Chinese Physics B

Li-Min, Ma; Zong-Min, Wu

doi: 10.1088/1674-1056/18/8/001pmid: N/A

In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.

Xiao-Yuan, Luo; Shao-Bao, Li; Xin-Ping, Guan

doi: 10.1088/1674-1056/18/8/002pmid: N/A

This paper researched into some methods for generating min-weighted rigid graphs and min-weighted persistent graphs. Rigidity and persistence are currently used in various studies on coordination and control of autonomous multi-agent formations. To minimize the communication complexity of formations and reduce energy consumption, this paper introduces the rigidity matrix and presents three algorithms for generating min-weighted rigid and min-weighted persistent graphs. First, the existence of a min-weighted rigid graph is proved by using the rigidity matrix, and algorithm 1 is presented to generate the min-weighted rigid graphs. Second, the algorithm 2 based on the rigidity matrix is presented to direct the edges of min-weighted rigid graphs to generate min-weighted persistent graphs. Third, the formations with range constraints are considered, and algorithm 3 is presented to find whether a framework can form a min-weighted persistent formation. Finally, some simulations are given to show the efficiency of our research.

Xiao-Hua, Zhou

doi: 10.1088/1674-1056/18/8/003pmid: N/A

We show some characteristics of three exact solutions to Einstein's gravity equation minimally coupled to a Quintessence field. Besides eternal inflation, several other interesting inflationary processes, such as transitory inflation, are obtained in these solutions. Singularity is avoided in some special cases.

Zhi-Sheng, Duan; Wen-Xu, Wang; Chao, Liu; Guan-Rong, Chen

doi: 10.1088/1674-1056/18/8/004pmid: N/A

In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.

Shan-Shan, Xu; Shu-Min, Li; Jamal, Berakdar

doi: 10.1088/1674-1056/18/8/005pmid: N/A

As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the ApellHamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces.

Hong-Sheng, Lü; Hong-Bin, Zhang; Shu-Long, Gu

doi: 10.1088/1674-1056/18/8/006pmid: N/A

This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results.

Xiang-Wei, Chen; Yong-Hong, Zhao; Yan-Min, Li

doi: 10.1088/1674-1056/18/8/007pmid: N/A

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Hui-Bin, Wu; Feng-Xiang, Mei

doi: 10.1088/1674-1056/18/8/008pmid: N/A

This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.

Ting, Pang; Jian-Hui, Fang; Ming-Jiang, Zhang; Peng, Lin; Kai, Lu

doi: 10.1088/1674-1056/18/8/009pmid: N/A

This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system's results.

Mei, Shang; Feng-Xiang, Mei

doi: 10.1088/1674-1056/18/8/010pmid: N/A

This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral.