For a nonholonomic mechanics system with the action of small disturbance, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations of...For a nonholonomic mechanics system with the action of small disturbance, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations of groups in which the generalized coordinates and time are variable. On the basis of the invariance of disturbed nonholonomic dynamical equations under general infinitesimal transformations, the determining equations, the constrained restriction equations and the additional restriction equations of Lie symmetries of the system are constructed, which only depend on the variables t, qs and q^.s. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for a nonholonomic system with the action of small disturbance is investigated, and the Lie symmetrical adiabatic invariants, the weakly Lie symmetrical adiabatic invariants and the strongly Lie symmetrical adiabatic invariants of generalized Hojman type of disturbed nonholonomic systems are obtained. An example is given to illustrate applications of the results.展开更多
For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the bas...For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries t＇or a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.展开更多
A novel phenolic rigid organic filler （named KD） with a high melting point was dispersed in an isotactic polypropylene （iPP） matrix by solution-mixing and/or melt-mixing. A series of KD/iPP blends was prepared wit...A novel phenolic rigid organic filler （named KD） with a high melting point was dispersed in an isotactic polypropylene （iPP） matrix by solution-mixing and/or melt-mixing. A series of KD/iPP blends was prepared with or without addition of maleic anhydride-grafted polypro- pylene （MAPP） as a compatibilizer. Influences of MAPP and mixing methods on the filler dispersion were studied using polaried optical microscope （POM）, scanning electron microscope （SEM） and tensile test. The filler particles are always inclined to form large irregular aggregates in the iPP matrix due to their significant differences in polarity and solubility in solvent. However, an iPP/MAPP/KD （PMK） blend containing filler particles with a quasi-spherical shape （-97.8 nm in diameter） and narrow particle size distribution （polydispersity index = 1.076） was successfully prepared by incorporating MAPP to reduce the interfacial tension and surface free energy between the dispersion phase and the continuous phase, and adopting a spray-drying method after solution-mixing to suppress the increase of the size of the dispersed phase during the removal of solvent.展开更多
Bulk poly-m-phenylene isophthalamide （PMIA） can achieve flexibility upon dissolution by a LiCI/dimethylacetamide co-solvent, but remains hydrophobic despite the occasional emergence of cis amide groups providing a w...Bulk poly-m-phenylene isophthalamide （PMIA） can achieve flexibility upon dissolution by a LiCI/dimethylacetamide co-solvent, but remains hydrophobic despite the occasional emergence of cis amide groups providing a weak negative charge. In this study, based on the significant surface differences between PMIA membranes processed by nanofiber electrospinning and casting, a series of chemical analyses, in-situ Au nanoparticle depositions, and dye-adsorption experiments revealed that more cisconfiguration amide groups appeared on the surface of the electrospun PMIA membrane than on that of the cast membrane. Based on this surface difference, a strategy was proposed to improve the dyeing properties of PMIA by reversibly changing the cisltrans configurations of electrospun and cast membranes. The reversible chain-segment switch mechanism is a novel method for tuning the macroscale properties of polymer materials based on inherent molecular characteristics.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10372053 and 10472040.
文摘For a nonholonomic mechanics system with the action of small disturbance, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations of groups in which the generalized coordinates and time are variable. On the basis of the invariance of disturbed nonholonomic dynamical equations under general infinitesimal transformations, the determining equations, the constrained restriction equations and the additional restriction equations of Lie symmetries of the system are constructed, which only depend on the variables t, qs and q^.s. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for a nonholonomic system with the action of small disturbance is investigated, and the Lie symmetrical adiabatic invariants, the weakly Lie symmetrical adiabatic invariants and the strongly Lie symmetrical adiabatic invariants of generalized Hojman type of disturbed nonholonomic systems are obtained. An example is given to illustrate applications of the results.
基金Sponsored by the National Natural Science Foundation of China under Grant Nos 10372053 and 10472040.
文摘For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries t＇or a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.
文摘A novel phenolic rigid organic filler （named KD） with a high melting point was dispersed in an isotactic polypropylene （iPP） matrix by solution-mixing and/or melt-mixing. A series of KD/iPP blends was prepared with or without addition of maleic anhydride-grafted polypro- pylene （MAPP） as a compatibilizer. Influences of MAPP and mixing methods on the filler dispersion were studied using polaried optical microscope （POM）, scanning electron microscope （SEM） and tensile test. The filler particles are always inclined to form large irregular aggregates in the iPP matrix due to their significant differences in polarity and solubility in solvent. However, an iPP/MAPP/KD （PMK） blend containing filler particles with a quasi-spherical shape （-97.8 nm in diameter） and narrow particle size distribution （polydispersity index = 1.076） was successfully prepared by incorporating MAPP to reduce the interfacial tension and surface free energy between the dispersion phase and the continuous phase, and adopting a spray-drying method after solution-mixing to suppress the increase of the size of the dispersed phase during the removal of solvent.
基金We thank the National Natural Science Foundation of China （Grant Nos. 51471153 and 51372227） and the 521 Talent Project of Zhejiang Sci-Tech University, Science and Technology Department of Zhejiang Province Foundation （No. 2017C37017） for providing financial support.
文摘Bulk poly-m-phenylene isophthalamide （PMIA） can achieve flexibility upon dissolution by a LiCI/dimethylacetamide co-solvent, but remains hydrophobic despite the occasional emergence of cis amide groups providing a weak negative charge. In this study, based on the significant surface differences between PMIA membranes processed by nanofiber electrospinning and casting, a series of chemical analyses, in-situ Au nanoparticle depositions, and dye-adsorption experiments revealed that more cisconfiguration amide groups appeared on the surface of the electrospun PMIA membrane than on that of the cast membrane. Based on this surface difference, a strategy was proposed to improve the dyeing properties of PMIA by reversibly changing the cisltrans configurations of electrospun and cast membranes. The reversible chain-segment switch mechanism is a novel method for tuning the macroscale properties of polymer materials based on inherent molecular characteristics.
