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variational principle and zero temperature limits of asymptotically （sub）-additive projection pressure

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Frontiers of Mathematics in China 2018年第5期13卷 1099-1120页

作者： Qiuhong WANG Yun ZHAO School of Mathematical Sciences Soochow University Suzhou 215006 China

Let {Si}li=l be an iterated function system （IFS） on Rd with an attractor K. Let （S,cr） denote the one-sided full shift over the finite alphabet {1,2,...,l}, and let π：∑ -K be the coding map. Given an asymptotically （sub）-additive sequence of continuous functions{Si}n≥1, we define the asymptotically additive projection pressure Pπ and show the variational principle for Pπunder certain affine IFS. We also obtain variational principle for the asymptotically sub-additive projection pressure if the IFS satisfies asymptotically weak separation condition （AWSC）. Furthermore, when the IFS satisfies AWSC, we investigate the zero temperature limits of the asymptotically sub-additive projection pressure Pπ（β） with positive parameter β.

关键词： Projection pressure asymptotically （sub）-additive potentials variational principle zero temperature limits

THE variational principle FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

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Acta Mathematica Scientia 2023年第4期43卷 1915-1924页

作者：张瑞丰朱姜慧 School of Mathematics Hefei University of TechnologyHefei 230009China

Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the v... 详细信息

关键词： packing entropy variational principle nonautonomous dynamical systems

On Chien's question to the Hu-Washizu three-field functional and variational principle

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Applied Mathematics and Mechanics(English Edition) 2022年第4期43卷 537-546页

作者： Bohua SUN School of Civil Engineering&Institute of Mechanics and Technology Xi'an University of Architecture and TechnologyXi'an 710055China

There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the combinations(A(ε_(ij))-σ_(ij)ε_(ij))or(B(σ_(ij))-σ_(ij)ε_(ij)),its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method.This research proves that the Hu-Washizu functionalΠ(u_(ij),ε_(ij),σ_(ij))is real three-field functional,and resolves the historic academic controversy on the issue of constructing a three-field functional.

关键词： variational principle elasticity Lagrangian multiplier thermodynamics entropy

variational principle for a special Cosserat rod

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Applied Mathematics and Mechanics(English Edition) 2009年第9期30卷 1169-1176页

作者：刘东生 Charles H-T WANG Applied Mathematics Department Nanjing University of Science and Technology School of Engineering and Physical Sciences University of Aberdeen

In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosse... 详细信息

关键词： rod variational principle Cosserat theory

THE variational principle AND APPLICATION OF NUMERICAL MANIFOLD METHOD

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Applied Mathematics and Mechanics(English Edition) 2001年第6期22卷 658-663页

作者：骆少明张湘伟蔡永昌 Mechtronic Department Shantou University 515063 Shantou P R China

The physical-cover-oriented variational principle of numerical manifold method (NMM) for the analysis of linear elastic static problems was put forward according to the displacement model and the characters of numerical manifold method. ne theoretical calculating formulations and the controlling equation of NMM were derived. As an example, the plate with a hole in the center is calculated and the results show that the solution precision and efficiency of NMM are agreeable.

关键词： variational principle numerical manifold method numerical analysis

variational principle and dynamical equations of discrete nonconservative holonomic systems

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Chinese Physics B 2006年第2期15卷 249-252页

作者：刘荣万张宏彬陈立群 Department of Physics Shaoguan University Shaoguan 512005 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler Lagrange equations and Hamilton＇s canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.

关键词： discrete mechanics variational principle dynamical equation

MODIFIED H-R MIXED variational principle FOR MAGNETOELECTROELASTIC BODIES AND STATE-VECTOR EQUATION

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Applied Mathematics and Mechanics(English Edition) 2005年第6期26卷 722-728页

作者：卿光辉邱家俊刘艳红 Aeronautical Mechanics & Avionics Engineering College Civil Aviation University of China Department of Mechanics and Engineering Measurement School of Mechanical Engineering

Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.

关键词： magnetoelectroelastic body variational principle laminated plates state-vector equation semi-analytical solution

Pre-image variational principle for Subadditive Sequence Functions

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Communications in Mathematical Research 2009年第3期25卷 231-240页

作者： MA XIAN-FENG CHEN ER-CAI School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 Department of Mathematics East China University of Science and Technology Shanghai 200237 Center of Nonlinear Science Nanjing University Nanjing 210093

In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very we... 详细信息

关键词： variational principle pre-image pressure pre-image entropy

Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems

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Chinese Physics B 2007年第3期16卷 570-577页

作者：傅景礼戴桂冬萨尔瓦多·希梅尼斯唐贻发 Department of Physics Zhejiang Sci-Tech University Hangzhou 310018 China State Key Laboratory of Scientific and Engineering Computing ICMSEC Academy of Mathematies and System Science Chinese Academy of Sciences Beijing 100080 China Departament de Matematica Aplicáda TTII E. T.S.I. Telecomunicación Universidad Politécnica de Madrid 28040-Madrid Spain Graduate School of the Chinese Academy of Sciences Beijing 100080 China

This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.

关键词： discrete variational principle first integral mechanico-electrical systems