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Control of COVID-19 transmission dynamics, a game theoretical approach

NONLINEAR DYNAMICS 2022年第1期110卷 857-877页

作者： Matusik, R. Nowakowski, A. Univ Lodz Fac Math & Comp Sci Banacha 22 PL-90238 Lodz Poland

We analyze a mathematical model of COVID-19 transmission control, which includes the interactions among different groups of the population: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, based on a system of ordinary differential equations, which describes compartment model of a disease and its treatment. The aim of the model is to predict the development disease under different types of treatment during some fixed time period. We develop a game theoretic approach and a dual dynamic programming method to formulate optimal conditions of the treatment for an administration of a vaccine. Next, we calculate numerically an optimal treatment.

关键词： COVID-19 Mathematical model of COVID-19 Game theoretic approach Dual dynamic programming Sufficient optimality conditions for Nash equilibrium numerical algorithm

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A 3D non-orthogonal plastic damage model for concrete

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2020年第0期360卷 112716-000页

作者： Zhou, Xin Lu, Dechun Du, Xiuli Wang, Guosheng Meng, Fanping Beijing Univ Technol Minist Educ Key Lab Urban Secur & Disaster Engn Beijing 100124 Peoples R China

A plastic damage model with the non-orthogonal flow rule is developed, which is consisted of the damage part driven by plastic strain and the plastic part based on effective stress. In the damage characterization, the degeneration law of elastic stiffness is described by the damage variable in the form of exponential function. In the plastic characterization, the evolution for plastic strain increment (PSI) is characterized from the magnitude and direction perspective. The direction of PSI is obtained directly by the fractional gradient of yield surface and the need for the construction of plastic potential function is bypassed. The magnitude of PSI is calculated based on the effective hardening function and the yield function, where the effective hardening function corresponding to the undamaged material is derived by both the normal hardening/softening function corresponding to the damaged material and the damage variable. The Next Increment Corrects Error (NICE) algorithm integrating the computational accuracy and efficiency is used for the numerical implementation of model. The ability of model to capture the complex mechanical behavior of concrete is assessed by the monotonous and cyclic test data from the literature. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Concrete Constitutive model Non-orthogonal flow rule Dilatancy Damage numerical algorithm

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Competition in defensive and offensive advertising strategies in a segmented market

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EUROPEAN JOURNAL OF CONTROL 2020年 53卷 98-108页

作者： Machowska, Dominika Nowakowski, Andrzej Univ Lodz Fac Econ & Sociol Dept Econometr Rewolucji 1905 R 41 PL-90214 Lodz Poland Univ Lodz Fac Math & Comp Sci S Banacha 22 PL-90238 Lodz Poland

We propose the new goodwill model ala Nerlove-Arrow defined on a competitive segmented market. Based on the dual dynamic approach, we give the sufficient condition under which the open-loop equilibrium exists for the new game. We also introduce e-open-loop equilibrium as a basis for the numerical algorithm using a construction of the optimal solution in the finite steps. The numerical algorithm enables an analysis of how the level of the homogeneity of given competitive products and customer recommendations modify optimal goodwill and the total profit of each player. (C) 2019 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： Open-loop Nash equilibrium Goodwill Market segmentation Dual dynamic approach numerical algorithm

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A Testing Tool for Converter-Dominated Power System: Stochastic Electromagnetic Transient Simulation

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IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 2022年第5期10卷 5304-5317页

作者： Chen, Pengwei Lu, Liang Ruan, Xinbo Liu, Nian Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Jiangsu Key Lab New Energy Generat & Power Conver Nanjing Jiangsu Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China

To investigate the impact of uncertain variability and provide a rigorous testing environment for converter-dominated power systems, this article develops a testing tool called stochastic electromagnetic transient simulation. The tool is derived from the stochastic differential equation (SDE) representing the stochastic process of parameter migration. By inheriting the principle of companion circuit, the dynamic companion circuits of the lumped elements with parameter migration are further established. Combined with the analysis of the numerical stability in discrete simulation as well as the stability of the continuous system with parameter migration, a numerical algorithm that is compatible with the electromagnetic transients program (EMTP) framework is designed, as well as a C program package. The verification results on a grid-connected three-phase two-level rectifier and a two-terminal dc distribution system demonstrate that the developed tool can simulate the parameter migrations and the stimulated system dynamic process simultaneously, which can also be used to efficiently reflect the real performance of various control subsystems and their coordination in extreme cases.

关键词： Mathematical models Stochastic processes numerical models Integrated circuit modeling Load modeling Power system dynamics Power system stability Converter-dominated power system electromagnetic transient (EMT) simulation numerical algorithm stochastic differential equation (SDE) stochastic dynamic

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A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems

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IMA JOURNAL OF APPLIED MATHEMATICS 2017年第6期82卷 1171-1191页

作者： Wang, Yanjiao Ding, Feng Jiangnan Univ Sch Internet Things Engn Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China

This article studies the problem for parameter identification of nonlinear dynamical systems (i.e., the Hammerstein-Wiener systems) with additive coloured noises. Based on the gradient search and the key term separation, a generalized extended stochastic gradient (GESG) algorithm is given for estimating the system parameters. To improve the computational efficiency, a data filtering based GESG algorithm and a data filtering based multi-innovation GESG algorithm are derived by applying the data filtering technique and the multi-innovation identification theory. Moreover, the proposed algorithms are proved to be convergent under proper conditions. Finally, the simulation results verify the theoretical analysis.

关键词： numerical algorithm data filtering gradient search multi-innovation identification dynamical system performance analysis

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Perturbation, extraction and refinement of invariant pairs for matrix polynomials

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LINEAR ALGEBRA AND ITS APPLICATIONS 2011年第3期435卷 514-536页

作者： Betcke, Timo Kressner, Daniel Swiss Fed Inst Technol Seminar Appl Math Zurich Switzerland Univ Reading Dept Math Reading RG6 2AH Berks England

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Polynomial eigenvalue problem Invariant pairs numerical algorithm Perturbation theory

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Experimental investigation and modeling study of the fiber orientation behavior

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ENGINEERING COMPUTATIONS 2021年第4期38卷 1453-1475页

作者： Li, Maoyuan Zhang, Yun Zhang, Shi Hou, Binkui Zhou, Huamin Huazhong Univ Sci & Technol State Key Lab Mat Proc & Die & Mold Technol Wuhan Peoples R China

Purpose The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar-Tucker equation can accurately describe the variation of orientation vector of fiber, whereas the stability of numerical algorithms was the major challenge. This paper aims to propose an accurate, stable algorithm to solve the Folgar-Tucker equation for the fiber orientation behavior. Design/methodology/approach First, the mismatch problem between the strain rate and the pressure field was solved by using the integral transformation method. Then, an accurate, stable algorithm to solve the Folgar-Tucker equation based on the invariant-based optimal fitting method was proposed. The equation was discretized by finite element/finite difference method, and the Lagrange multiplier method was applied to ensure stability. Findings The proposed algorithm is proven to accurately and steadily coincide with the experimental results for different cases, including the fiber orientation behaviors under combined flow field, rectangular sheet, three-dimensional computed tomography imaging of tensile specimen and box cases. Originality/value The fiber orientation behavior during the injection molding can be accurately predicted, which plays a significant role in determining the mechanical properties of products.

关键词： Composites Orientation Fiber numerical algorithm

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Simulation of tsunami waves generated by submarine landslides in the Black Sea

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RUSSIAN JOURNAL OF numerical ANALYSIS AND MATHEMATICAL MODELLING 2015年第4期30卷 227-237页

作者： Khakimzyanov, Gayaz S. Gusev, Oleg I. Beizel, Sofya A. Chubarov, Leonid B. Shokina, Nina Yu. RAS Siberian Branch Inst Computat Technol Novosibirsk 630090 Russia

numerical technique for studying surface waves appearing under the motion of a submarine land-slide is discussed. This technique is based on the application of the model of a quasi-deformable landslide and two shallow water models, namely, the classic (dispersion free) one and the completely nonlinear dispersivemodel of the second hydrodynamic approximation. numerical simulation of surface waves generated by a large model landslide on the continental slope of the Black Sea near the Russian coast is performed. It is shown that the dispersion has a significant impact on the picture of propagation of tsunami waves on sufficiently long paths.

关键词： The Black Sea submarine landslide tsunami waves dispersion numerical algorithm

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Recent Developments in the Pure Streamfunction Formulation of the Navier-Stokes System

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JOURNAL OF SCIENTIFIC COMPUTING 2010年第1-3期45卷 238-258页

作者： Fishelov, D. Ben-Artzi, M. Croisille, J-P. Afeka Tel Aviv Acad Coll Engn IL-69107 Tel Aviv Israel Hebrew Univ Jerusalem Inst Math IL-91904 Jerusalem Israel Univ Paul Verlaine Metz Dept Math LMAM UMR 7122 F-57045 Metz France

In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invokes also a sixth order Pade approximation for the first order derivatives, using an approximation suggested by Carpenter-Gottlieb-Abarbanel (J. Comput. Phys. 108:272-295, 1993). We also introduce the derivation of a pure streamfunction formulation for the Navier-Stokes equations in three dimensions.

关键词： Navier-Stokes equations Streamfunction formulation Vorticity numerical algorithm Compact schemes

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Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel

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PHYSICA SCRIPTA 2024年第7期99卷 075025-075025页

作者： Wireko, Fredrick A. Adu, Isaac K. Gyamfi, Kwame A. Asamoah, Joshua Kiddy K. Kwame Nkrumah Univ Sci & Technol Dept Math Kumasi Ghana Kumasi Tech Univ Dept Math Sci Kumasi Ghana Saveetha Sch Engn SIMATS Dept Math Chennai India

This work utilises a fractal-fractional operator to examine the dynamics of transmission of measles disease. The existence and uniqueness of the measles model have been thoroughly examined in the context of the fixed point theorem, specifically utilising the Atangana-Baleanu fractal and fractional operators. The model has been demonstrated to possess both Hyers-Ulam stability and Hyers-Ulam Rassias stability. Furthermore, a qualitative analysis of the model was performed, including examination of key parameters such as the fundamental reproduction number, the measles-free and measles-present equilibria, and assessment of global stability. This research has shown that the transmission of measles disease is affected by natural phenomena, as changes in the fractal-fractional order lead to changes in the disease dynamics. Furthermore, environmental contamination has been shown to play a significant role in the transmission of the measles disease.

关键词： measles Newton's approximation technique fractal-fractional derivative numerical algorithm

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