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Peeling of Magneto-responsive Beams with Large Deformation Mediated by the Parallel Magnetic Field

Acta Mechanica Solida Sinica 2024年第3期37卷 457-467页

作者： Gongqi Cao Zhangna Xue Shiyang Liu Yuchen Jin Jianlin Liu College of Pipeline and Civil Engineering China University of Petroleum(East China)Qingdao266580China

Elasto-capillarity phenomena are prevalent in various industrial fields such as mechanical engineering,material science,aerospace,soft robotics,and *** this study,two typical peeling processes of slender beams driven by the parallel magnetic field are investigated based on experimental and theoretical *** first is the adhesion of two parallel beams,and the second is the self-folding of a long *** these two cases,the energy variation method on the elastica is used,and then,the governing equations and transversality boundary conditions are *** is shown that the analytical solutions are in excellent agreement with the experimental *** effects of magnetic induction intensity,distance,and surface tension on the deflection curve and peeling length of the elastica are fully *** results are instrumental in accurately regulating elasto-capillarity in structures and provide insights for the engineering design of programmable microstructures on surfaces,microsensors,and bionic robots.

关键词： Magneto-responsive beam Adhesion and peeling Self-folding Elastica transversality condition

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A new look on wetting models:continuum analysis

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Science China(Physics,Mechanics & Astronomy) 2012年第11期55卷 2158-2166页

作者： LIU JianLin XIA Re ZHOU XiaoHua School of Pipeline and Civil Engineering China University of PetroleumQingdao 266555China School of Power and Mechanical Engineering Wuhan UniversityWuhan 430072China Department of Mathematics and Physics Fourth Military Medical UniversityXi’an 710032China

In this study,we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum *** analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates,and then elucidate the mechanism of the triple contact line(TCL) *** upon variational theory of the total free functional dealing with the movable boundary condition,we show that the macroscopic contact angle(MCA) expression is the corresponding transversality *** manifests that the MCA depends only on the chemical and geometric property at the TCL,and is not affected by the gravity of the droplet and the contact area beneath the *** continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different *** investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.

关键词： continuum field energy functional transversality condition mechanism-based model triple line moving

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Fractional Pfaff-Birkhoff Principle and Birkhoff′s Equations in Terms of Riesz Fractional Derivatives

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Transactions of Nanjing University of Aeronautics and Astronautics 2014年第1期31卷 63-69页

作者：周燕张毅 College of Mathematics and Physics Suzhou University of Science and Technology College of Civil Engineering Suzhou University of Science and Technology

The dynamical and physical behavior of a complex system can be more accurately described by using the fractional *** the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic *** mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s *** study on the Birkhoffian mechanics is an important developmental direction of modern analytical ***,the fractional Pfaff-Birkhoff variational problem is presented and *** definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly ***,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented ***,an example is given to illustrate the application of the results.

关键词： fractional derivative fractional Pfaff-Birkhoff principle fractional Birkhoff′s equation transversality condition

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Fractional Noether's Theorems for El-Nabulsi's Fractional Birkhoffian Systems in Terms of Riemann-Liouville Derivatives

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Journal of Donghua University(English Edition) 2017年第1期34卷 14-20页

作者：宋传静张毅 College of Science Nanjing University of Science and Technology Nanjing 210094 China College of Civil Engineering Suzhou University of Science and Technology Suzhou 215011 China

The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional *** problem of the calculus of variations with fractional derivatives is a hot topic ***,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were ***,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations ***,an example is given to illustrate the methods and results appeared in this paper.

关键词： fractional Birkhoff equations transversality condition calculus of variations fractional derivatives Noether’s theorem

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Optimal Control Analysis of Influenza Epidemic Model

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Applied Mathematics 2022年第10期13卷 845-857页

作者： Faizunnesa Khondaker Department of Mathematics Jagannath University Dhaka Bangladesh

The implementation of optimal control strategies involving preventive measures and antiviral treatment can significantly reduce the number of clinical cases of influenza. In this paper, a model for the transmission dynamics of influenza is formulated and two control strategies involving preventive measures (awareness campaign, washing hand, using hand sanitizer, wearing mask) and treatment are considered and used to minimize the total number of infected individuals and associated cost of using these two controls. The resulting optimality system is solved numerically. Hamiltonian is formulated to investigate the existence of the optimal control, in the optimal control model. Pontryagin’s Maximum Principle is applied to describe the control variables and the objective function is designed to reduce both the infection and the cost of interventions. From the numerical simulation, it is observed that in the case of high contact rate (β = 3), both the controls work for a longer period of time to reduce the disease burden. The optimal control analysis and numerical simulations reveal that the interventions reduce the number of exposed and infected individuals.

关键词： Influenza Optimal Control Pontryagin’s Maximum Principle transversality condition Hamiltonian

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Mathematical Analysis of Nipah Virus Infections Using Optimal Control Theory

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Journal of Applied Mathematics and Physics 2016年第6期4卷 1099-1111页

作者： Jakia Sultana Chandra N. Podder Department of Computer Science and Engineering Green University of Bangladesh Dhaka Bangladesh Department of Mathematics University of Dhaka Dhaka Bangladesh

The optimal use of intervention strategies to mitigate the spread of Nipah Virus (NiV) using optimal control technique is studied in this paper. First of all we formulate a dynamic model of NiV infections with variable size population and two control strategies where creating awareness and treatment are considered as controls. We intend to find the optimal combination of these two control strategies that will minimize the cost of the two control measures and as a result the number of infectious individuals will decrease. We establish the existence for the optimal controls and Pontryagin’s maximum principle is used to characterize the optimal controls. The numerical simulation suggests that optimal control technique is much more effective to minimize the infected individuals and the corresponding cost of the two controls. It is also monitored that in the case of high contact rate, controls have to work for longer period of time to get the desired result. Numerical simulation reveals that the spread of Nipah virus can be controlled effectively if we apply control strategy at early stage.

关键词： Nipah Virus (NiV) Optimal Control Existence of the State Existence of the Objective Functional Pontryagin’s Maximum Principle transversality condition Optimality condition Hamiltonian (H)

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A Maximum Principle for Forward-Backward Stochastic Control Systems with Integral-Type Constraint

A Maximum Principle for Forward-Backward Stochastic Control ...

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第32届中国控制与决策会议

作者： Hexiang Wan School of Control Science and Engineering Shandong University

In this paper,we investigate a stochastic optimal control problem driven by forward-backward stochastic differential equations,where the state is constrained by integral *** point out that state constraint here is of functional-type.A maximum principle is established by virtue of Clarke’s generalized gradient and Ekeland’s variational *** an application,a linear-quadratic control problem is studied.

关键词： Ekeland’s Variational Principle Forward-Backward Stochastic Differential Equation(FBSDE) Integral-Type State Constraint Stochastic Maximum Principle(SMP) transversality condition

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A unified analysis of a micro-beam,droplet and CNT ring adhered on a substrate:Variation with movable boundary condition

A unified analysis of a micro-beam,droplet and CNT ring adhe...

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第十二届全国物理力学学术会议

作者： Jian-Lin Liu School of Pipeline and Civil Engineering China University of Petroleum

In this study,we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy *** grouped the adhesion of a micro-beam,droplet and carbon nanotube(CNT) ring on a substrate into one framework,we used the developed line of reasoning to investigate the adhesion behaviors of these *** upon the derived governing equations and transversality conditions,the explicit solutions of the critical parameters and morphologies for the three systems are successfully obtained,and then the parameter analogies and common characteristics of them are thoroughly *** presented method has been verified via the concept of energy release rate in fracture *** analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of *** analysis results may be beneficial for the design of nano-structured materials,and hold potential for enhancing their mechanical,chemical,optical and electronic properties.

关键词： variational theory transversality condition veam adhesion

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