The adsorptive precipitation between eosin Y （EY） and AgCl colloids at pH 3.73 caused the sensitive color change of the solution. The reaction mechanism between EY and AgCl was analyzed and this reaction was used fo...The adsorptive precipitation between eosin Y （EY） and AgCl colloids at pH 3.73 caused the sensitive color change of the solution. The reaction mechanism between EY and AgCl was analyzed and this reaction was used for determination of Cl^- in trace level by the light-absorption radio variation approach.展开更多
In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TO...In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TOPEX/POSEIDON （T/P） derived datasets by means of the variational adjoint approach in such a way that unknown internal model parameters, bottom topography, friction coefficients and open boundary conditions, for example, are adjusted during the process. The numerical model is used as a forward model. After the along-track T/P data are processed, two classical methods, i.e. harmonic and response analysis, are implemented to estimate the tide from such datasets with a domain covering the model area extending from 0° to 41°N in latitude and from 99°E to 142°E in longitude. And the results of these two methods are compared and interpreted. The numerical simulation is performed for 16 major constituents. In the data assimilation experiments, three types of unknown parameters （water depth, bottom friction and tidal open boundary conditions in the model equations） are chosen as control variables. Among the various types of data assimilation experiments, the calibration of water depth brings the most promising results. By comparing the results with selected tide gauge data, the average absolute errors are decreased from 7.9 cm to 6.8 cm for amplitude and from 13.0° to 9.0° for phase with respect to the semidiurnal tide M2 constituent, which is the largest tidal constituent in the model area. After the data assimilation experiment is performed, the comparison between model results and tide gauge observation for water levels shows that the RMS errors decrease by 9 cm for a total of 14 stations, mostly selected along the coast of China's Mainland, when a one-month period is considered, and the correlation coefficients improve for most tidal stations among these stations.展开更多
One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, ...One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".展开更多
The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on varia...The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.展开更多
Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanag...Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanagisawa[Lr-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains,Indiana Univ.Math.J.58(2009),1853-1920],combined with global computations based on the Bochner technique.展开更多
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a one-dimensional(1D) harmonic potential. At the boundaries both the wave function and ...A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a one-dimensional(1D) harmonic potential. At the boundaries both the wave function and its first derivative are continuous and the quasi-momentum is determined by a more practical constraint condition which associates two variational parameters. The upper bound of the ground state energy is obtained by applying the variational principle to the expectation value of the Hamiltonian of relative motion on the trial wave function. The resulted energy and wave function show better agreement with the analytical solution than the original proposal.展开更多
We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-part...We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.展开更多
More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtain...More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.展开更多
Images obtained from hyperspectral sensors provide information about the target area that extends beyond the visible portions of the electromagnetic spectrum.However,due to sensor limitations and imperfections during ...Images obtained from hyperspectral sensors provide information about the target area that extends beyond the visible portions of the electromagnetic spectrum.However,due to sensor limitations and imperfections during the image acquisition and transmission phases,noise is introduced into the acquired image,which can have a negative impact on downstream analyses such as classification,target tracking,and spectral unmixing.Noise in hyperspectral images(HSI)is modelled as a combination from several sources,including Gaussian/impulse noise,stripes,and deadlines.An HSI restoration method for such a mixed noise model is proposed.First,a joint optimisation framework is proposed for recovering hyperspectral data corrupted by mixed Gaussian-impulse noise by estimating both the clean data as well as the sparse/impulse noise levels.Second,a hyper-Laplacian prior is used along both the spatial and spectral dimensions to express sparsity in clean image gradients.Third,to model the sparse nature of impulse noise,anℓ_(1)−norm over the impulse noise gradient is used.Because the proposed methodology employs two distinct priors,the authors refer to it as the hyperspectral dual prior(HySpDualP)denoiser.To the best of authors'knowledge,this joint optimisation framework is the first attempt in this direction.To handle the non-smooth and nonconvex nature of the generalℓ_(p)−norm-based regularisation term,a generalised shrinkage/thresholding(GST)solver is employed.Finally,an efficient split-Bregman approach is used to solve the resulting optimisation problem.Experimental results on synthetic data and real HSI datacube obtained from hyperspectral sensors demonstrate that the authors’proposed model outperforms state-of-the-art methods,both visually and in terms of various image quality assessment metrics.展开更多
The physical features exhibited by Hermite-Gaussian （HC） beams propagating in nonlocal nonlinear media with Gaussian-shaped response are discussed with an approximate variational method.Using direct numerical simula...The physical features exhibited by Hermite-Gaussian （HC） beams propagating in nonlocal nonlinear media with Gaussian-shaped response are discussed with an approximate variational method.Using direct numerical simulations,we find that the beam properties in the normalized system are different with the change of the degree of nonlocality.It is shown that initial HG profiles break up into several individual beams with propagation when the degree of nonlocality α is small.HG beams can propagate stably when a is large enough.展开更多
Amplification of seismic ground motions in the territory of Almaty city is evaluated by using different methods. The pattern and probable causes of ground motion variations in different engineering-geological conditio...Amplification of seismic ground motions in the territory of Almaty city is evaluated by using different methods. The pattern and probable causes of ground motion variations in different engineering-geological conditions are characterized. An expeditious application of these techniques within a complex methodical approach for Almaty city microzonation is considered.展开更多
Based on the variational approach for pile groups embedded in soil modeled using a load-transfer curve method, a practical method was conducted to estimate the settlement of symmetric pile group supported embankments....Based on the variational approach for pile groups embedded in soil modeled using a load-transfer curve method, a practical method was conducted to estimate the settlement of symmetric pile group supported embankments. The working mechanism of composite foundations improved by rigid or semi-rigid columns is analyzed by this method. Under equivalent strain conditions, the pile-soil stress ratio approaches the pile-soil modulus ratio up to a limited value of pile stiffness （Rm〈10）; in the subsequent stages of high pile stiffness （Rm〉10）, a further increase in the pile-soil modulus ratio cannot lead to a significant increase of stress transferred to the columns in composite foundations. The major influencing factor of the stress concentration from soil to pile in a high pile-soil modulus ratio is the padding stiffness. For the composite foundation improved by cement mixing columns, the effective column length is about 15 to 20 m and it is a more economical and effective design when the column length is less than 15 m.展开更多
Consider the following system of coupled Korteweg-de Vries equations, <img src="Edit_81ea1215-e696-403f-9d6c-1449e107359f.bmp" alt="" /><span style="white-space:nowrap;">where...Consider the following system of coupled Korteweg-de Vries equations, <img src="Edit_81ea1215-e696-403f-9d6c-1449e107359f.bmp" alt="" /><span style="white-space:nowrap;">where u, v <span style="white-space:nowrap;">⊆ W<sup>2,2</sup>, 2≤N≤7 and λ<sub>i</sub>,β > 0, β denotes a real coupling parameter. Firstly, we prove the existence of the solutions of a coupled system of Korteweg-de Vries equations using variation approach and minimization techniques on Nehari manifold. Then, we show the multiplicity of the equations by a bifurcation theory which is rare for studying higher order equations.展开更多
Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variat...Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.展开更多
Rayleigh-Taylor （R-T） instability is known as the fundamental mechanism of equatorial plasma bubbles （EPBs）. However, the sufficient conditions of R-T instability and stability have not yet been derived. In the pr...Rayleigh-Taylor （R-T） instability is known as the fundamental mechanism of equatorial plasma bubbles （EPBs）. However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily^derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows： if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments axe designed to validate the sufficient conditions. The results agree with the derived suf- ficient conditions.展开更多
By means of an extended variational approach,we study dynamics for gap solitons in a repulsive interactionBose-Einstein condensate under both a harmonic and an optical lattice confinement.The simplified analytic theor...By means of an extended variational approach,we study dynamics for gap solitons in a repulsive interactionBose-Einstein condensate under both a harmonic and an optical lattice confinement.The simplified analytic theorygives the critical strength ratio of harmonic to optical lattice necessary to support multiple stable lattice sites for thecondensate.Moreover,we use numerical experiments to guide and manipulate the gap solitons to an arbitrary positionvia a time-dependent potential.All predictions of the extended variational approach are reasonably close to results ofthe simulations.In particular,the variational model helps capture the composition relationship between the variationsof chirp and amplitude.展开更多
We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework ...We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework of a variational approach. The critical values of the screening parameters for the ground states of the systems under consideration are reported for which the three-body systems are stable, while all the possible fragments are unbound;that is, it shows windows for Borromean binding.展开更多
The dynamics of a dark soliton has been investigated in a Bose Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based ...The dynamics of a dark soliton has been investigated in a Bose Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.展开更多
The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtain...The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtained based on the variational approach,which provides reasonable accuracy.Linear-stability analysis shows that all the solitons are linearly stable.No collapses are found when the Levy index 1<α≤2.Forα=1,the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough.It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schrodinger equation still holds in the one-dimensional fractional Schr odinger equation.The physical mechanism for collapse prohibition is also given.展开更多
We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrodinger equations with time- varying interactions and time-varying harmonic potential. Using the variational approach, we investigate th...We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrodinger equations with time- varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright sol/tons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our modeh At the same time, we obtain the opposite situation for dark-dark solitons.展开更多
基金National Natural Science Foundation of China(No.20477030).
文摘The adsorptive precipitation between eosin Y （EY） and AgCl colloids at pH 3.73 caused the sensitive color change of the solution. The reaction mechanism between EY and AgCl was analyzed and this reaction was used for determination of Cl^- in trace level by the light-absorption radio variation approach.
文摘In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TOPEX/POSEIDON （T/P） derived datasets by means of the variational adjoint approach in such a way that unknown internal model parameters, bottom topography, friction coefficients and open boundary conditions, for example, are adjusted during the process. The numerical model is used as a forward model. After the along-track T/P data are processed, two classical methods, i.e. harmonic and response analysis, are implemented to estimate the tide from such datasets with a domain covering the model area extending from 0° to 41°N in latitude and from 99°E to 142°E in longitude. And the results of these two methods are compared and interpreted. The numerical simulation is performed for 16 major constituents. In the data assimilation experiments, three types of unknown parameters （water depth, bottom friction and tidal open boundary conditions in the model equations） are chosen as control variables. Among the various types of data assimilation experiments, the calibration of water depth brings the most promising results. By comparing the results with selected tide gauge data, the average absolute errors are decreased from 7.9 cm to 6.8 cm for amplitude and from 13.0° to 9.0° for phase with respect to the semidiurnal tide M2 constituent, which is the largest tidal constituent in the model area. After the data assimilation experiment is performed, the comparison between model results and tide gauge observation for water levels shows that the RMS errors decrease by 9 cm for a total of 14 stations, mostly selected along the coast of China's Mainland, when a one-month period is considered, and the correlation coefficients improve for most tidal stations among these stations.
基金National Natural Science Foundation of China ( No. 11171062 ) Natural Science Foundation for the Youth,China ( No.11101077) Innovation Program of Shanghai Municipal Education Commission,China ( No. 12ZZ063)
文摘One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".
基金funded by the Major National Scientific Research Plan(2013CB733305,2012CB957703)the National Natural Science Foundation of China(41174066,41131067,41374087,41431070)
文摘The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.
文摘Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanagisawa[Lr-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains,Indiana Univ.Math.J.58(2009),1853-1920],combined with global computations based on the Bochner technique.
基金supported by the National Natural Science Foundation of China(Grant Nos.11234008 and 11474189)the National Basic Research Program of China(Grant No.2011CB921601)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT13076)
文摘A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a one-dimensional(1D) harmonic potential. At the boundaries both the wave function and its first derivative are continuous and the quasi-momentum is determined by a more practical constraint condition which associates two variational parameters. The upper bound of the ground state energy is obtained by applying the variational principle to the expectation value of the Hamiltonian of relative motion on the trial wave function. The resulted energy and wave function show better agreement with the analytical solution than the original proposal.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12204545 and 12274294)the Program for NUE independent research and development。
文摘We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.
文摘More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.
文摘Images obtained from hyperspectral sensors provide information about the target area that extends beyond the visible portions of the electromagnetic spectrum.However,due to sensor limitations and imperfections during the image acquisition and transmission phases,noise is introduced into the acquired image,which can have a negative impact on downstream analyses such as classification,target tracking,and spectral unmixing.Noise in hyperspectral images(HSI)is modelled as a combination from several sources,including Gaussian/impulse noise,stripes,and deadlines.An HSI restoration method for such a mixed noise model is proposed.First,a joint optimisation framework is proposed for recovering hyperspectral data corrupted by mixed Gaussian-impulse noise by estimating both the clean data as well as the sparse/impulse noise levels.Second,a hyper-Laplacian prior is used along both the spatial and spectral dimensions to express sparsity in clean image gradients.Third,to model the sparse nature of impulse noise,anℓ_(1)−norm over the impulse noise gradient is used.Because the proposed methodology employs two distinct priors,the authors refer to it as the hyperspectral dual prior(HySpDualP)denoiser.To the best of authors'knowledge,this joint optimisation framework is the first attempt in this direction.To handle the non-smooth and nonconvex nature of the generalℓ_(p)−norm-based regularisation term,a generalised shrinkage/thresholding(GST)solver is employed.Finally,an efficient split-Bregman approach is used to solve the resulting optimisation problem.Experimental results on synthetic data and real HSI datacube obtained from hyperspectral sensors demonstrate that the authors’proposed model outperforms state-of-the-art methods,both visually and in terms of various image quality assessment metrics.
文摘The physical features exhibited by Hermite-Gaussian （HC） beams propagating in nonlocal nonlinear media with Gaussian-shaped response are discussed with an approximate variational method.Using direct numerical simulations,we find that the beam properties in the normalized system are different with the change of the degree of nonlocality.It is shown that initial HG profiles break up into several individual beams with propagation when the degree of nonlocality α is small.HG beams can propagate stably when a is large enough.
文摘Amplification of seismic ground motions in the territory of Almaty city is evaluated by using different methods. The pattern and probable causes of ground motion variations in different engineering-geological conditions are characterized. An expeditious application of these techniques within a complex methodical approach for Almaty city microzonation is considered.
文摘Based on the variational approach for pile groups embedded in soil modeled using a load-transfer curve method, a practical method was conducted to estimate the settlement of symmetric pile group supported embankments. The working mechanism of composite foundations improved by rigid or semi-rigid columns is analyzed by this method. Under equivalent strain conditions, the pile-soil stress ratio approaches the pile-soil modulus ratio up to a limited value of pile stiffness （Rm〈10）; in the subsequent stages of high pile stiffness （Rm〉10）, a further increase in the pile-soil modulus ratio cannot lead to a significant increase of stress transferred to the columns in composite foundations. The major influencing factor of the stress concentration from soil to pile in a high pile-soil modulus ratio is the padding stiffness. For the composite foundation improved by cement mixing columns, the effective column length is about 15 to 20 m and it is a more economical and effective design when the column length is less than 15 m.
文摘Consider the following system of coupled Korteweg-de Vries equations, <img src="Edit_81ea1215-e696-403f-9d6c-1449e107359f.bmp" alt="" /><span style="white-space:nowrap;">where u, v <span style="white-space:nowrap;">⊆ W<sup>2,2</sup>, 2≤N≤7 and λ<sub>i</sub>,β > 0, β denotes a real coupling parameter. Firstly, we prove the existence of the solutions of a coupled system of Korteweg-de Vries equations using variation approach and minimization techniques on Nehari manifold. Then, we show the multiplicity of the equations by a bifurcation theory which is rare for studying higher order equations.
文摘Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.
基金Project supported by the National Natural Science Foundation of China(Nos.41575026 and 41175025)
文摘Rayleigh-Taylor （R-T） instability is known as the fundamental mechanism of equatorial plasma bubbles （EPBs）. However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily^derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows： if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments axe designed to validate the sufficient conditions. The results agree with the derived suf- ficient conditions.
基金Supported by the National Natural Science Foundation of China under Grant No. 10672147the Natural Science Foundation of Zhejiang Province, China under Grant Nos. Y605312, Y1080959the Department of Education Foundation of Zhejiang Province under Grant No. 20030704
文摘By means of an extended variational approach,we study dynamics for gap solitons in a repulsive interactionBose-Einstein condensate under both a harmonic and an optical lattice confinement.The simplified analytic theorygives the critical strength ratio of harmonic to optical lattice necessary to support multiple stable lattice sites for thecondensate.Moreover,we use numerical experiments to guide and manipulate the gap solitons to an arbitrary positionvia a time-dependent potential.All predictions of the extended variational approach are reasonably close to results ofthe simulations.In particular,the variational model helps capture the composition relationship between the variationsof chirp and amplitude.
基金Supported by the National Natural Science Foundation of China under Grant No.11304086the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China under Grant No.UNPYSCT-2015019the Natural Science Foundation for Distinguished Young Scholars in Heilongjiang University under Grant No.JCL201503
文摘We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework of a variational approach. The critical values of the screening parameters for the ground states of the systems under consideration are reported for which the three-body systems are stable, while all the possible fragments are unbound;that is, it shows windows for Borromean binding.
基金Project supported by the Research Program of The Hong Kong Polytechnic University (Grant No A-PA2Q)the Scientific and Technological Research Program of Education Department of Hubei Province,China (Grant No Z200722001)
文摘The dynamics of a dark soliton has been investigated in a Bose Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.
基金supported by the National Natural Science Foundation of China(Grant No.11947122)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110935)+2 种基金the Research Start-up Foundation of Dongguan University of Technology,the Guangdong Science and Technology Planning Program(Grant No.2017A010102019)the Guangdong Province Natural Science Foundation of China(Grant Nos.2018A030307028 and 2019A1515010916)the Maoming Natural Science Foundation of Guangdong,China(Grant No.2019018001).
文摘The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtained based on the variational approach,which provides reasonable accuracy.Linear-stability analysis shows that all the solitons are linearly stable.No collapses are found when the Levy index 1<α≤2.Forα=1,the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough.It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schrodinger equation still holds in the one-dimensional fractional Schr odinger equation.The physical mechanism for collapse prohibition is also given.
基金Projects supported by the National Natural Science Foundation of China (Grant Nos. 10775049 and 10375022)
文摘We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrodinger equations with time- varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright sol/tons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our modeh At the same time, we obtain the opposite situation for dark-dark solitons.
