTV systems. Compared with the existing Lyapunov-like function method, one needn't constructing Lyapunov-like functions. Moreover, the obtained corollary just requires being checked at a limited number of time points. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the proposed results.

关键词： Linear time-varying system Uniform Finite-time stability numerical algorithm

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Enhancements of the numerical simulation algorithm for natural gas networks based on node potential analysis

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IFAC-PapersOnLine 2020年第2期53卷 13119-13124页

作者： Jens Rüdiger Technical University of Applied Sciences Wildau Hochschulring 1 15745 Wildau Germany

关键词： energy supply gas net pipelines natural gas simulation numerical algorithm

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Theoretical study on electronic excitation spectra: A matrix form of numerical algorithm for spectral shift

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CHEMICAL PHYSICS 2017年 492卷 27-34页

作者： Ming, Mei-Jun Xu, Long-Kun Wang, Fan Bi, Ting-Jun Li, Xiang-Yuan Sichuan Univ Coll Chem Chengdu 610064 Peoples R China Sichuan Univ Coll Chem Engn Chengdu 610065 Peoples R China Sichuan Univ Inst Atom & Mol Phys Chengdu 610065 Peoples R China

In this work, a matrix form of numerical algorithm for spectral shift is presented based on the novel nonequilibrium solvation model that is established by introducing the constrained equilibrium manipulation. This form is convenient for the development of codes for numerical solution. By means of the integral equation formulation polarizable continuum model (IEF-PCM), a subroutine has been implemented to compute spectral shift numerically. Here, the spectral shifts of absorption spectra for several popular chromophores, N,N-diethyl-p-nitroaniline (DEPNA), methylenecyclopropene (MCP), acrolein (ACL) and p-nitroaniline (PNA) were investigated in different solvents with various polarities. The computed spectral shifts can explain the available experimental findings reasonably. Discussions were made on the contributions of solute geometry distortion, electrostatic polarization and other non-electrostatic interactions to spectral shift. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Nonequilibrium solvation Spectral shift Constrained equilibrium Vertical excitation energy numerical algorithm

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A certified numerical algorithm for the topology of resultant and discriminant curves

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JOURNAL OF SYMBOLIC COMPUTATION 2017年第Part2期80卷 285-306页

作者： Imbach, Remi Moroz, Guillaume Pouget, Marc Inria Rocquencourt France LORIA Lab Nancy France

Let C be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces P (x, y, z) = Q (x, y, z) = 0 (resp. P(x, y, z) = az (x, y, z) = 0), and generically its singularities are nodes (resp. nodes and ordinary cusps). State-of-the-art numerical algorithms compute the topology of smooth curves but usually fail to certify the topology of singular ones. The main challenge is to find practical numerical criteria that guarantee the existence and the uniqueness of a singularity inside a given box B, while ensuring that B does not contain any closed loop of C. We solve this problem by first providing a square deflation system, based on subresultants, that can be used to certify numerically whether B contains a unique singularity p or not. Then we introduce a numeric adaptive separation criterion based on interval arithmetic to ensure that the topology of C in B is homeomorphic to the local topology at p. Our algorithms are implemented and experiments show their efficiency compared to state-of-the-art symbolic or homotopic methods. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Topology of algebraic curves Resultant Discriminant Subresultant numerical algorithm Singularities Interval arithmetic Node and cusp singularities

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