Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by ErGp(+i)(r-1) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r-1 of Sr...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by ErGp(+i)(r-1) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r-1 of Sr, while the i-th vertex of each component of (r-1)G be adjacented to r-1 vertices of degree 1 of Sr, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs ErGp(+i)(r-1) (r-1)K1 (1 ≤ i ≤ p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of fini...The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configu- rations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain criticM value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.展开更多
In concentrically rotating double cylinders consisting of a stationary outer cylinder a rotating inner cylinder, Taylor vortex flow appears. Taylor vortex flow occurs in journal bearings, various fluid machineries, co...In concentrically rotating double cylinders consisting of a stationary outer cylinder a rotating inner cylinder, Taylor vortex flow appears. Taylor vortex flow occurs in journal bearings, various fluid machineries, containers for chemical reaction, and other rotating components. Therefore, the analysis of the flow structure of Taylor vortex flow is highly effective for its control. The main parameters that determine the modes of Taylor vortex flow of a finite length are the aspect ratio, Reynolds number Re. Aspect ratio is defined as the ratio of the cylinder length to the gap length between cylinders, and Re is determined on the basis of the angular speed of the inner cylinder. Aspect ratio was set to be 4.0, and Re to be values in the range from 100 to 1000 at intervals of 100. Thus far, a large number of studies on Taylor vortex flow have been carried out;however, the effects of the differences in initial conditions have not yet been sufficiently clarified. In this study, we changed the acceleration time of the inner cylinder in a numerical analysis, and examined the resulting changes in the mode formation and bifurcation processes. The acceleration time was changed from 1.0 s to 10.0 s. As a result, a difference was observed in the final mode depending on the difference in the acceleration time. From this finding, non-uniqueness, which is a major characteristic of Taylor vortex flow, was confirmed. However, no regularities regarding the difference in mode formation were found and the tendency of the mode formation process was not specified. Moreover, the processes of developing the vortex resulting in different final modes were monitored over time by visual observation. Similar flow behaviors were initially observed after the start of the calculation. Then, a bifurcation point, at which the flow changed to a mode depending on the acceleration time observed, and finally the flow became steady. In addition, there was also a difference in the time taken for the well-developed flow to reach the steady state. Both EFD (Experimental Fluid Dynamics) and CFD (Computational Fluid Dynamics) results show good agreement qualitatively.展开更多
Metasurface-based polarimetry techniques have attracted lots of interests and been extensively studied in the past years,but are still hampered by narrow operating bandwidth and large crosstalk.Recently,Xian-Gang Luo&...Metasurface-based polarimetry techniques have attracted lots of interests and been extensively studied in the past years,but are still hampered by narrow operating bandwidth and large crosstalk.Recently,Xian-Gang Luo's group proposed a new method of polarization-dependent phase optimization for the design of crosstalk-free,broadband achromatic,and full Stokes imaging polarimeter,which offers a promising platform for a wide range of applications including bio-photonics and integrated optics.展开更多
Metalenses,which may effectively manipulate the wavefront of incident light,have been proposed and extensively utilized in the development of various planar optical devices for specialized purposes.However,similar to ...Metalenses,which may effectively manipulate the wavefront of incident light,have been proposed and extensively utilized in the development of various planar optical devices for specialized purposes.However,similar to traditional lenses,the metalens suffers from chromatic aberration problems due to the significant phase dispersion in each unit structure and the limited operational bandwidth.To mitigate the impact of chromatic aberration,we integrate a phase compensation approach with a novel utilization of a phase shift function to define the adjusted phase criterion satisfied by each α-Si resonance unit.This approach may lead to development of an innovative optical tweezer known as an achromatic optical vortex metalens(AOVM),offering reliable focusing capabilities across the 1300 nm and 1600 nm incident light range.Numerical simulations are conducted to investigate the optical properties of 200 nm diameter SiO_(2) particles at the focal plane of the AOVM.The trapping ability of the AOVM is successfully validated,exhibiting favorable characteristics including constant optical force,stable kinematic state of trapped particles,and consistent capture positions,surpassing those of the optical vortex metalens.展开更多
Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a ...Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a dilemma arises in that conspicuous colors may not only attract mates,but also alert predators.The"private channels of communication"hypothesis proposes that some intraspecific signals may not be visible to heterospecific animals because of different visual systems.To better understand the evolution of plumage colors and sexual selection in birds,here we studied the chromatic difference and achromatic differences of melanin-and carotenoid-based plumage coloration in five minivet species(Pericrocotus spp.)under conspecific and predator visual systems.We found that either the chromatic or achromatic difference among male or female minivets’plumage was consistently higher under conspecific vision than under predator vision for all five studied species of minivets.This result indicated that individual differences in plumage colors of minivets were visible to the conspecific receivers and hidden from potential predators as a result of evolution under predation risk and conspecific communication.However,males were under a higher risk of predation because they were more conspicuous than females to the vision of a nocturnal predator.展开更多
Strip-shaped chromatic aberration defects on the surface of an electro-galvanized fingerprint-resistant sheet were systematically studied using Thermo-Calc thermodynamic calculations,scanning electron microscope and X...Strip-shaped chromatic aberration defects on the surface of an electro-galvanized fingerprint-resistant sheet were systematically studied using Thermo-Calc thermodynamic calculations,scanning electron microscope and X-ray diffractometer analyses,and rapid heat treatment simulation technology.The formation mechanism of these defects was also analyzed.The results show a strong correlation between the defects and the uneven distribution of the Fe(001)component on the surface of the steel substrate.The relatively high proportion of Fe(001)components on the surface of the steel substrate affects the distribution density of the Zn crystal cells in different orientations during the electrodeposition process,which causes the reflection intensity of the light of the galvanized layer to differ from various visual perspectives,and macroscopic strip-shaped chromatic aberration defects are finally formed.The high proportion of the Fe(001)component on the surface of the steel substrate is mainly related to the following two factors.First,when the strip steel is hot-rolled,the finishing hot-rolling temperature is close to theγ→αphase transition temperature.When the local temperature on the upper surface of the strip steel is low,γ+αtwo-phase rolling easily occurs,and this results in an uneven stress distribution between theγandαphases after the hot-rolling process.This uneven distribution of hot-rolling stress results in the formation of a coarse grain structure in the local area on the surface of the hot-rolled sheet,which strongly affects the subsequent cold rolling and annealing process,and the annealed steel sheet substrate ultimately contains a greater proportion of the Fe(001)component.And second,a fast cooling rate(>10 K/s)during the slow cooling stage in the continuous annealing process inhibits the transformation of the Fe(001)to the Fe(111)component on the surface of the cold-rolled steel sheet,and it is then not possible to effectively eliminate the influence of the unevenly distributed Fe(001)component on the surface of the annealed steel sheet(originating from the uneven hot-rolled microstructure).This uneven distribution of the Fe(001)component on the surface of the annealed steel sheet following the continuous annealing heat treatment has a strong effect on the electrodeposition behavior of the Zn crystal cell in the subsequent electroplating process and the formation of macroscopic strip-shaped chromatic aberration defects on the surface of electro-galvanized fingerprint-resistant sheet.展开更多
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by ErGp(+i)(r-1) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r-1 of Sr, while the i-th vertex of each component of (r-1)G be adjacented to r-1 vertices of degree 1 of Sr, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs ErGp(+i)(r-1) (r-1)K1 (1 ≤ i ≤ p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
基金supported by the National Natural Science Foundation of China(No.10772104)the Shanghai Leading Academic Discipline Project(No.S30106)
文摘The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configu- rations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain criticM value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.
文摘In concentrically rotating double cylinders consisting of a stationary outer cylinder a rotating inner cylinder, Taylor vortex flow appears. Taylor vortex flow occurs in journal bearings, various fluid machineries, containers for chemical reaction, and other rotating components. Therefore, the analysis of the flow structure of Taylor vortex flow is highly effective for its control. The main parameters that determine the modes of Taylor vortex flow of a finite length are the aspect ratio, Reynolds number Re. Aspect ratio is defined as the ratio of the cylinder length to the gap length between cylinders, and Re is determined on the basis of the angular speed of the inner cylinder. Aspect ratio was set to be 4.0, and Re to be values in the range from 100 to 1000 at intervals of 100. Thus far, a large number of studies on Taylor vortex flow have been carried out;however, the effects of the differences in initial conditions have not yet been sufficiently clarified. In this study, we changed the acceleration time of the inner cylinder in a numerical analysis, and examined the resulting changes in the mode formation and bifurcation processes. The acceleration time was changed from 1.0 s to 10.0 s. As a result, a difference was observed in the final mode depending on the difference in the acceleration time. From this finding, non-uniqueness, which is a major characteristic of Taylor vortex flow, was confirmed. However, no regularities regarding the difference in mode formation were found and the tendency of the mode formation process was not specified. Moreover, the processes of developing the vortex resulting in different final modes were monitored over time by visual observation. Similar flow behaviors were initially observed after the start of the calculation. Then, a bifurcation point, at which the flow changed to a mode depending on the acceleration time observed, and finally the flow became steady. In addition, there was also a difference in the time taken for the well-developed flow to reach the steady state. Both EFD (Experimental Fluid Dynamics) and CFD (Computational Fluid Dynamics) results show good agreement qualitatively.
文摘Metasurface-based polarimetry techniques have attracted lots of interests and been extensively studied in the past years,but are still hampered by narrow operating bandwidth and large crosstalk.Recently,Xian-Gang Luo's group proposed a new method of polarization-dependent phase optimization for the design of crosstalk-free,broadband achromatic,and full Stokes imaging polarimeter,which offers a promising platform for a wide range of applications including bio-photonics and integrated optics.
基金supported by the National Natural Science Foundation of China(Grant Nos.62275269,60907003,61805278,61875168,and 22134005)the Chongqing Talents Program for Outstanding Scientists(Grant No.cstc2021ycjh-bgzxm0178)。
文摘Metalenses,which may effectively manipulate the wavefront of incident light,have been proposed and extensively utilized in the development of various planar optical devices for specialized purposes.However,similar to traditional lenses,the metalens suffers from chromatic aberration problems due to the significant phase dispersion in each unit structure and the limited operational bandwidth.To mitigate the impact of chromatic aberration,we integrate a phase compensation approach with a novel utilization of a phase shift function to define the adjusted phase criterion satisfied by each α-Si resonance unit.This approach may lead to development of an innovative optical tweezer known as an achromatic optical vortex metalens(AOVM),offering reliable focusing capabilities across the 1300 nm and 1600 nm incident light range.Numerical simulations are conducted to investigate the optical properties of 200 nm diameter SiO_(2) particles at the focal plane of the AOVM.The trapping ability of the AOVM is successfully validated,exhibiting favorable characteristics including constant optical force,stable kinematic state of trapped particles,and consistent capture positions,surpassing those of the optical vortex metalens.
基金supported by the National Natural Science Foundation of China(32260127)the Education Department of Hainan Province(HnjgY2022-12)+1 种基金the Hainan Provincial Natural Science Foundation of China(320CXTD437)the Hainan Provincial Innovative Research Program for Graduates(Qhys2022-241)。
文摘Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a dilemma arises in that conspicuous colors may not only attract mates,but also alert predators.The"private channels of communication"hypothesis proposes that some intraspecific signals may not be visible to heterospecific animals because of different visual systems.To better understand the evolution of plumage colors and sexual selection in birds,here we studied the chromatic difference and achromatic differences of melanin-and carotenoid-based plumage coloration in five minivet species(Pericrocotus spp.)under conspecific and predator visual systems.We found that either the chromatic or achromatic difference among male or female minivets’plumage was consistently higher under conspecific vision than under predator vision for all five studied species of minivets.This result indicated that individual differences in plumage colors of minivets were visible to the conspecific receivers and hidden from potential predators as a result of evolution under predation risk and conspecific communication.However,males were under a higher risk of predation because they were more conspicuous than females to the vision of a nocturnal predator.
文摘Strip-shaped chromatic aberration defects on the surface of an electro-galvanized fingerprint-resistant sheet were systematically studied using Thermo-Calc thermodynamic calculations,scanning electron microscope and X-ray diffractometer analyses,and rapid heat treatment simulation technology.The formation mechanism of these defects was also analyzed.The results show a strong correlation between the defects and the uneven distribution of the Fe(001)component on the surface of the steel substrate.The relatively high proportion of Fe(001)components on the surface of the steel substrate affects the distribution density of the Zn crystal cells in different orientations during the electrodeposition process,which causes the reflection intensity of the light of the galvanized layer to differ from various visual perspectives,and macroscopic strip-shaped chromatic aberration defects are finally formed.The high proportion of the Fe(001)component on the surface of the steel substrate is mainly related to the following two factors.First,when the strip steel is hot-rolled,the finishing hot-rolling temperature is close to theγ→αphase transition temperature.When the local temperature on the upper surface of the strip steel is low,γ+αtwo-phase rolling easily occurs,and this results in an uneven stress distribution between theγandαphases after the hot-rolling process.This uneven distribution of hot-rolling stress results in the formation of a coarse grain structure in the local area on the surface of the hot-rolled sheet,which strongly affects the subsequent cold rolling and annealing process,and the annealed steel sheet substrate ultimately contains a greater proportion of the Fe(001)component.And second,a fast cooling rate(>10 K/s)during the slow cooling stage in the continuous annealing process inhibits the transformation of the Fe(001)to the Fe(111)component on the surface of the cold-rolled steel sheet,and it is then not possible to effectively eliminate the influence of the unevenly distributed Fe(001)component on the surface of the annealed steel sheet(originating from the uneven hot-rolled microstructure).This uneven distribution of the Fe(001)component on the surface of the annealed steel sheet following the continuous annealing heat treatment has a strong effect on the electrodeposition behavior of the Zn crystal cell in the subsequent electroplating process and the formation of macroscopic strip-shaped chromatic aberration defects on the surface of electro-galvanized fingerprint-resistant sheet.
