Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH...Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH at temperatures in the range of 90~300℃.It is found that different solution produces different etch figure on the surfaces of a sample.KOH based solutions produce rectangular pits rather than square pits.The etch pits elongate in 1 0] direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers. direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers.展开更多
Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherprob...Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.展开更多
With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usi...With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.展开更多
The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the...The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.展开更多
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the ...Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.展开更多
We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two...We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.展开更多
Conformal Ricei collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating eonformal Rieei eollineations is found when the Rieei tensor is non-degenerate, in...Conformal Ricei collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating eonformal Rieei eollineations is found when the Rieei tensor is non-degenerate, in which ease the number of independent eonformal Rieei eollineations is 15, the maximum number for four-dimensional manifolds. In the degenerate ease it is found that the static spherically symmetric spaeetimes always have an infinite number of eonformal Rieei eollineations. Some examples are provided which admit non-trivial eonformal Rieei eollineations, and perfect fluid source of the matter.展开更多
The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. ...The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
A new chiral monomer,(S)‐5,5′‐divinyl‐BINAP,was successfully synthesized and embedded intotwo different porous organic polymers(Poly‐1and Poly‐2).After loading a Rh species,the catalystswere applied for the hete...A new chiral monomer,(S)‐5,5′‐divinyl‐BINAP,was successfully synthesized and embedded intotwo different porous organic polymers(Poly‐1and Poly‐2).After loading a Rh species,the catalystswere applied for the heterogeneous asymmetric hydroformylation of styrene.Compared with thehomogeneous BINAP analogue,the enantioselectivity of Rh/Poly‐1catalyst was drastically increasedby approximately70%.The improved enantioselectivity of the porous Rh/BINAP polymerswas attributed to the presence of flexible chiral nanopockets resulting from the increased bulk ofthe R groups near the catalytic center.展开更多
The properties of neutron stars are studied in a relativistic mean-field model with SU(2) chiral symmetry spontaneous breaking being considered. The calculation results indicate that the effects of the chiral symmetry...The properties of neutron stars are studied in a relativistic mean-field model with SU(2) chiral symmetry spontaneous breaking being considered. The calculation results indicate that the effects of the chiral symmetry spontaneous breaking are not negligible.展开更多
The (2+1)-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-di...The (2+1)-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-dimensional reduction equations are obtained.展开更多
We study the symmetries of a (2+1)-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of sim...We study the symmetries of a (2+1)-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.展开更多
Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented i...Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. (Beijing, China) 42 (2004) 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.展开更多
In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model: an interacting collective spin system without external magnetic field. It is shown that this m...In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model: an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a flrst-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another flrst-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.展开更多
In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new s...In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.展开更多
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. ...Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.展开更多
Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the (2+1 )-dimensional differential Sawada Kotera (SK) equation by the classical Lie point group method, are presented...Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the (2+1 )-dimensional differential Sawada Kotera (SK) equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair's compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.展开更多
文摘Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH at temperatures in the range of 90~300℃.It is found that different solution produces different etch figure on the surfaces of a sample.KOH based solutions produce rectangular pits rather than square pits.The etch pits elongate in 1 0] direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers. direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers.
基金Supported by the National Natural Science Foundation of China under Grant No.10875059
文摘Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.
基金Supported by National Natural Science Foundation of China and China Academy of Engineering Physics (NSAF 11076015)
文摘With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.
文摘The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.
文摘Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.
基金Supported by National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065,and 90503006National Basic Research Program of China (973 Program) under Grant No.2007CB814800+2 种基金PCSIRT (IRT0734)the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.
文摘Conformal Ricei collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating eonformal Rieei eollineations is found when the Rieei tensor is non-degenerate, in which ease the number of independent eonformal Rieei eollineations is 15, the maximum number for four-dimensional manifolds. In the degenerate ease it is found that the static spherically symmetric spaeetimes always have an infinite number of eonformal Rieei eollineations. Some examples are provided which admit non-trivial eonformal Rieei eollineations, and perfect fluid source of the matter.
基金Supported by the Key Disciplines' Building Foundation of Henan Institute of Educationthe Natural Science Foundation of Education Bureau of Henan Province of China under Grant No. 2009A14003
文摘The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.
基金supported by the Strategic priority Research Program of the Chinese Academy of Sciences (XDB17020400)~~
文摘A new chiral monomer,(S)‐5,5′‐divinyl‐BINAP,was successfully synthesized and embedded intotwo different porous organic polymers(Poly‐1and Poly‐2).After loading a Rh species,the catalystswere applied for the heterogeneous asymmetric hydroformylation of styrene.Compared with thehomogeneous BINAP analogue,the enantioselectivity of Rh/Poly‐1catalyst was drastically increasedby approximately70%.The improved enantioselectivity of the porous Rh/BINAP polymerswas attributed to the presence of flexible chiral nanopockets resulting from the increased bulk ofthe R groups near the catalytic center.
文摘The properties of neutron stars are studied in a relativistic mean-field model with SU(2) chiral symmetry spontaneous breaking being considered. The calculation results indicate that the effects of the chiral symmetry spontaneous breaking are not negligible.
基金The project supported by National Natural Science Foundation of China under Grant No. 40333030, the Program for New Century Excellent Talents in Universities (NCET-05-0591), the Shanghai Post-doctoral Foundation under Grant No. 06R214139, and the Shandong Taishan Scholar Foundation
文摘The (2+1)-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-dimensional reduction equations are obtained.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475055 and 10547124 and partly by Shanghai Leading Academic Discipline Project under Grant No. T0401.Acknowledgments The authors would like to thank Prof. S.Y. Lou for his helpful discussions.
文摘We study the symmetries of a (2+1)-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.
基金The project supported by the Alexander von Humboldt Foundationthe Youth Foundation of Shanghai Jiao Tong UniversityNational Natural Science Foundation of China under Grant No.10475055
文摘Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. (Beijing, China) 42 (2004) 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.
基金supported by National Natural Science Foundation of China under Grant Nos.10775091 and 10704049
文摘In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model: an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a flrst-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another flrst-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10871165 and 10926036the Education Department under Grant No.Y200906909the Natural Science Foundation of under Grant No.Y6100126 of Zhejiang Province
文摘In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.
基金Supported by the Graduate Students' Innovative Foundation of China University of Petrolem (East China) under Grant No.S2009-19
文摘Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.
文摘Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the (2+1 )-dimensional differential Sawada Kotera (SK) equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair's compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.