In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with ...In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili （KP） equation are obtained.展开更多
Darboux transformation （DT） provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV （eKdV） equation, by which some new solutions such as singular solito...Darboux transformation （DT） provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV （eKdV） equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 （1999） 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail.展开更多
Using cluster Monte Carlo method, we numerically investigate the coupling on the simple cubic lattice. We determine critical lines belong to the criticality in the XY model with nematic three-dimensional XY universali...Using cluster Monte Carlo method, we numerically investigate the coupling on the simple cubic lattice. We determine critical lines belong to the criticality in the XY model with nematic three-dimensional XY universality class in variable of θ （2θ） between the XY-ferromagnetic （nematic） and disordered states. Fhrthermore, the phase transition between the XY-ferromagnetic and the nematie states is found to be in the three-dimensional Ising universality class. The critical points are determined from the intersections of Binder ratios for various system sizes. With two sets of critical points obtained, we finally construct the phase diagram on the A-J plane.展开更多
Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of ...Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of (2+1)-dimensional generalization of mKd V equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this (2+ 1)-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions.展开更多
A novel modular self-reconfigurable robot called UBot is presented.This robot consists of severalstandard modules.The module is cubic structure based on double rotational DOF,and has four connect-ing surfaces that can...A novel modular self-reconfigurable robot called UBot is presented.This robot consists of severalstandard modules.The module is cubic structure based on double rotational DOF,and has four connect-ing surfaces that can connect to adjacent modules.A hook-type mechanism is designed,which can quick-ly and reliably connect to or disconnect from adjacent module.This mechanism is self-locking after con-nected,and energy-saving.To achieve small overall size and mass,compact mechanical structures andelectrical systems are adopted in modular design.The modules have embedded power supply and adoptwireless communication,which can avoid cable-winding and improve flexibility of locomotion and self-re-configuration.A group of UBot modules can adapt their configuration and function to the changing envi-ronment without external help by changing their connections and positions .The basic motion and self-re-configuration are proposed,and the experiments of worm-like locomotion are implemented.展开更多
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced...We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the nae continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak,intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.展开更多
基金supported by the State Key Basic Research Program of China under Grant No.2004CB318000the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20060269006
文摘In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili （KP） equation are obtained.
基金supported by National Natural Science Foundation of China under Grant No.10601028
文摘Darboux transformation （DT） provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV （eKdV） equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 （1999） 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail.
基金Supported by National Natural Science Foundation of China under Grant No. 10974180
文摘Using cluster Monte Carlo method, we numerically investigate the coupling on the simple cubic lattice. We determine critical lines belong to the criticality in the XY model with nematic three-dimensional XY universality class in variable of θ （2θ） between the XY-ferromagnetic （nematic） and disordered states. Fhrthermore, the phase transition between the XY-ferromagnetic and the nematie states is found to be in the three-dimensional Ising universality class. The critical points are determined from the intersections of Binder ratios for various system sizes. With two sets of critical points obtained, we finally construct the phase diagram on the A-J plane.
基金浙江省自然科学基金，中国博士后科学基金，中国科学院资助项目，教育部留学回国人员科研启动基金，Scientific Research Foundation for Returned Overseas Chinese Scholars of Ministry of Education of China
文摘Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of (2+1)-dimensional generalization of mKd V equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this (2+ 1)-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions.
基金Supported by the National High Technology Research and Development Programme of China（2006AA04Z220）； the National Natural Science Foundation of China（60705027）；Partially Supported by Progranl for Changjiang SchoLars and Innovative Research Team in University（PCSIRT）（IRT0423）.
文摘A novel modular self-reconfigurable robot called UBot is presented.This robot consists of severalstandard modules.The module is cubic structure based on double rotational DOF,and has four connect-ing surfaces that can connect to adjacent modules.A hook-type mechanism is designed,which can quick-ly and reliably connect to or disconnect from adjacent module.This mechanism is self-locking after con-nected,and energy-saving.To achieve small overall size and mass,compact mechanical structures andelectrical systems are adopted in modular design.The modules have embedded power supply and adoptwireless communication,which can avoid cable-winding and improve flexibility of locomotion and self-re-configuration.A group of UBot modules can adapt their configuration and function to the changing envi-ronment without external help by changing their connections and positions .The basic motion and self-re-configuration are proposed,and the experiments of worm-like locomotion are implemented.
基金supported by Engineering and Physical Sciences Research Council (EPSRC) (Grant No. EP/J001392/1)the Danish Council for Independent Research under the Sapere Aude program
文摘We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the nae continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak,intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.
