One-dimensional(1D)nanomaterials easily bend due to perturbations from their surroundings or their own behaviors.This phenomenon not only impacts the performances of various devices but has also been employed to devel...One-dimensional(1D)nanomaterials easily bend due to perturbations from their surroundings or their own behaviors.This phenomenon not only impacts the performances of various devices but has also been employed to develop a variety of new functional devices,in which the bending energies of the nanomaterials determine the device performances.However,measuring the energies of such nanomaterials is extremely difficult.Herein,pseudo-break imaging of 1D nanomaterials has been proposed and realized on individual carbon nanotubes(CNTs),in which a CNT appears to break and has a fracture but is actually intact.This imaging approach provides the values of the bending energies of the CNTs with an accuracy of 1–50 eV.Furthermore,this imaging approach can manipulate the bending shapes and energies of CNTs.This work presents a protocol for bending analysis and manipulation,which are vital to fundamental and applied studies of 1D nanomaterials.展开更多
采用高精度的拟谱方法,数值模拟了层结海洋中小振幅内行进波的演变和破碎过程.在演变过程中,导致内波破碎的PSI不稳定机制在共振相互作用中逐渐占据主导地位,能量从初级波向低频、高波数运动缓慢传递并形成一次级波包,随即破碎发生.破...采用高精度的拟谱方法,数值模拟了层结海洋中小振幅内行进波的演变和破碎过程.在演变过程中,导致内波破碎的PSI不稳定机制在共振相互作用中逐渐占据主导地位,能量从初级波向低频、高波数运动缓慢传递并形成一次级波包,随即破碎发生.破碎后产生的层化湍流引起的强烈混合以及湍流间歇性可从总能量和涡度峰度随时间的变化趋势看出.我们分析了层化湍流的一些统计特性,包括动能和有效位能沿垂向波数ky的功率谱.结果表明,动能和有效位能谱都存在一个谱段满足k-3y律,且分别可表示为0.1N4k-3y和0.2N4k-3y(N为Brunt V is l频率),通常称其为浮力子区.另外,我们分析了Cox数(湍流扩散系数与分子扩散系数之比),在层化湍流维持在一定强度时,计算结果和由海洋内区观测(远离内波强生成源和复杂地形)所推测的结论较为吻合.展开更多
The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is te...The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.展开更多
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the...Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.展开更多
The effect of the waving bed on the surface wave was investigated. The wave equation was reduced from the potential flow theory with the perturbation technique, and then was solved by using the pseudo-spectral method....The effect of the waving bed on the surface wave was investigated. The wave equation was reduced from the potential flow theory with the perturbation technique, and then was solved by using the pseudo-spectral method. The waterfall of the surface wave was simulated with the Matlab. It is shown that for the waving bed, an additional harmonic wave appears on the surface together with the solitary wave existing for the non-waving bed, and two kinds of waves do not interfere with each other. With the development of time, the waveform for the waving bed is kept invariable, and just the amplitude is reduced gradually. Wave-breaking phenomenon for the non-waving bed does not appear, so the waving bed seems useful to prevent the breaking of the wave.展开更多
基金the National Natural Science Foundation of China(Nos.51971157 and 12102307)Shenzhen Science and Technology Program(Nos.JCYJ20210324115412035 and ZDSYS20210813095534001)+1 种基金Tianjin Science Fund for Distinguished Young Scholars(No.19JCJQJC61800)the Natural Science Foundation of Hubei Province,China(No.2021CFB138).
文摘One-dimensional(1D)nanomaterials easily bend due to perturbations from their surroundings or their own behaviors.This phenomenon not only impacts the performances of various devices but has also been employed to develop a variety of new functional devices,in which the bending energies of the nanomaterials determine the device performances.However,measuring the energies of such nanomaterials is extremely difficult.Herein,pseudo-break imaging of 1D nanomaterials has been proposed and realized on individual carbon nanotubes(CNTs),in which a CNT appears to break and has a fracture but is actually intact.This imaging approach provides the values of the bending energies of the CNTs with an accuracy of 1–50 eV.Furthermore,this imaging approach can manipulate the bending shapes and energies of CNTs.This work presents a protocol for bending analysis and manipulation,which are vital to fundamental and applied studies of 1D nanomaterials.
文摘采用高精度的拟谱方法,数值模拟了层结海洋中小振幅内行进波的演变和破碎过程.在演变过程中,导致内波破碎的PSI不稳定机制在共振相互作用中逐渐占据主导地位,能量从初级波向低频、高波数运动缓慢传递并形成一次级波包,随即破碎发生.破碎后产生的层化湍流引起的强烈混合以及湍流间歇性可从总能量和涡度峰度随时间的变化趋势看出.我们分析了层化湍流的一些统计特性,包括动能和有效位能沿垂向波数ky的功率谱.结果表明,动能和有效位能谱都存在一个谱段满足k-3y律,且分别可表示为0.1N4k-3y和0.2N4k-3y(N为Brunt V is l频率),通常称其为浮力子区.另外,我们分析了Cox数(湍流扩散系数与分子扩散系数之比),在层化湍流维持在一定强度时,计算结果和由海洋内区观测(远离内波强生成源和复杂地形)所推测的结论较为吻合.
基金The National Nature Science Foundation of China under contract No.40706002the National High Technology Development Project of China under contract No.2007AA09Z122.
文摘The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.
基金supported by the National Natural Science Foundation of China (Grant No. 10671130)the Science Foundation of Shanghai Municipal Education Commission (Grant No. 05DZ07)+2 种基金Shanghai Leading Academic Discipline Project (Grant No. T0401)Leading Foundation of Shanghai Science and Technology Commission (Grant No. 06JC14092)the Foundation of the Scientific Computing Key Laboratory of Shang-hai Universities
文摘Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
基金Project supported by the National Nature Science Foundation of China (Grant No: 10272044), Research Fund for the Doctoral Program of Higher Education of China (Grant No: 20040079004) and the China Postdoctoral Science Foundation.
文摘The effect of the waving bed on the surface wave was investigated. The wave equation was reduced from the potential flow theory with the perturbation technique, and then was solved by using the pseudo-spectral method. The waterfall of the surface wave was simulated with the Matlab. It is shown that for the waving bed, an additional harmonic wave appears on the surface together with the solitary wave existing for the non-waving bed, and two kinds of waves do not interfere with each other. With the development of time, the waveform for the waving bed is kept invariable, and just the amplitude is reduced gradually. Wave-breaking phenomenon for the non-waving bed does not appear, so the waving bed seems useful to prevent the breaking of the wave.
