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Exploring the dynamical bifurcation and stability analysis of Nipah virus;novel perspectives utilizing fractional calculus

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MODELING EARTH SYSTEMS AND ENVIRONMENT 2024年第4期10卷 5427-5448页

作者： Ramzan, Sehrish Rashid, Saima Shah, Muzamil Abbas Elagan, Sayed K. Govt Coll Univ Faisalabad Dept Math Faisalabad 38000 Pakistan Lebanese Amer Univ Dept Comp Sci & Math Beirut 11022 Lebanon Richmond Amer Univ London Dept Business London England Taif Univ Coll Sci Dept Math & Stat POB 11099 Taif 21944 Saudi Arabia

A zoonotic virus called the Nipah virus (NV) can create deadly illness epidemics in humans. The animal host repository for NV is the fruit bat, sometimes referred to as the flying fox. It has been documented to infect pigs, which are regarded as intermediary carriers. Scientists' interest in infectious disease modeling has surged because non-integer-order derivatives work so well. In this work, we present a model of NV infection propagation that accounts for both the disappearance of antibodies in rehabilitated people and all human-to-host animal propagation. Taking into consideration the fractal-fractional operator in the generalized Mittag-Leffler kernel sense, we contemplated the numerical solutions for the proposed model via the Lagrange interpolation polynomial technique. Several qualitative aspects of the NV model, such as positive bounded solution, disease-free equilibrium, and the basic reproduction number (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_numerical$$\end{document}), are presented with a graphic illustration to demonstrate the effectiveness of the system parameters. To establish efficient time-dependent oversight, sensitive evaluation of the framework's components is also carried out. Besides that, the local and global stability at the disease-free equilibrium point is provided in detail. Meanwhile, a fractional bifurcation framework is developed according to the sensitivity indices, and numerical simulations are used to identify the most efficient prevention approach. The mathematical mechanism of the NV model is characterized by the Atangana-Baleanu fractal-fractional differential operators, which are newly described as fractal-fractional differential operators. Three approaches were taken to examine the numerical behavior of the NV: (i) varying both the fractal

关键词： Fractal-fractional operators Nipah virus epidemic Bifurcation analysis Sensitivity analysis Reproduction number Local and global stability numerical algorithm Fractional lagrange polynomial Fractal newton approximation

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numerical Solution of High-Precision Multiconstant Equations of State

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MOSCOW UNIVERSITY PHYSICS BULLETIN 2025年第1期80卷 189-193页

作者： Koldoba, E. V. Lomonosov Moscow State Univ Fac Mech & Math Dept Computat Mech Moscow 119991 Russia

In certain pressure and temperature ranges, high-precision thermal equations of state possess multiple roots, with only one being the desired physical solution to the problem. This paper considers methods for setting initial values to calculate the desired root of the equation. A method for verifying the found root has been developed, enabling the exclusion of nonphysical solutions. The proposed approach allows for the construction of a robust algorithm for numerically solving transcendental equations of state for practical applications.

关键词： numerical algorithm multiparameter equation of state Benedict-Webb-Rubin equation Pedersen's model

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An algorithm for Solving Boundary Value Problems for Delay Differential Equations with Loadings

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2024年第10期45卷 5032-5042页

作者： Iskakova, N. B. Bakirova, E. A. Khanzharova, B. S. Kadirbayeva, Zh. M. Inst Math & Math Modeling Dept Differential Equat A26G7T5 Alma Ata 050000 Kazakhstan Kazakh Natl Womens Teacher Training Univ Dept Math A05M0T6 Alma Ata 050026 Kazakhstan Int Informat Technol Univ Dept Math & Comp Modeling A15M0F0 Alma Ata 050040 Kazakhstan

In this paper, we propose an efficient numerical algorithm for solving linear two-point boundary value problem for delay differential equations with loadings. The Dzhumabaev parametrization method is applied to construct the numerical solutions. The application of the this method leads the considering problem to a system of algebraic equations and Cauchy problems for differential equation without delay argument that are easy to solve. Several illustrative examples are given to demonstrate the effectiveness of the proposed algorithm.

关键词： delay differential equation loadings parametrization method numerical algorithm

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Kinematics of a planar slider-crank linkage in screw form

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2022年第3期236卷 1588-1597页

作者： Zhao, Jing-Shan Wei, Songtao Ji, Junjie Tsinghua Univ Dept Mech Engn State Key Lab Tribol Beijing Peoples R China

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

关键词： Screw kinematics open kinematic chain closed kinematic chain numerical algorithm

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

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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 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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Matrix numerical method for probability densities of stochastic delay differential equations

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2024年第23期57卷 235001-235001页

作者： Antary, Nils Holubec, Viktor Univ Leipzig Inst Theoret Phys D-04081 Leipzig Germany Leibniz Assoc Potsdam Inst Climate Impact Res PIK D-14473 Potsdam Germany Charles Univ Prague Fac Math & Phys Dept Macromol Phys V Holesovickach 2 CZ-18000 Prague Czech Republic

Stochastic processes with time delay are invaluable for modeling in science and engineering when finite signal transmission and processing speeds can not be neglected. However, they can seldom be treated with sufficient precision analytically if the corresponding stochastic delay differential equations (SDDEs) are nonlinear. This work presents a numerical algorithm for calculating the probability densities of processes described by nonlinear SDDEs. The algorithm is based on Markovian embedding and solves the problem by basic matrix operations. We validate it for a broad class of parameters using exactly solvable linear SDDEs and a cubic SDDE. Besides, we show how to apply the algorithm to calculate transition rates and first passage times for a Brownian particle diffusing in a time-delayed cusp potential.

关键词： stochastic delay differential equations probability density numerical algorithm numerical methods transition rates non-Markovian dynamics

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numerical algorithm for Distribution-Map Derivations of Switching Converters

Numerical Algorithm for Distribution-Map Derivations of Swit...

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Annual Conference of the IEEE Industrial Electronics Society

作者： Yuta Yamada Tomoharu Nagashima Yoshifumi Ibuki Yoshiki Fukumoto Hiroo Sekiya Graduate School of Advanced Integration Science Chiba University DAIHEN Corp.

ISBN: (纸本)9781479940318

This paper proposes a numerical algorithm for drawing distribution maps of switching power-converter characteristics on parameter spaces. The concept of the proposed algorithm is that parameters satisfying the assigned conditions are derived and followed with low computation cost. Zero-Voltage-Switching (ZVS) region, output power distribution map, and contour map of power-conversion efficiency of the phase-controlled class-D inverter are drawn as application examples of the proposed algorithm. It is possible from these maps to design the phase-controlled class-D inverter achieving the ZVS at entire control regions. The validity and effectiveness of the proposed algorithm were confirmed by carrying out circuit experiments.

关键词： numerical algorithm Distribution map Switching power converter Converter design ZVS region Phase-controlled class-D inverter

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A robust numerical treatment of solid-phase diffusion in pseudo two-dimensional lithium-ion battery models

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JOURNAL OF POWER SOURCES 2023年 556卷

作者： Kim, Jinyong Mallarapu, Anudeep Santhanagopalan, Shriram Newman, John Natl Renewable Energy Lab Ctr Energy Convers & Storage Syst Golden CO 80401 USA

Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of dis-cretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

关键词： numerical algorithm Battery modeling Fast charging Battery solver Solid-state diffusion Pseudo-two-dimensional model

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Online modeling of environmental constraint region for complex-shaped parts assembly

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ASSEMBLY AUTOMATION 2022年第6期42卷 881-890页

作者： Gan, Shuai Liu, Yang Chen, Ziyu Univ Sci & Technol Beijing Sch Mech Engn Beijing Peoples R China Chinese Acad Sci Inst Automat Beijing Peoples R China

PurposeThe paper aims to propose a method to build environmental constraint region online in complex-shaped peg-in-hole assembly tasks. Design/methodology/approachCompared with conventional way which using computer-aided design (CAD) models of assembly parts to construct the environmental constraint region offline, the paper provides an online approach that consists of three aspects: modeling assembly parts through visual recognition, decomposing complex shapes into multiple primitive convex shapes and a numerical algorithm to simulate the peg-in-hole insertion contact. Besides, a contrast experiment is performed to validate the feasibility and effectiveness of the method. FindingsThe experiment result indicates that online construction takes less time than the offline way under the same task conditions. Furthermore, due to the CAD models of the parts are not required to be known, the method proposed in the paper has a broader application in most assembly scenarios. Originality/valueWith the improvement of customization and complexity of manufactured parts, the assembly of complex-shaped parts has drawn greater attention of many researchers. The assembly methods based on attractive region in environment (ARIE) have shown great performance to achieve high-precision manipulation with low-precision systems. The construction of environmental constraint region serves as an essential part of ARIE-based theory, directly affect the formulation and application of assembly strategies.

关键词： numerical algorithm Environmental constraint region Online modeling Configuration decomposition

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