Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by ...Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.展开更多
With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for th...With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.展开更多
In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have be...In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.展开更多
Deep learning-based semantic communication has achieved remarkable progress with CNNs and Transformers.However,CNNs exhibit constrained performance in high-resolution image transmission,while Transformers incur high c...Deep learning-based semantic communication has achieved remarkable progress with CNNs and Transformers.However,CNNs exhibit constrained performance in high-resolution image transmission,while Transformers incur high computational cost due to quadratic complexity.Recently,VMamba,a novel state space model with linear complexity and exceptional long-range dependency modeling capabilities,has shown great potential in computer vision tasks.Inspired by this,we propose MNTSCC,an efficient VMamba-based nonlinear joint source-channel coding(JSCC)model for wireless image transmission.Specifically,MNTSCC comprises a VMamba-based nonlinear transform module,an MCAM entropy model,and a JSCC module.In the encoding stage,the input image is first encoded into a latent representation via the nonlinear transformation module,which is then processed by the MCAM for source distribution modeling.The JSCC module then optimizes transmission efficiency by adaptively assigning transmission rate to the latent representation according to the estimated entropy values.The proposedMCAMenhances the channel-wise autoregressive entropy model with attention mechanisms,which enables the entropy model to effectively capture both global and local information within latent features,thereby enabling more accurate entropy estimation and improved rate-distortion performance.Additionally,to further enhance the robustness of the system under varying signal-to-noise ratio(SNR)conditions,we incorporate SNR adaptive net(SAnet)into the JSCCmodule,which dynamically adjusts the encoding strategy by integrating SNRinformationwith latent features,thereby improving SNR adaptability.Experimental results across diverse resolution datasets demonstrate that the proposed method achieves superior image transmission performance compared to existing CNN-and Transformer-based semantic communication models,while maintaining competitive computational efficiency.In particular,under an Additive White Gaussian Noise(AWGN)channel with SNR=10 dB and a channel bandwidth ratio(CBR)of 1/16,MNTSCC consistently outperforms NTSCC,achieving a 1.72 dB Peak Signal-to-Noise Ratio(PSNR)gain on the Kodak24 dataset,0.79 dB on CLIC2022,and 2.54 dB on CIFAR-10,while reducing computational cost by 32.23%.The code is available at https://github.com/WanChen10/MNTSCC(accessed on 09 July 2025).展开更多
In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to ana...In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.展开更多
The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simul...The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simulated cases, while the incident wave amplitude is made increase progressively, so that the interaction with the shelf is dominated by almost inviscid non-linear flow for the smallest and by breaking for the highest incident waves. A parameter identification（PI） procedure is used to adapt a reduced model to the highly resolved time-space matrix of wave elevations obtained from the numerical simulations, on the weather and lee side respectively. In particular the wave number and the frequency of the component waves in the reduced model are left uncoupled, thus computed by the PI independently. The comparison of simulated data with experiments generally shows a very good agreement. Free/locked, incident/reflected, first/higher order wave components are quantified accurately by the PI and the energy transfer to super-harmonics is clearly evidenced. Moreover the results of the PI show clearly a very large increase in the phase speed of the higher order free waves on the lee side of the shelf, with increasing deviation from the linear behavior with increasing incident wave amplitude.展开更多
Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study...Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.展开更多
A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over prediction of both Hedges′ modified relation and...A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1< kh <1 5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.展开更多
We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, th...We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.展开更多
By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a m...By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.展开更多
The paper examines the weakly nonlinear behavior of a 5-layer beam-like piezo- electric transformer operating near resonance, where the main structure of the device consists of properly poled and electroded flexible p...The paper examines the weakly nonlinear behavior of a 5-layer beam-like piezo- electric transformer operating near resonance, where the main structure of the device consists of properly poled and electroded flexible piezoceramic four-layers separated by a central metallic layer. Nonlinear effects of the large deflection to induce the incidental implane extension near res- onance are considered, which is shown that on one side of the resonant frequency the output-input relation becomes nonlinear, and the other side output voltage experiences jumps.展开更多
In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series...In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series of Backlund transformations of the equation are constructed by means of the symmetries. The exact solutions of two boundary-initial value problems on the half straight line for the equation are given m terms of the solutions of the corresponding linear problems.展开更多
In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomi...In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomials [1]. The analytical results of examples are calculated in terms of convergent series with easily computed components [2].展开更多
A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986). and which has a better...A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986). and which has a better approximation to Hedges' empirical relation than the modified relations by Hedges (1987). Kirby and Dalrymple (1987) for shallow waters. The new dispersion relation is simple in form, thus it can be used easily in practice. Meanwhile, a general explicit approximation to the new dispersion and other and other nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking into account weakly nonlinenr effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed with the new dispersion relation predicts wave transformation over complicated topography quite well.展开更多
The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to ...The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors （BVs） are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector （NLLV） scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more com- ponents in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random pertur- bation （RP） technique, and the BV method, as well as its improved version--the ensemble transform Kalman filter （ETKF） method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.展开更多
This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite trans...This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a secondorder nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.展开更多
The linear multi-core pulse transformer is an important primary driving source used in pulsed power apparatus for the production of dense plasma owing to its compact, relatively low-cost and easy-to-handle characteris...The linear multi-core pulse transformer is an important primary driving source used in pulsed power apparatus for the production of dense plasma owing to its compact, relatively low-cost and easy-to-handle characteristics. The evaluation of the magnetic saturation of the transformer cores is essential to the transformer design, because the energy transfer efficiency of the transformer will degrade significantly after magnetic saturation. This work proposes analytical formulas of the criterion of magnetic saturation for the cores when the transformer drives practical loads. Furthermore, an electric circuit model based on a dependent source treatment for simulating the electric behavior of the cores related to their nonlinear magnetization is developed using the initial magnetization curve of the cores. The numerical simulation with the model is used to evaluate the validity of the criterion. Both the criterion and the model are found to be in agreement with the experimental data.展开更多
The peculiarities of energy dissipation transferred by solitary waves on defects such as freesurface, grain boundary, region with high concentration of vacancies are studied. One of theways of description of the long ...The peculiarities of energy dissipation transferred by solitary waves on defects such as freesurface, grain boundary, region with high concentration of vacancies are studied. One of theways of description of the long range effect taking place at ion implantation in metallic materialsis suggested.展开更多
In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the ...In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and a simple physical ex- planation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the proposed theory and method.展开更多
基金supported by the Key Program of the National Natural Science Foundation of China(Grant No.62031013)Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project(Grant No.2022ZDJS117).
文摘Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.
基金Natural Science Foundation of Gansu Province of China
文摘With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.
基金supported by the Natural Science Basic Research Program of Shaanxi (Program No. 2023-JCYB-048)the National Natural Science Foundation of China (Program No. 11601406)。
文摘In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.
文摘Deep learning-based semantic communication has achieved remarkable progress with CNNs and Transformers.However,CNNs exhibit constrained performance in high-resolution image transmission,while Transformers incur high computational cost due to quadratic complexity.Recently,VMamba,a novel state space model with linear complexity and exceptional long-range dependency modeling capabilities,has shown great potential in computer vision tasks.Inspired by this,we propose MNTSCC,an efficient VMamba-based nonlinear joint source-channel coding(JSCC)model for wireless image transmission.Specifically,MNTSCC comprises a VMamba-based nonlinear transform module,an MCAM entropy model,and a JSCC module.In the encoding stage,the input image is first encoded into a latent representation via the nonlinear transformation module,which is then processed by the MCAM for source distribution modeling.The JSCC module then optimizes transmission efficiency by adaptively assigning transmission rate to the latent representation according to the estimated entropy values.The proposedMCAMenhances the channel-wise autoregressive entropy model with attention mechanisms,which enables the entropy model to effectively capture both global and local information within latent features,thereby enabling more accurate entropy estimation and improved rate-distortion performance.Additionally,to further enhance the robustness of the system under varying signal-to-noise ratio(SNR)conditions,we incorporate SNR adaptive net(SAnet)into the JSCCmodule,which dynamically adjusts the encoding strategy by integrating SNRinformationwith latent features,thereby improving SNR adaptability.Experimental results across diverse resolution datasets demonstrate that the proposed method achieves superior image transmission performance compared to existing CNN-and Transformer-based semantic communication models,while maintaining competitive computational efficiency.In particular,under an Additive White Gaussian Noise(AWGN)channel with SNR=10 dB and a channel bandwidth ratio(CBR)of 1/16,MNTSCC consistently outperforms NTSCC,achieving a 1.72 dB Peak Signal-to-Noise Ratio(PSNR)gain on the Kodak24 dataset,0.79 dB on CLIC2022,and 2.54 dB on CIFAR-10,while reducing computational cost by 32.23%.The code is available at https://github.com/WanChen10/MNTSCC(accessed on 09 July 2025).
基金The project partly supported by the Foundation of Zhongshan University Advanced Research Center
文摘In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.
基金The "Programma Attuativo Regionale del Fondo per lo Sviluppo e la Coesione (PAR FSC 2007-2013) Linea 3.1.2" is acknowledged for providing the support of the OpenViewSHIP Project
文摘The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simulated cases, while the incident wave amplitude is made increase progressively, so that the interaction with the shelf is dominated by almost inviscid non-linear flow for the smallest and by breaking for the highest incident waves. A parameter identification（PI） procedure is used to adapt a reduced model to the highly resolved time-space matrix of wave elevations obtained from the numerical simulations, on the weather and lee side respectively. In particular the wave number and the frequency of the component waves in the reduced model are left uncoupled, thus computed by the PI independently. The comparison of simulated data with experiments generally shows a very good agreement. Free/locked, incident/reflected, first/higher order wave components are quantified accurately by the PI and the energy transfer to super-harmonics is clearly evidenced. Moreover the results of the PI show clearly a very large increase in the phase speed of the higher order free waves on the lee side of the shelf, with increasing deviation from the linear behavior with increasing incident wave amplitude.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61475099 and 61922040)Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices,China(Grant No.KF201701)the Key R&D Program of Guangdong Province,China(Grant No.2018B030325002)。
文摘Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.
文摘A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1< kh <1 5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.
基金supported by the National Natural Science Foundation of China (Grant Nos 10674045 and 60538010)the National Natural Science Foundation of Hunan Province,China (Grant No 08jj3001)
文摘We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.
基金Supported by National Natural Science Foundation of China under Grant Nos.11775121 and 11435005K.C.Wong Magna Fund in Ningbo University
文摘By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.
基金Project supported by the National Science Foundation of China(Nos.10932004 and 11272127)
文摘The paper examines the weakly nonlinear behavior of a 5-layer beam-like piezo- electric transformer operating near resonance, where the main structure of the device consists of properly poled and electroded flexible piezoceramic four-layers separated by a central metallic layer. Nonlinear effects of the large deflection to induce the incidental implane extension near res- onance are considered, which is shown that on one side of the resonant frequency the output-input relation becomes nonlinear, and the other side output voltage experiences jumps.
文摘In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series of Backlund transformations of the equation are constructed by means of the symmetries. The exact solutions of two boundary-initial value problems on the half straight line for the equation are given m terms of the solutions of the corresponding linear problems.
文摘In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomials [1]. The analytical results of examples are calculated in terms of convergent series with easily computed components [2].
文摘A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986). and which has a better approximation to Hedges' empirical relation than the modified relations by Hedges (1987). Kirby and Dalrymple (1987) for shallow waters. The new dispersion relation is simple in form, thus it can be used easily in practice. Meanwhile, a general explicit approximation to the new dispersion and other and other nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking into account weakly nonlinenr effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed with the new dispersion relation predicts wave transformation over complicated topography quite well.
文摘The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors （BVs） are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector （NLLV） scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram-Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more com- ponents in analysis errors than the BVs. In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model. The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random pertur- bation （RP） technique, and the BV method, as well as its improved version--the ensemble transform Kalman filter （ETKF） method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.
基金financially supported by the Major Project of the Ministry of Education and the Ministry of Finance of China(Grant No.GKZY010004)
文摘This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a secondorder nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.
基金This work was supported by the National Natural Science Foundation of China,No.10035020
文摘The linear multi-core pulse transformer is an important primary driving source used in pulsed power apparatus for the production of dense plasma owing to its compact, relatively low-cost and easy-to-handle characteristics. The evaluation of the magnetic saturation of the transformer cores is essential to the transformer design, because the energy transfer efficiency of the transformer will degrade significantly after magnetic saturation. This work proposes analytical formulas of the criterion of magnetic saturation for the cores when the transformer drives practical loads. Furthermore, an electric circuit model based on a dependent source treatment for simulating the electric behavior of the cores related to their nonlinear magnetization is developed using the initial magnetization curve of the cores. The numerical simulation with the model is used to evaluate the validity of the criterion. Both the criterion and the model are found to be in agreement with the experimental data.
文摘The peculiarities of energy dissipation transferred by solitary waves on defects such as freesurface, grain boundary, region with high concentration of vacancies are studied. One of theways of description of the long range effect taking place at ion implantation in metallic materialsis suggested.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61173122, 60970098, 60803024, 90715043, and 61144006)the Postdoctoral Startup Foundation of Central South University, China (Grant No. 1332/74341016030)
文摘In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and a simple physical ex- planation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the proposed theory and method.
