The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained...The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.展开更多
Based on the concept of adiabatic invariant,the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied.The criterion of the Noether-Lie symmetry for the perturb...Based on the concept of adiabatic invariant,the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied.The criterion of the Noether-Lie symmetry for the perturbed system is given,and the definition of the perturbation to Noether-Lie symmetry for the system under the action of small disturbance is presented.Meanwhile,the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained.展开更多
A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical system, is presented. Under general infinitesimal transformations, the ...A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical system, is presented. Under general infinitesimal transformations, the determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the corresponding holonomic mechanical system, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomie controllable mechanical system are obtained. An example is given to illustrate the application of the results.展开更多
The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of non...The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of nonholonomic systems with servoconstraints without perturbations are given. Based on the definition of higher-order adiabatic invariants of mechanical systems, the perturbation of Mei symmetries for nonholonomic .systems with servoconstraints under the action of small disturbance is investigated, and Mei adiabatic invatiants of the system are obtained. An example is given to illustrate the application of the results.展开更多
A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solu...A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solutions assoeiated with the potential symmetries are obtained.展开更多
All components of a turbocharger compressor are axisymmetric except for the spiral-shaped,gas-collecting overhung volute.In this paper,a novel experimental method to evaluate the impact of the volute's asymmetry o...All components of a turbocharger compressor are axisymmetric except for the spiral-shaped,gas-collecting overhung volute.In this paper,a novel experimental method to evaluate the impact of the volute's asymmetry on centrifugal compressor performance is proposed and applied to a high pressure-ratio turbocharger compressor.This method can isolate the impact of the volute's asymmetry on the compressor performance for the first time.Experiments prove the considerable impact of the volute's asymmetry on the compressor performance,especially the stability and efficiency.The impact of the volute's asymmetry on compressor stability correlates with rotational speed and thus with the pressure ratio,constricting the stable flow range by up to 47 percent and decreasing the maximum efficiency by 4.8 percent at the design speed.The results provide evidence to exploit the potential of intrinsic non-axisymmetric flow induced by asymmetric volute to improve the performance of turbocharger compressor with a high pressure ratio.展开更多
We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to sev...We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to several other interesting properties in symmetric tensor spaces.We then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius norm function of a symmetric tensor.Furthermore,we characterize the symmetric positive semidefinite tensor(SDT)cone by employing the properties of linear operators,design some face structures of its dual cone,and analyze its relationship to many other tensor cones.In particular,we show that the cone is self-dual if and only if the polynomial is quadratic,give specific characterizations of tensors that are in the primal cone but not in the dual for higher order cases,and develop a complete relationship map among the tensor cones appeared in the literature.展开更多
In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic ord...In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic order parameter, we carefully characterized the diversified phases and phase transitions, and established the phase diagram of such symmetric ternary blends. It can be generally divided into four regions: disordered phase (DIS) region at high temperature, ordered lameUar phase (LAM) region, bicontinuous microemulsion (BμE) channel and phase-separated phase (2P) region at low temperature with the increase of the total volume fractions of homopolymers φn, which shows good accordance with that in previous experimental and theoretical reports. Furthermore, we calculated the elastic constants of 2P and LAM phase, and discussed the transition mechanisms from 2P and LAM to BμE phase, respectively. The results show a direct relevance between the phase transitions and the change of interfacial properties. Finally, we also demonstrate that the B,uE channel becomes narrower in lower temperature caused by the temperature dependence of interfacial properties of ternary blends.展开更多
文摘The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.
文摘Based on the concept of adiabatic invariant,the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied.The criterion of the Noether-Lie symmetry for the perturbed system is given,and the definition of the perturbation to Noether-Lie symmetry for the system under the action of small disturbance is presented.Meanwhile,the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained.
基金supported by the Key Disciplines Building Foundation of Henan Institute of Education
文摘A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical system, is presented. Under general infinitesimal transformations, the determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the corresponding holonomic mechanical system, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomie controllable mechanical system are obtained. An example is given to illustrate the application of the results.
基金the Theoretical Physics (the Key Disciplines) Foundation of Henan Institute of Education
文摘The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of nonholonomic systems with servoconstraints without perturbations are given. Based on the definition of higher-order adiabatic invariants of mechanical systems, the perturbation of Mei symmetries for nonholonomic .systems with servoconstraints under the action of small disturbance is investigated, and Mei adiabatic invatiants of the system are obtained. An example is given to illustrate the application of the results.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10371098 and 10447007 and the Program for New Century Excellent Talents in Universities (NCET)
文摘A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solutions assoeiated with the potential symmetries are obtained.
基金supported by the National Natural Science Foundation of China (Grant No. 50806040)
文摘All components of a turbocharger compressor are axisymmetric except for the spiral-shaped,gas-collecting overhung volute.In this paper,a novel experimental method to evaluate the impact of the volute's asymmetry on centrifugal compressor performance is proposed and applied to a high pressure-ratio turbocharger compressor.This method can isolate the impact of the volute's asymmetry on the compressor performance for the first time.Experiments prove the considerable impact of the volute's asymmetry on the compressor performance,especially the stability and efficiency.The impact of the volute's asymmetry on compressor stability correlates with rotational speed and thus with the pressure ratio,constricting the stable flow range by up to 47 percent and decreasing the maximum efficiency by 4.8 percent at the design speed.The results provide evidence to exploit the potential of intrinsic non-axisymmetric flow induced by asymmetric volute to improve the performance of turbocharger compressor with a high pressure ratio.
基金supported by National Natural Science Foundation of China(Grant No.11301022)the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University(Grant Nos.RCS2014ZT20 and RCS2014ZZ001)+1 种基金Beijing Natural Science Foundation(Grant No.9144031)the Hong Kong Research Grant Council(Grant Nos.Poly U 501909,502510,502111 and 501212)
文摘We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to several other interesting properties in symmetric tensor spaces.We then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius norm function of a symmetric tensor.Furthermore,we characterize the symmetric positive semidefinite tensor(SDT)cone by employing the properties of linear operators,design some face structures of its dual cone,and analyze its relationship to many other tensor cones.In particular,we show that the cone is self-dual if and only if the polynomial is quadratic,give specific characterizations of tensors that are in the primal cone but not in the dual for higher order cases,and develop a complete relationship map among the tensor cones appeared in the literature.
基金supported by the National Natural Science Foundation of China(21174154,20874110,50930002)
文摘In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic order parameter, we carefully characterized the diversified phases and phase transitions, and established the phase diagram of such symmetric ternary blends. It can be generally divided into four regions: disordered phase (DIS) region at high temperature, ordered lameUar phase (LAM) region, bicontinuous microemulsion (BμE) channel and phase-separated phase (2P) region at low temperature with the increase of the total volume fractions of homopolymers φn, which shows good accordance with that in previous experimental and theoretical reports. Furthermore, we calculated the elastic constants of 2P and LAM phase, and discussed the transition mechanisms from 2P and LAM to BμE phase, respectively. The results show a direct relevance between the phase transitions and the change of interfacial properties. Finally, we also demonstrate that the B,uE channel becomes narrower in lower temperature caused by the temperature dependence of interfacial properties of ternary blends.