The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid i...The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.展开更多
Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expr...Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.展开更多
To understand and control the interfacial properties of polydiacetylenes(PDAs)vesicles withπ-conjugated backbone is very important for their colorimetric sensing of chemical and biological targets.In this work,we ado...To understand and control the interfacial properties of polydiacetylenes(PDAs)vesicles withπ-conjugated backbone is very important for their colorimetric sensing of chemical and biological targets.In this work,we adopted 10,12-pentacosadiynoic acid(PCDA)as the model molecule to prepare PDAs vesicles in aqueous solution with different forms(from monomer to blue-to-purple-to-red phase)by controlling the UV irradiation dose.The variations of the interfacial conformation of PDAs vesicles during chromatic transitions were inspected by the adsorption behaviors of probe molecules(4-(4-diethylaminostyry)-1-methylpyridinium iodide,D289)on vesicle surface with surface-specific second harmonic generation(SHG)and zeta potential measurements.Resonant SHG signal from D289 adsorbed on vesicle surface attenuated sharply,and the adsorption free energy as well as the corresponding two-photon fluorescence signal decreased slightly in chromatic transitions.While,the change in the surface density of the adsorbed D289 molecules for PDAs vesicles with different forms was relatively small as estimated from zeta potential measurements.The attenuation of the SHG intensity was thus attributed to the overall order-disorder transition and the changed orientation of D289 molecules caused by the gradual distortion of carboxyl head group driven by backbone perturbation.展开更多
For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a s...For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva'n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva'n's results in this paper.展开更多
The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanic...The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.展开更多
Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic pa...Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized secondharmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.展开更多
With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theo...With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.展开更多
The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for ...The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.展开更多
A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general para...A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.展开更多
This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived fi...This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.展开更多
Some new oscillation criteria are given for forced second order differential equations with mixed nonlinearities by using the generalized variational principle and Riccati technique. Our results generalize and extend ...Some new oscillation criteria are given for forced second order differential equations with mixed nonlinearities by using the generalized variational principle and Riccati technique. Our results generalize and extend some known oscillation results in the literature.展开更多
针对常规基于二阶广义积分发生器的锁频环(second-order generalized integrator based frequency locked-loop,SOGI-FLL)在单相并网逆变器电压控制中对直流及谐波分量抑制能力不足,从而引起输出电压频率、相位振荡的问题,提出一种基于...针对常规基于二阶广义积分发生器的锁频环(second-order generalized integrator based frequency locked-loop,SOGI-FLL)在单相并网逆变器电压控制中对直流及谐波分量抑制能力不足,从而引起输出电压频率、相位振荡的问题,提出一种基于改进型SOGI-FLL的单相并网逆变器电压控制方法。该方法在常规SOGI-FLL控制的基础上,在电压信号输入端加入级联型谐振滤波环节来消除谐波分量;同时引入直流控制环节,借助输入电压误差估计值来消除直流分量,达到电网电压频率和相位快速跟踪效果,从而实现电压的自适应控制。使用MATLAB及RT-LAB硬件在环半实物平台,在频率突变、含直流分量及谐波分量的非理想电网环境中,对二阶广义积分器锁相环、双二阶广义积分器锁频环与改进型SOGI-FLL 3种控制方法进行仿真及实验。结果表明,所提改进型SOGI-FLL控制方法在消除直流及谐波干扰的同时,能在0.025 s内实现频率锁定,且频率偏差小于2%,可增强系统对非理想电网信号的适应能力,实现并网电压的快速跟踪,具有良好动态性能。展开更多
文摘The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
文摘Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.
基金This work was supported by the National Natural Science Foundation of China(No.21403292,No.21403293,No.21473249,and No.21673285),and the funding from the Shenzhen city(No.JCYJ20170307150520453).
文摘To understand and control the interfacial properties of polydiacetylenes(PDAs)vesicles withπ-conjugated backbone is very important for their colorimetric sensing of chemical and biological targets.In this work,we adopted 10,12-pentacosadiynoic acid(PCDA)as the model molecule to prepare PDAs vesicles in aqueous solution with different forms(from monomer to blue-to-purple-to-red phase)by controlling the UV irradiation dose.The variations of the interfacial conformation of PDAs vesicles during chromatic transitions were inspected by the adsorption behaviors of probe molecules(4-(4-diethylaminostyry)-1-methylpyridinium iodide,D289)on vesicle surface with surface-specific second harmonic generation(SHG)and zeta potential measurements.Resonant SHG signal from D289 adsorbed on vesicle surface attenuated sharply,and the adsorption free energy as well as the corresponding two-photon fluorescence signal decreased slightly in chromatic transitions.While,the change in the surface density of the adsorbed D289 molecules for PDAs vesicles with different forms was relatively small as estimated from zeta potential measurements.The attenuation of the SHG intensity was thus attributed to the overall order-disorder transition and the changed orientation of D289 molecules caused by the gradual distortion of carboxyl head group driven by backbone perturbation.
基金Project supported by the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva'n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva'n's results in this paper.
文摘The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.
基金Project supported by the Natural Science Foundation of Heilongjiang Province, China (Grant No A200406).
文摘Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized secondharmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579038,51739010,51490672,51879037)
文摘With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.
文摘The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.
基金This work was supported by the Chinese National Natural Science Foundation ( No. 69925308).
文摘A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.
基金supported by the National Natural Science Foundation of China(Nos.11101069,11171237,11471059,and 81171411)the China Postdoctoral Science Foundation(Nos.2014M552328 and2015T80967)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.
文摘Some new oscillation criteria are given for forced second order differential equations with mixed nonlinearities by using the generalized variational principle and Riccati technique. Our results generalize and extend some known oscillation results in the literature.
文摘针对常规基于二阶广义积分发生器的锁频环(second-order generalized integrator based frequency locked-loop,SOGI-FLL)在单相并网逆变器电压控制中对直流及谐波分量抑制能力不足,从而引起输出电压频率、相位振荡的问题,提出一种基于改进型SOGI-FLL的单相并网逆变器电压控制方法。该方法在常规SOGI-FLL控制的基础上,在电压信号输入端加入级联型谐振滤波环节来消除谐波分量;同时引入直流控制环节,借助输入电压误差估计值来消除直流分量,达到电网电压频率和相位快速跟踪效果,从而实现电压的自适应控制。使用MATLAB及RT-LAB硬件在环半实物平台,在频率突变、含直流分量及谐波分量的非理想电网环境中,对二阶广义积分器锁相环、双二阶广义积分器锁频环与改进型SOGI-FLL 3种控制方法进行仿真及实验。结果表明,所提改进型SOGI-FLL控制方法在消除直流及谐波干扰的同时,能在0.025 s内实现频率锁定,且频率偏差小于2%,可增强系统对非理想电网信号的适应能力,实现并网电压的快速跟踪,具有良好动态性能。