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A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

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Chinese Physics B 2008年第2期17卷 394-398页

作者：张小妮方建会庞婷蔺鹏 College of Physics Science and Technology China University of Petroleum

In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

关键词： relativity phase space Mei symmetry new type of conserved quantity

New conserved quantities of Noether-Mei symmetry of mechanical system in phase space

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Chinese Physics B 2008年第6期17卷 1962-1966页

作者：方建会刘仰魁张小妮 College of Physics Science and Technology China University of Petroleum College of Physics and Electronic Engineering Longdong University

This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.

关键词： mechanical system phase space Noether-Mei symmetry new conserved quantity

Local Stress Field in Wafer Thinning Simulations with phase space Averaging

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Computers, Materials & Continua 2021年第7期68卷 743-759页

作者： Miaocao Wang Yuhua Huang Jinming Li Ling Xu Fulong Zhu School of Mechanical Science and Engineering Huazhong University of Science and TechnologyWuhan430074China School of Microelectronics Fudan UniversityShanghai200433China

From an ingot to a wafer then to a die,wafer thinning plays an important role in the semiconductor *** reveal the material removal mechanism of semiconductor at nanoscale,molecular dynamics has been widely used to investigate the grinding ***,most simulation analyses were conducted with a single phase space trajectory,which is stochastic and *** this paper,the stress field in wafer thinning simulations of 4H-SiC was obtained from 50 trajectories with spatial averaging and phase space *** spatial averaging was conducted on a uniform spatial grid for each trajectory.A variable named mask was assigned to the spatial point to reconstruct the shape of the *** spatial averaging parameters were applied and *** result shows that the summation of Voronoi volumes of the atoms in the averaging domain is more appropriate for spatial *** phase space averaging was conducted with multiple trajectories after spatial *** stress field converges with increasing the number of *** maximum and average relative difference(absolute value)of Mises stress was used as the convergence *** obtained hydrostatic stress in the compression zone is close to the phase transition pressure of 4H-SiC from first principle calculations.

关键词： Local stress field phase space alpha shape wafer thinning molecular simulation

Conformal invariance and conserved quantities of general holonomic systems in phase space

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Chinese Physics B 2009年第8期18卷 3158-3162页

作者：夏丽莉蔡建乐李元成 Department of Physics Henan Institute of Education College of Science Hangzhou Normal University College of Physics Science and Technology China University of Petroleum

This paper studies the conformed invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformed invariance for general holonomic systems in phase space are provided. The conformed factor expression is deduced from conformed invariance and Lie symmetry. The relationship between the conformed invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

关键词： phase space conformal invariance conformal factor conserved quantity

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in phase space

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Communications in Theoretical Physics 2007年第7期48卷 23-26页

作者： XIA Li-Li LI Yuan-Cheng College of Physics Science and Technology,China University of Petroleum,Dongying 257061,China College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase *** of motion of the controllable mechanical systems in phase space are *** definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are *** example is given to illustrate the application of the results.

关键词： nonholonomic controllable mechanical system phase space Noether-form invariance conserved quantity

Perturbation to Noether-Mei Symmetry and Adiabatic Invariants for Nonholonomic Mechanical Systems in phase space

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Communications in Theoretical Physics 2009年第4期51卷 600-604页

作者： ZHANG Ming-Jiang FANG Jian-Hui LU Kai College of Physics Science and Technology China University of Petroleum Dongying 257061 China

Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.

关键词： Noether-Mei symmetry perturbation adiabatic invariant nonholonomic mechanical system phase space

New Type of Conserved Quantities of Lie Symmetry for Nonholonomic Mechanical Systems in phase space

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Communications in Theoretical Physics 2009年第12期52卷 977-980页

作者： PANG Ting FANG Jian-Hui LIN Peng ZHANG Ming-Jiang LU Kai College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The new types of conserved quantities, which are directly induced by Lie symmetry of nonholonomie mechanical systems in phase space, are studied. Firstly, the criterion of the weak Lie symmetry and the strong Lie symmetry are given. Secondly, the conditions of existence of the new type of conserved quantities induced by the weak Lie symmetry and the strong Lie symmetry directly are obtained, and their form is presented. Finaily, an Appell-Hamel example is discussed to further illustrate the applications of the results.

关键词： Lie symmetry conserved quantity nonholonomic mechanical system phase space

A New Type of Conserved Quantity of Mei Symmetry for Relativistic Variable Mass Mechanical System in phase space

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Communications in Theoretical Physics 2008年第5期49卷 1145-1147页

作者： ZHANG Xiao-Ni FANG Jian-Hui LIN Peng PANG Ting College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.

关键词： relativity variable mass system phase space Mei symmetry new conserved quantity

A New Type of Conserved Quantity Deduced from Mei Symmetry for Relativistic Mechanical System in phase space

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Communications in Theoretical Physics 2008年第6期49卷 1421-1424页

作者： ZHANG Xiao-Ni FANG Jian-Hui College of Physical Science and Technology China University of Petroleum Dongying 257061 China

In this paper, a new type of conserved quantity indirectly deduced from the Mei symmetry for relativistic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The condition for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.

关键词： relativity mechanical system phase space Mei symmetry new conserved quantity