Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber susp...Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.展开更多
Diverse spatial mode bases can be exploited in mode-division multiplexing(MDM)to sustain the capacity growth in fiber-optic communications,such as linearly polarized(LP)modes,vector modes,LP orbital angular momentum(L...Diverse spatial mode bases can be exploited in mode-division multiplexing(MDM)to sustain the capacity growth in fiber-optic communications,such as linearly polarized(LP)modes,vector modes,LP orbital angular momentum(LP-OAM)modes,and circularly polarized OAM(CP-OAM)modes.Nevertheless,which kind of mode bases is more appropriate to be utilized in fiber still remains unclear.Here,we aim to find the superior mode basis in MDM fiber-optic communications via a system-level comparison in air-core fiber(ACF).We first investigate the walk-off effect of four spatial mode bases over 1-km ACF,where LP and LP-OAM modes show intrinsic mode walk-off,while it is negligible for vector and CP-OAM modes.We then study the mode coupling effect of degenerate vector and CP-OAM modes over 1-km ACF under fiber perturbations,where degenerate even and odd vector modes suffer severe mode cross talk,while negligible for highorder degenerate CP-OAM modes based on the laws of angular momentum conservation.Moreover,we comprehensively evaluate the system-level performance for data-carrying single-channel and two-channel MDM transmission with different spatial mode bases under various kinds of fiber perturbations(bending,twisting,pressing,winding,and out-of-plane moving).The obtained results indicate that the CP-OAM mode basis shows superiority compared to other mode bases in MDM fiber-optic communications without using multiple-input multiple-output digital signal processing.Our findings may pave the way for robust shortreach MDM optical interconnects for data centers and high-performance computing.展开更多
We obtain exact spatial localized mode solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation with constant diffraction and cubic-quintic nonlinearity in PT-symmetric potential, and study the linear stab...We obtain exact spatial localized mode solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation with constant diffraction and cubic-quintic nonlinearity in PT-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and PT-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated.展开更多
Large span spatial lattice structures have many natural frequencies in a narrow frequency range, the conventional frequency domain method is difficult to contain all significant contribution modes. Through numerical e...Large span spatial lattice structures have many natural frequencies in a narrow frequency range, the conventional frequency domain method is difficult to contain all significant contribution modes. Through numerical examples, it is found that some high order modes are likely to be overlooked because of their higher positions of modal order, in spite of their significance to wind response. According to the contributions of modes to strain energy of system, the paper presented an efficient method to compensate the errors owing to missing out some significant high order modes. The effectiveness of the proposed method is verified through a numerical analysis of the wind responses of a spherical dome.展开更多
This paper aims to compare the results of two techniques of Kriging (Ordinary Kriging and Indicator Kriging) that are applied to estimate the Private Motorized (PM) travel mode use (car or motorcycle) in several geogr...This paper aims to compare the results of two techniques of Kriging (Ordinary Kriging and Indicator Kriging) that are applied to estimate the Private Motorized (PM) travel mode use (car or motorcycle) in several geographical coordinates of non-sampled values of the concerning variable. The data used was from the Origin/Destination and Public Transportation Opinion Survey, carried out in 2007/2008 at S?o Carlos (SP, Brazil). The techniques were applied in the region with 110 sample points (households). Initially, Decision Tree was applied to estimate the probability of mode choice in surveyed households, thus determining the numeric variable to be used in Ordinary Kriging. For application of Indicator Kriging it was used the variable “main travel mode” in a discrete manner, where “1” represented the use of PM travel mode and “0” characterized others travel modes. The results obtained by the two spatial estimation techniques were similar (Kriging maps and cross-validation procedure). However, the Indicator Kriging (KI) obtained the highest number of hit rates. In addition, with the KI it was possible to use the variable in its original form, avoiding error propagation. Finally, it was concluded that spatial statistics was thriving in travel demand forecasting issues, giving rise, for the both Kriging methods, to a travel mode choice surface on a confirmatory way.展开更多
The relationships between soil total nitrogen(STN)and influencing factors are scale-dependent.The objective of this study was to identify the multi-scale spatial relationships of STN with selected environmental factor...The relationships between soil total nitrogen(STN)and influencing factors are scale-dependent.The objective of this study was to identify the multi-scale spatial relationships of STN with selected environmental factors(elevation,slope and topographic wetness index),intrinsic soil factors(soil bulk density,sand content,silt content,and clay content)and combined environmental factors(including the first two principal components(PC1 and PC2)of the Vis-NIR soil spectra)along three sampling transects located at the upstream,midstream and downstream of Taiyuan Basin on the Chinese Loess Plateau.We separated the multivariate data series of STN and influencing factors at each transect into six intrinsic mode functions(IMFs)and one residue by multivariate empirical mode decomposition(MEMD).Meanwhile,we obtained the predicted equations of STN based on MEMD by stepwise multiple linear regression(SMLR).The results indicated that the dominant scales of explained variance in STN were at scale 995 m for transect 1,at scales 956 and 8852 m for transect 2,and at scales 972,5716 and 12,317 m for transect 3.Multi-scale correlation coefficients between STN and influencing factors were less significant in transect 3 than in transects 1 and 2.The goodness of fit root mean square error(RMSE),normalized root mean square error(NRMSE),and coefficient of determination(R2)indicated that the prediction of STN at the sampling scale by summing all of the predicted IMFs and residue was more accurate than that by SMLR directly.Therefore,the multi-scale method of MEMD has a good potential in characterizing the multi-scale spatial relationships between STN and influencing factors at the basin landscape scale.展开更多
Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of th...Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to an Nth-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.展开更多
In this article,it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small,but crucial error.
基金Foundation item: the National Natural Science Foundation of China for Outstanding Young Sci-entists (19925210)
文摘Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.
基金supported by the National Natural Science Foundation of China(Grant Nos.62125503 and 62261160388)the National Key R&D Program of China(Grant No.2019YFB2203604)+2 种基金the Key R&D Program of Hubei Province of China(Grant Nos.2020BAB001 and 2021BAA024)the Shenzhen Science and Technology Program(Grant No.JCYJ20200109114018750)the Innovation Project of Optics Valley Laboratory(Grant No.OVL2021BG004)。
文摘Diverse spatial mode bases can be exploited in mode-division multiplexing(MDM)to sustain the capacity growth in fiber-optic communications,such as linearly polarized(LP)modes,vector modes,LP orbital angular momentum(LP-OAM)modes,and circularly polarized OAM(CP-OAM)modes.Nevertheless,which kind of mode bases is more appropriate to be utilized in fiber still remains unclear.Here,we aim to find the superior mode basis in MDM fiber-optic communications via a system-level comparison in air-core fiber(ACF).We first investigate the walk-off effect of four spatial mode bases over 1-km ACF,where LP and LP-OAM modes show intrinsic mode walk-off,while it is negligible for vector and CP-OAM modes.We then study the mode coupling effect of degenerate vector and CP-OAM modes over 1-km ACF under fiber perturbations,where degenerate even and odd vector modes suffer severe mode cross talk,while negligible for highorder degenerate CP-OAM modes based on the laws of angular momentum conservation.Moreover,we comprehensively evaluate the system-level performance for data-carrying single-channel and two-channel MDM transmission with different spatial mode bases under various kinds of fiber perturbations(bending,twisting,pressing,winding,and out-of-plane moving).The obtained results indicate that the CP-OAM mode basis shows superiority compared to other mode bases in MDM fiber-optic communications without using multiple-input multiple-output digital signal processing.Our findings may pave the way for robust shortreach MDM optical interconnects for data centers and high-performance computing.
基金Supported by the Project of Technology Office in Zhejiang Province under Grant No.2014C32006the Special Foundation for theoretical physics Research Program of China under Grant No.11447124+1 种基金National Natural Science Foundation of China under Grant No.11374254the Higher School Visiting Scholar Development under Grant No.FX2013103
文摘We obtain exact spatial localized mode solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation with constant diffraction and cubic-quintic nonlinearity in PT-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and PT-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated.
文摘Large span spatial lattice structures have many natural frequencies in a narrow frequency range, the conventional frequency domain method is difficult to contain all significant contribution modes. Through numerical examples, it is found that some high order modes are likely to be overlooked because of their higher positions of modal order, in spite of their significance to wind response. According to the contributions of modes to strain energy of system, the paper presented an efficient method to compensate the errors owing to missing out some significant high order modes. The effectiveness of the proposed method is verified through a numerical analysis of the wind responses of a spherical dome.
文摘This paper aims to compare the results of two techniques of Kriging (Ordinary Kriging and Indicator Kriging) that are applied to estimate the Private Motorized (PM) travel mode use (car or motorcycle) in several geographical coordinates of non-sampled values of the concerning variable. The data used was from the Origin/Destination and Public Transportation Opinion Survey, carried out in 2007/2008 at S?o Carlos (SP, Brazil). The techniques were applied in the region with 110 sample points (households). Initially, Decision Tree was applied to estimate the probability of mode choice in surveyed households, thus determining the numeric variable to be used in Ordinary Kriging. For application of Indicator Kriging it was used the variable “main travel mode” in a discrete manner, where “1” represented the use of PM travel mode and “0” characterized others travel modes. The results obtained by the two spatial estimation techniques were similar (Kriging maps and cross-validation procedure). However, the Indicator Kriging (KI) obtained the highest number of hit rates. In addition, with the KI it was possible to use the variable in its original form, avoiding error propagation. Finally, it was concluded that spatial statistics was thriving in travel demand forecasting issues, giving rise, for the both Kriging methods, to a travel mode choice surface on a confirmatory way.
基金financially supported by the Research Project of Shanxi Scholarship Council of China (2017– 075)the Natural Science foundation for Young Scientists of Shanxi Province (201801D221103)the Innovation Grant of Shanxi Agricultural University (2017ZZ07)
文摘The relationships between soil total nitrogen(STN)and influencing factors are scale-dependent.The objective of this study was to identify the multi-scale spatial relationships of STN with selected environmental factors(elevation,slope and topographic wetness index),intrinsic soil factors(soil bulk density,sand content,silt content,and clay content)and combined environmental factors(including the first two principal components(PC1 and PC2)of the Vis-NIR soil spectra)along three sampling transects located at the upstream,midstream and downstream of Taiyuan Basin on the Chinese Loess Plateau.We separated the multivariate data series of STN and influencing factors at each transect into six intrinsic mode functions(IMFs)and one residue by multivariate empirical mode decomposition(MEMD).Meanwhile,we obtained the predicted equations of STN based on MEMD by stepwise multiple linear regression(SMLR).The results indicated that the dominant scales of explained variance in STN were at scale 995 m for transect 1,at scales 956 and 8852 m for transect 2,and at scales 972,5716 and 12,317 m for transect 3.Multi-scale correlation coefficients between STN and influencing factors were less significant in transect 3 than in transects 1 and 2.The goodness of fit root mean square error(RMSE),normalized root mean square error(NRMSE),and coefficient of determination(R2)indicated that the prediction of STN at the sampling scale by summing all of the predicted IMFs and residue was more accurate than that by SMLR directly.Therefore,the multi-scale method of MEMD has a good potential in characterizing the multi-scale spatial relationships between STN and influencing factors at the basin landscape scale.
基金supported by the National Natural Science Foundation of China(Nos.1133200711202147+2 种基金and 9216111)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120032120007)the Open Fund from State Key Laboratory of Aerodynamics(Nos.SKLA201201 and SKLA201301)
文摘Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to an Nth-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.
文摘In this article,it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small,but crucial error.
