First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bi...First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.展开更多
A novel torsion sensor,which can be embedded in the engineering material,is proposed.Based on the coupled mode theory and the characteristic of twisted high birefringence fiber,we have established the mathematical mod...A novel torsion sensor,which can be embedded in the engineering material,is proposed.Based on the coupled mode theory and the characteristic of twisted high birefringence fiber,we have established the mathematical model of twisted high birefringence fiber grating transfer matrix.Two numerical simulation methods based on the transfer matrix method and coupled mode theory were used to analyze the consequent changes in reflection spectra.The simulation results of the two methods show good agreement with each other.The two main peak wavelengths of the high birefringence fiber grating shift as the twist angle changes from 0 to 360.And a peak was produced among the wavelengths of two main peaks.Its wavelength basically does not change and is about 1 552.225 nm.Its corresponding reflected peak value R_c basically presents the linear relationship with the twist angle α.The experiments show that the system has a wide measurement range.The resolution is 0.012° and the sensitivity is 0.13/rad.Good agreements between experimental results and numerical simulations have been obtained.展开更多
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its...In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.展开更多
Are quantum states real? This most fundamental question in quantum mechanics has not yet been satisfactorily resolved, although its realistic interpretation seems to have been rejected by various delayedchoice experim...Are quantum states real? This most fundamental question in quantum mechanics has not yet been satisfactorily resolved, although its realistic interpretation seems to have been rejected by various delayedchoice experiments. Here, to address this long-standing issue, we present a quantum twisted double-slit experiment. By exploiting the subluminal feature of twisted photons, the real nature of a photon during its time in flight is revealed for the first time. We found that photons' arrival times were inconsistent with the states obtained in measurements but agreed with the states during propagation. Our results demonstrate that wavefunctions describe the realistic existence and evolution of quantum entities rather than a pure mathematical abstraction providing a probability list of measurement outcomes. This finding clarifies the long-held misunderstanding of the role of wavefunctions and their collapse in the evolution of quantum entities.展开更多
The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essentia...The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect.We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures.Using a two-dimensional area-preserving twist mapping as the model,we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit.We show how the stickiness effect and the orbital diffusion speed are related to the angle.展开更多
The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, the...The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.展开更多
文摘First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.
基金Supported by National Natural Science Foundation of China(60377002)
文摘A novel torsion sensor,which can be embedded in the engineering material,is proposed.Based on the coupled mode theory and the characteristic of twisted high birefringence fiber,we have established the mathematical model of twisted high birefringence fiber grating transfer matrix.Two numerical simulation methods based on the transfer matrix method and coupled mode theory were used to analyze the consequent changes in reflection spectra.The simulation results of the two methods show good agreement with each other.The two main peak wavelengths of the high birefringence fiber grating shift as the twist angle changes from 0 to 360.And a peak was produced among the wavelengths of two main peaks.Its wavelength basically does not change and is about 1 552.225 nm.Its corresponding reflected peak value R_c basically presents the linear relationship with the twist angle α.The experiments show that the system has a wide measurement range.The resolution is 0.012° and the sensitivity is 0.13/rad.Good agreements between experimental results and numerical simulations have been obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11101269 and 11431010)
文摘In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.
基金supported by the National Natural Science Funds for Distinguished Young Scholars of China(61525504)the National Natural Science Foundation of China(11574065,11604322,61275115,61378003,61435011 and 61605194)+2 种基金China Postdoctoral Science Foundation(2016M590570)the Fundamental Research Funds for the Central Universities(11604322)the Key Programs of the Natural Science Foundation of Heilongjiang Province of China(ZD201415).
文摘Are quantum states real? This most fundamental question in quantum mechanics has not yet been satisfactorily resolved, although its realistic interpretation seems to have been rejected by various delayedchoice experiments. Here, to address this long-standing issue, we present a quantum twisted double-slit experiment. By exploiting the subluminal feature of twisted photons, the real nature of a photon during its time in flight is revealed for the first time. We found that photons' arrival times were inconsistent with the states obtained in measurements but agreed with the states during propagation. Our results demonstrate that wavefunctions describe the realistic existence and evolution of quantum entities rather than a pure mathematical abstraction providing a probability list of measurement outcomes. This finding clarifies the long-held misunderstanding of the role of wavefunctions and their collapse in the evolution of quantum entities.
基金supported by the National Natural Science Foundation of China(Grant Nos.11073012,11078001 and 11003008)the Qing Lan Project(Jiangsu Province)the National Basic Research Program of China(Grant Nos.2013CB834103 and 2013CB834904)
文摘The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect.We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures.Using a two-dimensional area-preserving twist mapping as the model,we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit.We show how the stickiness effect and the orbital diffusion speed are related to the angle.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10902040, A020602)the Specialized Research Fund for the Doctoral Program of Higher Education(New Teachers)+2 种基金the Foundation for Distinguished Young Talents in Higher Education of Guangdong(Grant No. LYM08016)the Foundation for Outstanding Doctoral Dissertation of Guangdongthe Fundamental Research Funds for the Central Universities, South China University of Technology (Grant Nos.2009ZM0238,2009ZM0280)
文摘The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.
