In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continent...Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea(19°35'N,112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors,and an acoustic Doppler current profiler(ADCP).We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories.Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width.Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries(KdV) theory than the first-order KdV model.These results indicate that the northwestern South China Sea(SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.展开更多
CMOS platforms with a high nonlinear figure of merit are highly sought after for high photonic quantum efficiencies, enabling functionalities not possible from purely linear effects and ease of integration with CMOS e...CMOS platforms with a high nonlinear figure of merit are highly sought after for high photonic quantum efficiencies, enabling functionalities not possible from purely linear effects and ease of integration with CMOS electronics. Silicon-based platforms have been prolific amongst the suite of advanced nonlinear optical signal processes demonstrated to date. These include crystalline silicon, amorphous silicon, Hydex glass, and stoichio- metric silicon nitride. Residing between stoichiometric silicon nitride and amorphous silicon in composition, silicon-rich nitride films of various formulations have emerged recently as promising nonlinear platforms for high nonlinear figure of merit nonlinear optics. Silicon-rich nitride films are compositionally engineered to create bandgaps that are sufficiently large to eliminate two-photon absorption at telecommunications wavelengths while enabling much larger nonlinear waveguide parameters （5x-500x） than those in stoichiometric silicon uitride. This paper reviews recent developments in the field of nonlinear optics using silicon-rich nitride platforms, as well as the outlook and future opportunities in this burgeoning field.展开更多
In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance （e,g., asymptotical stability） and reducing the control e...In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance （e,g., asymptotical stability） and reducing the control effort. By introducing a new reseating transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs all improved output-feedback controller. The output-feedback controller guarantees the globally asymptotieal stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and resealing transformation parameter are obtained to effectively reduce the control effort.展开更多
In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designe...In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system.展开更多
In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector fini...In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.展开更多
The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz ...The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz continuous state feedback.By using the finite-time Lyapunov stability theorem and the method of non-smooth feedback design,a recursive design procedure is provided,which guarantees the finite-time stability of the closed-loop system.The simulation results show the effectiveness of the theoretical results.展开更多
The all-optical wavelength conversion using cascaded four-wave mixing(FWM)phenomena with graphene oxide(GO)and a highly nonlinear fiber(HNLF)device is demonstrated experimentally.GO has a strong third-order nonlinear ...The all-optical wavelength conversion using cascaded four-wave mixing(FWM)phenomena with graphene oxide(GO)and a highly nonlinear fiber(HNLF)device is demonstrated experimentally.GO has a strong third-order nonlinear effect and is an excellent nonlinear optical material for nonlinear optical wavelength conversion.The group velocity matching of pump and signal,HNLF,and GO amplification promote the cascaded nonlinear frequency mixing process.From the experimental and analytical results,the maximum spacing between signal and pump is 21 nm,and specifically,the order of cascaded FWM light increases from order 1 to order 2 with increasing GO,and the first-order FWM conversion effi-ciency increases to a maximum of−14.5 dB.To the best of our knowledge,this is the first time that cascaded FWM-based all-optical wavelength conversion in HNLF-GO with wide wavelength selectivity is investigated with combined pump and signal light.Our findings not only provide an effective method for achieving all-optical wavelength conversion in cascaded FWM but also offer the possibility of fabricating high-performance nonlinear optical devices.展开更多
In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.W...In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).展开更多
High-frequency signals are pervasive in many science and engineering fields.In this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is d...High-frequency signals are pervasive in many science and engineering fields.In this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is derived by extending the inertial approximation for the direct separation of fast and slow motions.Based on this theory,a high-frequency force can induce various phase transitions of a system by changing its amplitude and frequency.Numerical simulations on several nonlinear oscillator systems show a very good agreement with the theoretic results.These findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.展开更多
By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients,...By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.展开更多
A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a G...A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.展开更多
High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of ...High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).展开更多
In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization...In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.展开更多
Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime.However, existing S-parameter based parameter retrieval approaches developed for linear metamaterials d...Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime.However, existing S-parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived.Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power,high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposed approach can be widely used in the research of active metamaterials.展开更多
According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by o...According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck-Kolmogorov （FPK） equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.展开更多
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences (No.KZCX1-YW-12)the National High Technology Research and Development Program of China (863 program) (No.2008AA09A401,No.2006AA09A109)
文摘Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea(19°35'N,112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors,and an acoustic Doppler current profiler(ADCP).We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories.Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width.Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries(KdV) theory than the first-order KdV model.These results indicate that the northwestern South China Sea(SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.
基金MOE Academic Research Fund Tier 2 GrantNational Research Foundation Competitive Research Grant+3 种基金National Research Foundation Land and Liveability National Innovation Challenge GrantSUTD-MIT International Design CenterTemasek Laboratories grantNational Research Foundation,Prime Minister’s Office,Singapore,under its Medium Sized Centre Program
文摘CMOS platforms with a high nonlinear figure of merit are highly sought after for high photonic quantum efficiencies, enabling functionalities not possible from purely linear effects and ease of integration with CMOS electronics. Silicon-based platforms have been prolific amongst the suite of advanced nonlinear optical signal processes demonstrated to date. These include crystalline silicon, amorphous silicon, Hydex glass, and stoichio- metric silicon nitride. Residing between stoichiometric silicon nitride and amorphous silicon in composition, silicon-rich nitride films of various formulations have emerged recently as promising nonlinear platforms for high nonlinear figure of merit nonlinear optics. Silicon-rich nitride films are compositionally engineered to create bandgaps that are sufficiently large to eliminate two-photon absorption at telecommunications wavelengths while enabling much larger nonlinear waveguide parameters （5x-500x） than those in stoichiometric silicon uitride. This paper reviews recent developments in the field of nonlinear optics using silicon-rich nitride platforms, as well as the outlook and future opportunities in this burgeoning field.
基金supported by National Natural Science Founda-tion of China (No. 60774010)Natural Science Foundation of JiangsuProvince, Jiangsu "Six Top Talents" (No. 07-A-020)+1 种基金Program for Fundamental Research of Natural Sciences in Universities of JiangsuProvince (No. 07KJB510114)Natural Science Foundation ofXuzhou Normal University (No. 08XLB20)
文摘In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance （e,g., asymptotical stability） and reducing the control effort. By introducing a new reseating transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs all improved output-feedback controller. The output-feedback controller guarantees the globally asymptotieal stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and resealing transformation parameter are obtained to effectively reduce the control effort.
基金Supported by National Natural Science Foundation of China（60774010 10971256） Natural Science Foundation of Jiangsu Province（BK2009083）+1 种基金 Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province（07KJB510114） Shandong Provincial Natural Science Foundation of China（ZR2009GM008 ZR2009AL014）
基金Supported by National Natural Science Foundation of China （60774010）, Program for New Century Excellent Talents in University of China （NCET-05-0607）, Program for Summit of Six Types of Talents of Jiangsu Province （07-A-020）, and Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
文摘适应州反馈的稳定为在的高顺序的随机的非线性的系统的一个类被调查函数 fi 的上面的界限(?? 铄吗？？
基金supported by National Natural Science Foundation of China (Nos. 61273125 and 61104222)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20103705110002)+3 种基金Program for the Scientific Research Innovation Team in Colleges and Universities of Shandong ProvinceShandong Provincial Natural Science Foundation of China (No. ZR2012FM018)Natural Science Foundation of Jiangsu Province (No. BK2011205)Natural Science Foundation of Jiangsu Normal University(No. 11XLR08)
文摘In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system.
基金Project partly supported by the State Major Basic Research Development Program of China(Grant No.2010CB327604)the National Natural Science Foundation of China(Grant No.61377100)
文摘In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.
基金Supported by Program for New Century Excellent Talents in University of China （NCET-05-0607）, National Natural Science Foundation of China （60774010）, Program for Summit of Six Types of Talents of Jiangsu Province （07-A-020）, Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
基金Sponsored by the National Natural Science Foundation of China (Grant No. 61174001)
文摘The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz continuous state feedback.By using the finite-time Lyapunov stability theorem and the method of non-smooth feedback design,a recursive design procedure is provided,which guarantees the finite-time stability of the closed-loop system.The simulation results show the effectiveness of the theoretical results.
基金supported by the National Natural Science Foundation of China(Nos.61775032,11604042)the Fundamental Research Funds for the Central Universities(Nos.N2104022,N2004021)the"111 Project"(No.B16009).
文摘The all-optical wavelength conversion using cascaded four-wave mixing(FWM)phenomena with graphene oxide(GO)and a highly nonlinear fiber(HNLF)device is demonstrated experimentally.GO has a strong third-order nonlinear effect and is an excellent nonlinear optical material for nonlinear optical wavelength conversion.The group velocity matching of pump and signal,HNLF,and GO amplification promote the cascaded nonlinear frequency mixing process.From the experimental and analytical results,the maximum spacing between signal and pump is 21 nm,and specifically,the order of cascaded FWM light increases from order 1 to order 2 with increasing GO,and the first-order FWM conversion effi-ciency increases to a maximum of−14.5 dB.To the best of our knowledge,this is the first time that cascaded FWM-based all-optical wavelength conversion in HNLF-GO with wide wavelength selectivity is investigated with combined pump and signal light.Our findings not only provide an effective method for achieving all-optical wavelength conversion in cascaded FWM but also offer the possibility of fabricating high-performance nonlinear optical devices.
基金This work was financially supported by the National United University[Grant Numbers T110M20600].
文摘In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11205103 and 11075202)
文摘High-frequency signals are pervasive in many science and engineering fields.In this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is derived by extending the inertial approximation for the direct separation of fast and slow motions.Based on this theory,a high-frequency force can induce various phase transitions of a system by changing its amplitude and frequency.Numerical simulations on several nonlinear oscillator systems show a very good agreement with the theoretic results.These findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.
基金Project supported by the National Natural Science Foundation of China (Grant No.10735030)Natural Science Foundation of Zhejiang Province of China (Grant No.Y6090592)+1 种基金Natural Science Foundation of Ningbo City (Grant No.2008A610017)K.C.Wong Magna Fund in Ningbo University
文摘By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.
基金supported by the National Natural Science Foundation of China(Nos.11502103 and11421062)the Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ15115)
文摘A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.
文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).
基金Program for New Century Excellent Talents in University of China (NCET-05-0607)National Natural Science Fou-ndation of China (No.60774010)Project for Fundamental Research of Natural Sciences in Universities of Jingsu Province (No.07KJB510114)
文摘In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61401395 and 61604128)the Scientific Research Fund of Zhejiang Provincial Education Department,China(Grant No.Y201533913)the Fundamental Research Funds for the Central Universities,China(Grant Nos.2016QNA4025 and 2016QN81002)
文摘Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime.However, existing S-parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived.Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power,high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposed approach can be widely used in the research of active metamaterials.
基金National Key R&D Program of China under Grant No.2016YFC0401705Science Fund for Creative Research Groups of the National Natural Science Foundation of China Grant No.51621092+3 种基金the National Natural Science Foundation of China Grant No.51579173,No.51379140,No.51309177 and No.51509180the Fund for Key Research Area Innovation Groups of China Ministry of Science and Technology Grant No.2014RA4031the Program of Introducing Talents of Discipline to Universities Grant No.B14012the Tianjin Innovation Team Foundation of Key Research Areas Grant No.2014TDA001
文摘According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck-Kolmogorov （FPK） equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.
