In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed...In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed DCM is based on a feedforward deep neural network(DNN)and differs from most previous applications of deep learning for mechanical problems.First,batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries.A loss function is built with the aim that the governing partial differential equations(PDEs)of Kirchhoff plate bending problems,and the boundary/initial conditions are minimised at those collocation points.A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters.In Kirchhoff plate bending problems,the C^1 continuity requirement poses significant difficulties in traditional mesh-based methods.This can be solved by the proposed DCM,which uses a deep neural network to approximate the continuous transversal deflection,and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.展开更多
Rare earth-doped fibres are a diode-pumped,solid-state laser architecture that is highly scalable in average power.The performance of pulsed fibre laser systems is restricted due to nonlinear effects.Hence,fibre desig...Rare earth-doped fibres are a diode-pumped,solid-state laser architecture that is highly scalable in average power.The performance of pulsed fibre laser systems is restricted due to nonlinear effects.Hence,fibre designs that allow for very large mode areas at high average powers with diffraction-limited beam quality are of enormous interest.Ytterbium-doped,rod-type,large-pitch fibres(LPF)enable extreme fibre dimensions,i.e.,effective single-mode fibres with mode sizes exceeding 100 times the wavelength of the guided radiation,by exploiting the novel concept of delocalisation of higher-order transverse modes.The non-resonant nature of the operating principle makes LPF suitable for high power extraction.This design allows for an unparalleled level of performance in pulsed fibre lasers.展开更多
A Time-domain Higher-Order Boundary Element Method（THOBEM） is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is f...A Time-domain Higher-Order Boundary Element Method（THOBEM） is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is formulated to the first-order in the wave steepness and in the current velocity,respectively.The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem.Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching.An artificial damping layer is adopted to dissipate the scattering waves.Different from the other time-domain numerical models,which are often focused on the wave-current interaction with restrained bodies,the present model deals with a floating hemisphere.The numerical results of wave forces,wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods.The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry.In this work,the regular and focused wave combined with current interacting with a truss-spar platform is investigated.展开更多
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
For magnetotelluric sounding (MT), many processing methods based on power spectrum have put forward lots of hypotheses, such as MT signals are Gaussian, linear and minimum-phase. If practical signals do not satisfy th...For magnetotelluric sounding (MT), many processing methods based on power spectrum have put forward lots of hypotheses, such as MT signals are Gaussian, linear and minimum-phase. If practical signals do not satisfy these requirements, the results will have a few problems as follows. Firstly, when signals are non-linear and non-Gaussian, the information of the earth contained in the MT signals cannot be sufficiently extracted; Secondly, when signals are non-Gaussian and non-minimum phase, the processed results cannot reflect the minimum phase characteristics of the signals. Hence, it is necessary for us to do further research on characteristics of MT signals (YAO, SUN, 1999; LI, CHENG, 2002; Nikias, Petropulu, 1993; ZHANG, 1996). Otherwise, we cannot judge the reliability of the processed results based on power spectrum.……展开更多
An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundar...An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.展开更多
This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.
Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broe...Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.展开更多
Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-or...Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.展开更多
An optimal control strategy of winner-take-all(WTA)model is proposed for target tracking and cooperative competition of multi-UAVs(unmanned aerial vehicles).In this model,firstly,based on the artificial potential fiel...An optimal control strategy of winner-take-all(WTA)model is proposed for target tracking and cooperative competition of multi-UAVs(unmanned aerial vehicles).In this model,firstly,based on the artificial potential field method,the artificial potential field function is improved and the fuzzy control decision is designed to realize the trajectory tracking of dynamic targets.Secondly,according to the finite-time convergence high-order differentiator,a double closed-loop UAV speed tracking the controller is designed to realize the speed control and tracking of the target tracking trajectory.Numerical simulation results show that the designed speed tracking controller has the advantages of fast tracking,high precision,strong stability and avoiding chattering.Finally,a cooperative competition scheme of multiple UAVs based on WTA is designed to find the minimum control energy from multiple UAVs and realize the optimal control strategy.Theoretical analysis and numerical simulation results show that the model has the fast convergence,high control accuracy,strong stability and good robustness.展开更多
The transmission systems of the differential velocity vane pumps （DVVP） have periodic vibrations under loads. And it is not easy to find the reason. In order to optimize the performance of the pump, the authors prop...The transmission systems of the differential velocity vane pumps （DVVP） have periodic vibrations under loads. And it is not easy to find the reason. In order to optimize the performance of the pump, the authors proposed DVVP driven by the hybrid Higher-order Fourier non-circular gears and tested it. There were also simi- lar periodic vibrations and noises under loads. Taking into account this phenomenon, the paper proposes fluid mechanics and solid mechanics simulation methodology to analyze the coupling dynamics between fluid and transmission system and reveals the reason. The results show that the pump has the reverse drive phenomenon, which is that the blades drive the non-circular gears when the suction and discharge is alternating. The reverse drive phenomenon leads the sign of the shaft torque to be changed in positive and negative way. So the transmis- sion system produces torsional vibrations. In order to confirm the simulation results, micro strains of the input shaft of the pump impeller are measured by the Wheatstone bridge and wireless sensor technology. The relation- ships between strain and torque are obtained by experimental calibration, and then the （rue torque of input shaft is calculated indirectly. The experimental results are consistent to the simulation results. It is proven that the peri- odic vibrations are mainly caused by fluid solid coupling, which leads to periodic torsional vibration of the trans- mission system.展开更多
We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make a...We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H<sub>1</sub>) - (H<sub>4</sub>). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.展开更多
It can be optimized for the work of the point estimate on the Newton iteration, reported by Smale at the 20th Congress of Mathematicians in 1986. It has been proved that iffα(z,f) , for every analytic map f:E→F, z ...It can be optimized for the work of the point estimate on the Newton iteration, reported by Smale at the 20th Congress of Mathematicians in 1986. It has been proved that iffα(z,f) , for every analytic map f:E→F, z ∈ is an approximate zero of f,whereE and F are real or complex Banach spaces. In addition, if α,(z,f) , z is anapproximate zero of the second kind of f.展开更多
This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We der...This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .展开更多
The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008.Photonic band structures embraced topological phases of matter,ha...The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008.Photonic band structures embraced topological phases of matter,have spawned a novel platform for studying topological phase transitions and designing topological optical devices.Here,we present a brief review of topological photonic crystals based on different material platforms,including all-dielectric systems,metallic materials,optical resonators,coupled waveguide systems,and other platforms.Furthermore,this review summarizes recent progress on topological photonic crystals,such as higherorder topological photonic crystals,non-Hermitian photonic crystals,and nonlinear photonic crystals.These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.展开更多
Background:To evaluate the precision of corneal higher-order aberrations measurements after small incision lenticule extraction(SMILE)using the Sirius Scheimpfug-Placido topographer(CSO,Italy).Methods:Seventy-fve eyes...Background:To evaluate the precision of corneal higher-order aberrations measurements after small incision lenticule extraction(SMILE)using the Sirius Scheimpfug-Placido topographer(CSO,Italy).Methods:Seventy-fve eyes from 75 postoperative subjects were included in this prospective study.Three consecutive corneal aberrometric measurements were obtained with the Scheimpfug-Placido topographer by two experienced operators to assess intra-and inter-observer reproducibility.The within-subject standard deviation(Sw),test-retest repeatability(TRT)and the intraclass correlation coefcient(ICC)were calculated.Results:For intraobserver repeatability of anterior and total corneal aberrations,all ICCs were more than 0.922,except for trefoil(0.722 to 0.768).The ICCs of total root mean square(RMS),coma Z(3,±1),and spherical aberration Z(4,0)were over 0.810 while higher-order RMS,trefoil Z(3,±3),and astigmatism II Z(4,±2)were below 0.634 for posterior corneal surface aberrations.All Sw values for all types of aberrations were equal to or below 0.07μm.Regarding interobserver reproducibility,all TRT values were no more than 0.12μm,0.05μm,and 0.11μm for anterior,posterior,and total corneal aberrations,respectively.The ICC values ranged from 0.875 to 0.989,from 0.686 to 0.976 and over 0.834 for anterior,posterior,and total corneal aberrations,respectively.Conclusions:The repeatability of measurements of anterior and total corneal aberrations with the Sirius system in corneas after SMILE surgery was high,except for trefoil.There was some variability in posterior corneal aberrometric measurements.High reproducibility of corneal aberrometric measurements was observed between measurements of both examiners,except for trefoil,with poor to moderate reproducibility.展开更多
AIM:To explore the long-term efficacy,safety,and optical mechanism of orthokeratology with increased compression factor in adolescent myopia control.METHODS:A prospective,double-masked,and randomized clinical trial wa...AIM:To explore the long-term efficacy,safety,and optical mechanism of orthokeratology with increased compression factor in adolescent myopia control.METHODS:A prospective,double-masked,and randomized clinical trial was performed from May 2016 to June 2020.Subjects aged between 8 and 16y,with myopia(-5.00 to-1.00 D),low astigmatism(≥-1.50 D)and anisometropia(≤1.00 D),were stratified into low(-2.75 to-1.00 D)and moderate(-5.00 to-3.00 D)myopia groups.Then they were randomly assigned to wear either increased compression factor(ICF;1.75 D)orthokeratology or conventional compression factor(CCF;0.75 D)orthokeratology.The data were recorded including axial length(AL),spherical equivalent(SE),best corrected visual acuity(BCVA),near visual acuity(NVA),corneal staining(using Efron grading scales),corneal hysteresis(CH),corneal resistance factor(CRF),higher-order aberrations(HOAs,expressed as root mean square,RMS_(h)),and subfoveal choroidal thickness(SFCh T)in the 2-year followup period.Pearson's correlation coefficient was conducted to analyze the association between the changes in AL and RMS_(h),SFCh T.RESULTS:At the 2-year visit,there were no statistical differences in all the parameters between the ICF group and the CCF group in low myopia subjects(P>0.05).For the moderate myopia subjects,the ICF group had shorter AL elongation(0.23±0.08 vs 0.30±0.11 mm,P=0.015),higher RMS_(h)(1.94±0.50 vs 1.65±0.51μm,P=0.041),and higher SFCh T(279.04±35.72 vs 254.08±29.60μm,P=0.008)than those in CCF group.The change in AL was negatively correlated with RMS_(h)(r=-0.687,P<0.001)and SFCh T(r=-0.464,P=0.013).CONCLUSION:ICF orthokeratology can control the progression of moderate myopia more effectively,which might be related to greater RMS_(h) and SFCh T.展开更多
At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual io...At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning（PPP） are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service（IGS） tracking stations. Numerical experimental results show that, the root mean square（RMS） in three dimensions of satellite orbit is 36.6 mme35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.展开更多
Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are use...Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.展开更多
文摘In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed DCM is based on a feedforward deep neural network(DNN)and differs from most previous applications of deep learning for mechanical problems.First,batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries.A loss function is built with the aim that the governing partial differential equations(PDEs)of Kirchhoff plate bending problems,and the boundary/initial conditions are minimised at those collocation points.A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters.In Kirchhoff plate bending problems,the C^1 continuity requirement poses significant difficulties in traditional mesh-based methods.This can be solved by the proposed DCM,which uses a deep neural network to approximate the continuous transversal deflection,and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
基金The research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme(FP7/2007-2013)/ERC Grant Agreement No.[240460]the Thuringian Ministry of Education,Science and Culture under contract PE203-2-1(MOFA)and contract B514-10061(Green Photonics).FJ acknowledges financial support from the Abbe School of Photonics.
文摘Rare earth-doped fibres are a diode-pumped,solid-state laser architecture that is highly scalable in average power.The performance of pulsed fibre laser systems is restricted due to nonlinear effects.Hence,fibre designs that allow for very large mode areas at high average powers with diffraction-limited beam quality are of enormous interest.Ytterbium-doped,rod-type,large-pitch fibres(LPF)enable extreme fibre dimensions,i.e.,effective single-mode fibres with mode sizes exceeding 100 times the wavelength of the guided radiation,by exploiting the novel concept of delocalisation of higher-order transverse modes.The non-resonant nature of the operating principle makes LPF suitable for high power extraction.This design allows for an unparalleled level of performance in pulsed fibre lasers.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772040, 50709005 and 5092100)the Important National Science and Technology Specific Projects of China (Grant No. 2008ZX05026-02)the Open Fund of Stabe Key Laboratory of Sabllite Ocean Environment Dynamics (Grant No. SOED1002)
文摘A Time-domain Higher-Order Boundary Element Method（THOBEM） is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is formulated to the first-order in the wave steepness and in the current velocity,respectively.The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem.Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching.An artificial damping layer is adopted to dissipate the scattering waves.Different from the other time-domain numerical models,which are often focused on the wave-current interaction with restrained bodies,the present model deals with a floating hemisphere.The numerical results of wave forces,wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods.The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry.In this work,the regular and focused wave combined with current interacting with a truss-spar platform is investigated.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
基金National Natural Science Foundation of China (40274039).
文摘For magnetotelluric sounding (MT), many processing methods based on power spectrum have put forward lots of hypotheses, such as MT signals are Gaussian, linear and minimum-phase. If practical signals do not satisfy these requirements, the results will have a few problems as follows. Firstly, when signals are non-linear and non-Gaussian, the information of the earth contained in the MT signals cannot be sufficiently extracted; Secondly, when signals are non-Gaussian and non-minimum phase, the processed results cannot reflect the minimum phase characteristics of the signals. Hence, it is necessary for us to do further research on characteristics of MT signals (YAO, SUN, 1999; LI, CHENG, 2002; Nikias, Petropulu, 1993; ZHANG, 1996). Otherwise, we cannot judge the reliability of the processed results based on power spectrum.……
基金supported by the Fundamental Research Funds forthe Central Universities (DVT10LK43)the Returned Overseas Chinese Scholars,State Education Ministry (2007[24])
文摘An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.
基金the National Natural Science Foundation of China(1 0 1 71 0 88) and the National Natural Science Foundation of Jiangsu Educational Committee(99KJ1 1 0 0 0 5 )
文摘This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.
文摘Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.
基金supported by National 973 Program (No. 2007CB209600)
文摘Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.
基金This work was supported by the National Natural Science Foundation of China(71462018,71761018)the Science and Technology Program of Education Department of Jiangxi Province in China(GJJ171503).
文摘An optimal control strategy of winner-take-all(WTA)model is proposed for target tracking and cooperative competition of multi-UAVs(unmanned aerial vehicles).In this model,firstly,based on the artificial potential field method,the artificial potential field function is improved and the fuzzy control decision is designed to realize the trajectory tracking of dynamic targets.Secondly,according to the finite-time convergence high-order differentiator,a double closed-loop UAV speed tracking the controller is designed to realize the speed control and tracking of the target tracking trajectory.Numerical simulation results show that the designed speed tracking controller has the advantages of fast tracking,high precision,strong stability and avoiding chattering.Finally,a cooperative competition scheme of multiple UAVs based on WTA is designed to find the minimum control energy from multiple UAVs and realize the optimal control strategy.Theoretical analysis and numerical simulation results show that the model has the fast convergence,high control accuracy,strong stability and good robustness.
基金financially supported by the Project of fundamental Commonweal Research of Zhejiang Province(Grant No.LGG18E050004)the National Natural Science Foundation of China(Grant No.51305403 and No.51675486)
文摘The transmission systems of the differential velocity vane pumps （DVVP） have periodic vibrations under loads. And it is not easy to find the reason. In order to optimize the performance of the pump, the authors proposed DVVP driven by the hybrid Higher-order Fourier non-circular gears and tested it. There were also simi- lar periodic vibrations and noises under loads. Taking into account this phenomenon, the paper proposes fluid mechanics and solid mechanics simulation methodology to analyze the coupling dynamics between fluid and transmission system and reveals the reason. The results show that the pump has the reverse drive phenomenon, which is that the blades drive the non-circular gears when the suction and discharge is alternating. The reverse drive phenomenon leads the sign of the shaft torque to be changed in positive and negative way. So the transmis- sion system produces torsional vibrations. In order to confirm the simulation results, micro strains of the input shaft of the pump impeller are measured by the Wheatstone bridge and wireless sensor technology. The relation- ships between strain and torque are obtained by experimental calibration, and then the （rue torque of input shaft is calculated indirectly. The experimental results are consistent to the simulation results. It is proven that the peri- odic vibrations are mainly caused by fluid solid coupling, which leads to periodic torsional vibration of the trans- mission system.
文摘We investigate the global well-posedness and the global attractors of the solutions for the Higher-order Kirchhoff-type wave equation with nonlinear strongly damping: . For strong nonlinear damping σ and ?, we make assumptions (H<sub>1</sub>) - (H<sub>4</sub>). Under of the proper assume, the main results are existence and uniqueness of the solution in proved by Galerkin method, and deal with the global attractors.
基金Porject supported by the National Natural Science Foundation of China and the Provincial Natural Science Foundation
文摘It can be optimized for the work of the point estimate on the Newton iteration, reported by Smale at the 20th Congress of Mathematicians in 1986. It has been proved that iffα(z,f) , for every analytic map f:E→F, z ∈ is an approximate zero of f,whereE and F are real or complex Banach spaces. In addition, if α,(z,f) , z is anapproximate zero of the second kind of f.
文摘This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .
基金supported by the National Key R&D Program of China(Nos.2018YFA0306200,and 2017YFA0303702)the National Natural Science Foundation of China(Grant Nos.11625418,51732006,and 11890700)as well as the Academic Program Development of Jiangsu Higher Education(PAPD).
文摘The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008.Photonic band structures embraced topological phases of matter,have spawned a novel platform for studying topological phase transitions and designing topological optical devices.Here,we present a brief review of topological photonic crystals based on different material platforms,including all-dielectric systems,metallic materials,optical resonators,coupled waveguide systems,and other platforms.Furthermore,this review summarizes recent progress on topological photonic crystals,such as higherorder topological photonic crystals,non-Hermitian photonic crystals,and nonlinear photonic crystals.These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.
基金the Medical and Health Science and Technology Program of Zhejiang Province(2019KY111)Foundation of Wenzhou City Science&Technology Bureau(Y2020037)+1 种基金EYE&ENT Hospital of Fudan University High-level Talents Program(2021318)Clinical Research Plan of SHDC(SHDC2020CR1043B)。
文摘Background:To evaluate the precision of corneal higher-order aberrations measurements after small incision lenticule extraction(SMILE)using the Sirius Scheimpfug-Placido topographer(CSO,Italy).Methods:Seventy-fve eyes from 75 postoperative subjects were included in this prospective study.Three consecutive corneal aberrometric measurements were obtained with the Scheimpfug-Placido topographer by two experienced operators to assess intra-and inter-observer reproducibility.The within-subject standard deviation(Sw),test-retest repeatability(TRT)and the intraclass correlation coefcient(ICC)were calculated.Results:For intraobserver repeatability of anterior and total corneal aberrations,all ICCs were more than 0.922,except for trefoil(0.722 to 0.768).The ICCs of total root mean square(RMS),coma Z(3,±1),and spherical aberration Z(4,0)were over 0.810 while higher-order RMS,trefoil Z(3,±3),and astigmatism II Z(4,±2)were below 0.634 for posterior corneal surface aberrations.All Sw values for all types of aberrations were equal to or below 0.07μm.Regarding interobserver reproducibility,all TRT values were no more than 0.12μm,0.05μm,and 0.11μm for anterior,posterior,and total corneal aberrations,respectively.The ICC values ranged from 0.875 to 0.989,from 0.686 to 0.976 and over 0.834 for anterior,posterior,and total corneal aberrations,respectively.Conclusions:The repeatability of measurements of anterior and total corneal aberrations with the Sirius system in corneas after SMILE surgery was high,except for trefoil.There was some variability in posterior corneal aberrometric measurements.High reproducibility of corneal aberrometric measurements was observed between measurements of both examiners,except for trefoil,with poor to moderate reproducibility.
基金Supported by Education Department Foundation of Sichuan Province(No.15ZA0262)。
文摘AIM:To explore the long-term efficacy,safety,and optical mechanism of orthokeratology with increased compression factor in adolescent myopia control.METHODS:A prospective,double-masked,and randomized clinical trial was performed from May 2016 to June 2020.Subjects aged between 8 and 16y,with myopia(-5.00 to-1.00 D),low astigmatism(≥-1.50 D)and anisometropia(≤1.00 D),were stratified into low(-2.75 to-1.00 D)and moderate(-5.00 to-3.00 D)myopia groups.Then they were randomly assigned to wear either increased compression factor(ICF;1.75 D)orthokeratology or conventional compression factor(CCF;0.75 D)orthokeratology.The data were recorded including axial length(AL),spherical equivalent(SE),best corrected visual acuity(BCVA),near visual acuity(NVA),corneal staining(using Efron grading scales),corneal hysteresis(CH),corneal resistance factor(CRF),higher-order aberrations(HOAs,expressed as root mean square,RMS_(h)),and subfoveal choroidal thickness(SFCh T)in the 2-year followup period.Pearson's correlation coefficient was conducted to analyze the association between the changes in AL and RMS_(h),SFCh T.RESULTS:At the 2-year visit,there were no statistical differences in all the parameters between the ICF group and the CCF group in low myopia subjects(P>0.05).For the moderate myopia subjects,the ICF group had shorter AL elongation(0.23±0.08 vs 0.30±0.11 mm,P=0.015),higher RMS_(h)(1.94±0.50 vs 1.65±0.51μm,P=0.041),and higher SFCh T(279.04±35.72 vs 254.08±29.60μm,P=0.008)than those in CCF group.The change in AL was negatively correlated with RMS_(h)(r=-0.687,P<0.001)and SFCh T(r=-0.464,P=0.013).CONCLUSION:ICF orthokeratology can control the progression of moderate myopia more effectively,which might be related to greater RMS_(h) and SFCh T.
基金funded by the China Natural Science Funds the National Natural Science Foundation of China (41374009)Postdoctoral Applied Research Project (2015186)
文摘At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning（PPP） are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service（IGS） tracking stations. Numerical experimental results show that, the root mean square（RMS） in three dimensions of satellite orbit is 36.6 mme35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.
基金Project supported by the National Natural Science Foundation of China (Grant No 40775069)
文摘Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.
