Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high v...Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.展开更多
In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks, Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generat...In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks, Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generate when the hysteretic behavior of couplings in the shaft systems is considered. In this paper, the intrinsic multiple-scale harmonic balance method is extended to the nonlinear autonomous system with the non-analytic property, and the dynamic complexities of the system near the Hopf bifurcation point are analyzed.展开更多
Background:The habitat resources are structured across different spatial scales in the environment,and thus animals perceive and select habitat resources at different spatial scales.Failure to adopt the scale-dependen...Background:The habitat resources are structured across different spatial scales in the environment,and thus animals perceive and select habitat resources at different spatial scales.Failure to adopt the scale-dependent framework in species habitat relationships may lead to biased inferences.Multi-scale species distribution models(SDMs)can thus improve the predictive ability as compared to single-scale approaches.This study outlines the importance of multi-scale modeling in assessing the species habitat relationships and may provide a methodological framework using a robust algorithm to model and predict habitat suitability maps(HSMs)for similar multi-species and multi-scale studies.Results:We used a supervised machine learning algorithm,random forest(RF),to assess the habitat relationships of Asiatic wildcat(Felis lybica ornata),jungle cat(Felis chaus),Indian fox(Vulpes bengalensis),and golden-jackal(Canis aureus)at ten spatial scales(500-5000 m)in human-dominated landscapes.We calculated out-of-bag(OOB)error rates of each predictor variable across ten scales to select the most influential spatial scale variables.The scale optimization(OOB rates)indicated that model performance was associated with variables at multiple spatial scales.The species occurrence tended to be related strongest to predictor variables at broader scales(5000 m).Multivariate RF models indicated landscape composition to be strong predictors of the Asiatic wildcat,jungle cat,and Indian fox occurrences.At the same time,topographic and climatic variables were the most important predictors determining the golden jackal distribution.Our models predicted range expansion in all four species under future climatic scenarios.Conclusions:Our results highlight the importance of using multiscale distribution models when predicting the distribution and species habitat relationships.The wide adaptability of meso-carnivores allows them to persist in human-dominated regions and may even thrive in disturbed habitats.These meso-carnivores are among the few spe展开更多
The aim of this paper is to propose a fast meshless numerical scheme for the simulation of non-linear Schrodinger equations.In the proposed scheme,the implicit-Euler scheme is used for the temporal discretization and ...The aim of this paper is to propose a fast meshless numerical scheme for the simulation of non-linear Schrodinger equations.In the proposed scheme,the implicit-Euler scheme is used for the temporal discretization and the localized method of approximate particular solution(LMAPS)is utilized for the spatial discretization.The multiple-scale technique is introduced to obtain the shape parameters of the multiquadric radial basis function for 2D problems and the Gaussian radial basis function for 3D problems.Six numerical examples are carried out to verify the accuracy and efficiency of the proposed scheme.Compared with well-known techniques,numerical results illustrate that the proposed scheme is of merits being easy-to-program,high accuracy,and rapid convergence even for long-term problems.These results also indicate that the proposed scheme has great potential in large scale problems and real-world applications.展开更多
Soil water-retention characteristics at measurement scales are generally different from those at application scales, and there is scale disparity between them and soil physical properties. The relationships between tw...Soil water-retention characteristics at measurement scales are generally different from those at application scales, and there is scale disparity between them and soil physical properties. The relationships between two water-retention parameters, the scaling parameter related to the inverse of the air-entry pressure （avG, cm- 1） and the curve shape factor related to soil pore-size distribution （n） of the van Genuchten water-retention equation, and soil texture （sand, silt, and clay contents） were examined at multiple scales. One hundred twenty-eight undisturbed soil samples were collected from a 640-m transect located in Fuxin, China. Soil water-retention curves were measured and the van Genuchten parameters were obtained by curve fitting. The relationships between the two parameters and soil texture at the observed scale and at multiple scales were evaluated using Pearson correlation and joint multifractal analyses, respectively. The results of Pearson correlation analysis showed that the parameter c^vG was significantly correlated with sand, silt, and clay contents at the observed scale. Joint multifractal analyses, however, indicated that the parameter ~vG was not correlated with silt and sand contents at multiple scales. The parameter n was positively correlated with clay content at multiple scales. Sand content was significantly correlated with the parameter n at the observed scale but not at multiple scales. Clay contents were strongly correlated to both water-retention parameters because clay content was relatively low in the soil studied, indicating that water retention was dominated by clay content in the field of this study at all scales. These suggested that multiple-scale analyses were necessary to fully grasp the spatial variability of soil water-retention characteristics.展开更多
The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into a...The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then,the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.展开更多
Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark...Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.展开更多
A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multi...A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multiple-scale method. Our results show that the granular chain model can support an asymmetric high-order envelope soliton under the certain condition. It is found that the second-harmonic term of this high-order envelope soliton has an additional phase. In addition, the influence of both the material parameter and the static load on the localized features of the high-order envelope soliton is discussed.展开更多
This paper describes a newly developednon-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum co...This paper describes a newly developednon-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model performs significantly better than the single-scale k-e model. The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.展开更多
The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings,...The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .展开更多
The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the act...The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic aonlineax equation of motion with damping is established by employing Hamilton＇s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve axe analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.展开更多
A deep-ocean mooring system was deployed 100 m away from an active hydrothermal vent over the Southwest Indian Ridge （SWIR）, where the water depth is about 2,800 m. One year of data on ocean temperature 50 m away fr...A deep-ocean mooring system was deployed 100 m away from an active hydrothermal vent over the Southwest Indian Ridge （SWIR）, where the water depth is about 2,800 m. One year of data on ocean temperature 50 m away from the ocean floor and on velocities at four levels （44 m, 40 m, 36 m, and 32 m away from the ocean floor） were collected by the mooring system. Multiple- scale variations were extracted from these data： seasonal, tidal, super-tidal, and eddy scales. The semidiumal tide was the strongest tidal signal among all the tidal constituents in both currents and temperature. With the multiple-scale variation presented in the data, a new method was developed to decompose the data into five parts in terms of temporal scales： time-mean, seasonal, tidal, super-tidal, and eddy. It was shown that both eddy and tidal heat （momentum） fluxes were characterized by variation in the bottom topography： the tidal fluxes of heat and momentum in the along-isobath direction were much stronger than those in the cross-isobath direction. For the heat flux, eddy heat flux was stronger than tidal heat flux in the cross-isobath direction, while eddy heat flux was weaker in the along-isobath direction. For the momentum flux, the eddy momentum flux was weaker than tidal momentum flux in both directions. The eddy momen^m fluxes at the four levels had a good relationship with the magnitude of mean currents： it increased with the mean current in an exponential relationship.展开更多
By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensa...By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.展开更多
We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple...We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectr展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.12002089)the Science and Technology Projects in Guangzhou(Grant No.2023A04J1323)UKRI Horizon Europe Guarantee(Grant No.EP/Y016130/1)。
文摘Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.
基金The project supported by the National Natural Science Foundation of China(as a key project)the State Education Committee Pre-research Foundation.
文摘In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks, Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generate when the hysteretic behavior of couplings in the shaft systems is considered. In this paper, the intrinsic multiple-scale harmonic balance method is extended to the nonlinear autonomous system with the non-analytic property, and the dynamic complexities of the system near the Hopf bifurcation point are analyzed.
基金The study had no central budget.The field assistance,including accommodation,vehicle,and field assistants were facilitated by a local NGO(The Corbett Foundation).
文摘Background:The habitat resources are structured across different spatial scales in the environment,and thus animals perceive and select habitat resources at different spatial scales.Failure to adopt the scale-dependent framework in species habitat relationships may lead to biased inferences.Multi-scale species distribution models(SDMs)can thus improve the predictive ability as compared to single-scale approaches.This study outlines the importance of multi-scale modeling in assessing the species habitat relationships and may provide a methodological framework using a robust algorithm to model and predict habitat suitability maps(HSMs)for similar multi-species and multi-scale studies.Results:We used a supervised machine learning algorithm,random forest(RF),to assess the habitat relationships of Asiatic wildcat(Felis lybica ornata),jungle cat(Felis chaus),Indian fox(Vulpes bengalensis),and golden-jackal(Canis aureus)at ten spatial scales(500-5000 m)in human-dominated landscapes.We calculated out-of-bag(OOB)error rates of each predictor variable across ten scales to select the most influential spatial scale variables.The scale optimization(OOB rates)indicated that model performance was associated with variables at multiple spatial scales.The species occurrence tended to be related strongest to predictor variables at broader scales(5000 m).Multivariate RF models indicated landscape composition to be strong predictors of the Asiatic wildcat,jungle cat,and Indian fox occurrences.At the same time,topographic and climatic variables were the most important predictors determining the golden jackal distribution.Our models predicted range expansion in all four species under future climatic scenarios.Conclusions:Our results highlight the importance of using multiscale distribution models when predicting the distribution and species habitat relationships.The wide adaptability of meso-carnivores allows them to persist in human-dominated regions and may even thrive in disturbed habitats.These meso-carnivores are among the few spe
基金The authors thank the editor and anonymous reviewers for their constructive comments on the manuscript.The research of the authors was supported by the Natural Science Foundation of Jiangsu Province(No.BK20150795)the Fundamental Research Funds for the Central Universities(No.2018B16714)+3 种基金the National Natural Science Foundation of China(Nos.11702083,51679150,51579153,51739008,51527811)the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0218G01)the National Key R&D Program of China(No.2016YFC0401902)the Fund Project of NHRI(Nos.Y417002,Y417015).
文摘The aim of this paper is to propose a fast meshless numerical scheme for the simulation of non-linear Schrodinger equations.In the proposed scheme,the implicit-Euler scheme is used for the temporal discretization and the localized method of approximate particular solution(LMAPS)is utilized for the spatial discretization.The multiple-scale technique is introduced to obtain the shape parameters of the multiquadric radial basis function for 2D problems and the Gaussian radial basis function for 3D problems.Six numerical examples are carried out to verify the accuracy and efficiency of the proposed scheme.Compared with well-known techniques,numerical results illustrate that the proposed scheme is of merits being easy-to-program,high accuracy,and rapid convergence even for long-term problems.These results also indicate that the proposed scheme has great potential in large scale problems and real-world applications.
基金Supported by the National Key Technology R&D Program in the 11th Five-Year Plan of China (Nos.2008BADA4B03 and 2009BADB3B07)
文摘Soil water-retention characteristics at measurement scales are generally different from those at application scales, and there is scale disparity between them and soil physical properties. The relationships between two water-retention parameters, the scaling parameter related to the inverse of the air-entry pressure （avG, cm- 1） and the curve shape factor related to soil pore-size distribution （n） of the van Genuchten water-retention equation, and soil texture （sand, silt, and clay contents） were examined at multiple scales. One hundred twenty-eight undisturbed soil samples were collected from a 640-m transect located in Fuxin, China. Soil water-retention curves were measured and the van Genuchten parameters were obtained by curve fitting. The relationships between the two parameters and soil texture at the observed scale and at multiple scales were evaluated using Pearson correlation and joint multifractal analyses, respectively. The results of Pearson correlation analysis showed that the parameter c^vG was significantly correlated with sand, silt, and clay contents at the observed scale. Joint multifractal analyses, however, indicated that the parameter ~vG was not correlated with silt and sand contents at multiple scales. The parameter n was positively correlated with clay content at multiple scales. Sand content was significantly correlated with the parameter n at the observed scale but not at multiple scales. Clay contents were strongly correlated to both water-retention parameters because clay content was relatively low in the soil studied, indicating that water retention was dominated by clay content in the field of this study at all scales. These suggested that multiple-scale analyses were necessary to fully grasp the spatial variability of soil water-retention characteristics.
基金Project supported by the National Natural Science Foundation of China(No.11672071)the Fundamental Research Funds for the Central Universities(No.N170504023)
文摘The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then,the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.
基金The project supported by National Natural Science Foundation of China under Grant No. 10674113, Foundation of New Century Excellent Talent under Grant No. NCET-060707, Natural Science Foundation of Hunan Province of China under Grant No. 06JJ50006, the Scientific Research Foundation of Education Bureau of Hunan Province of China under Grant Nos. 02C573 and 04A058
文摘Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.
基金Supported by the National Natural Science Foundation of China under Grant Nos.1604121 and 11464012
文摘A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multiple-scale method. Our results show that the granular chain model can support an asymmetric high-order envelope soliton under the certain condition. It is found that the second-harmonic term of this high-order envelope soliton has an additional phase. In addition, the influence of both the material parameter and the static load on the localized features of the high-order envelope soliton is discussed.
文摘This paper describes a newly developednon-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model performs significantly better than the single-scale k-e model. The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.
文摘The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .
基金Project supported by the National Natural Science Foundation of China (Nos. 11172084, 10672017,and 50935002)
文摘The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic aonlineax equation of motion with damping is established by employing Hamilton＇s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve axe analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.
基金The data used in this paper are from Chinese DY115- 21 cruise. We thank all the staff for their hard work, especially our colleague Tao Ding, who brought back the mooring system successfully and acquired these invaluable observational data. We express our sincere gratitude to Weifang Jin and Tao Ding, for their help during the early-stage data processing. This study was support by the National Basic Research Program of China on hydrothermal plume characteristics and environmental effects （No. 2012CB417303）, the project of global change and interaction between ocean and atmosphere （GASI-03-01-01-07）. CD appreciates the support from the National Natural Science Foundation of China （Grant Nos. 41376033, 41476022, and 41490640）, and the NUIST startup grants. We appreciate Jian Zhu＇s help to make Figure 1.
文摘A deep-ocean mooring system was deployed 100 m away from an active hydrothermal vent over the Southwest Indian Ridge （SWIR）, where the water depth is about 2,800 m. One year of data on ocean temperature 50 m away from the ocean floor and on velocities at four levels （44 m, 40 m, 36 m, and 32 m away from the ocean floor） were collected by the mooring system. Multiple- scale variations were extracted from these data： seasonal, tidal, super-tidal, and eddy scales. The semidiumal tide was the strongest tidal signal among all the tidal constituents in both currents and temperature. With the multiple-scale variation presented in the data, a new method was developed to decompose the data into five parts in terms of temporal scales： time-mean, seasonal, tidal, super-tidal, and eddy. It was shown that both eddy and tidal heat （momentum） fluxes were characterized by variation in the bottom topography： the tidal fluxes of heat and momentum in the along-isobath direction were much stronger than those in the cross-isobath direction. For the heat flux, eddy heat flux was stronger than tidal heat flux in the cross-isobath direction, while eddy heat flux was weaker in the along-isobath direction. For the momentum flux, the eddy momentum flux was weaker than tidal momentum flux in both directions. The eddy momen^m fluxes at the four levels had a good relationship with the magnitude of mean currents： it increased with the mean current in an exponential relationship.
基金Project supported by the National Natural Science Foundation of China (Grant No 10875098)the Science Foundation of the Northwest Normal University (Grant Nos NWNU-KJCXGC-03-17 and NWNU-KJCXGC-03-48)
文摘By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.
文摘We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectr
