As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered a...As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.展开更多
Aiming at the mode mixture in local wave decomposition（LWD） caused by a noise signal, the original data is preprocessed using the lifting wavelet transformation to suppress abnormal interference of noise and improve...Aiming at the mode mixture in local wave decomposition（LWD） caused by a noise signal, the original data is preprocessed using the lifting wavelet transformation to suppress abnormal interference of noise and improve the quality of decomposition. It is employed to analyze the vibration signal of rotor rub-impact for extracting the weak impulsive feature. The signal is decomposed into intrinsic mode functions by LWD, then the high-frequency components are analyzed by Hilbert envelop demodulation. The period of the impulse response can be achieved, and the modulate fault feature of the vibration signal of a rotor system with rub-impact fault can be extracted exactly. Analysis results show that the proposed method is accurate and efficient, and is expected to be applied in engineering practice effectively.展开更多
The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noi...The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.展开更多
A new method of fault analysis and detection by signal classification inrotating machines is presented. The Local Wave time-frequency spectrum which is a new method forprocessing a non-stationary signal is used to pro...A new method of fault analysis and detection by signal classification inrotating machines is presented. The Local Wave time-frequency spectrum which is a new method forprocessing a non-stationary signal is used to produce the representation of the signal. This methodallows the decomposition of one-dimensional signals into intrinsic mode functions (IMFs) usingempirical mode decomposition and the calculation of a meaningful multi-component instantaneousfrequency. Applied to fault signals , it provides new time-frequency attributes. Then the momentsand margins of the time-frequency spectrum are calculated as the feature vectors. The probabilisticneural network is used to classify different fault modes. The accuracy and robustness of theproposed methods is investigated on signals obtained during the different fault modes (early rub,loose, misalignment of the rotor).展开更多
To diagnosethe reciprocating mechanical fault.We utilizedlocal waveti me-frequency approach.Firstly,we gave the principle.Secondly,the application of local wave ti me-frequency was given.Finally,we discusseditsvirtue ...To diagnosethe reciprocating mechanical fault.We utilizedlocal waveti me-frequency approach.Firstly,we gave the principle.Secondly,the application of local wave ti me-frequency was given.Finally,we discusseditsvirtue in reciprocating mechanical fault diagnosis.展开更多
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a c...The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method.From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation,we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation.These solutions,including soliton solutions,Jordan-block solutions and interaction solutions,exhibit localized structure,whose dynamics are analyzed with graphical illustration.The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.展开更多
In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of media.The nonisospectral Korteweg–de Vries,modified Korte...In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of media.The nonisospectral Korteweg–de Vries,modified Korteweg–de Vries and the Hirota equations are employed to demonstrate the idea.Their solutions are presented in terms of Wronskians and double Wronskians and space-time localized dynamics are illustrated.展开更多
The 1 dimensional localization of elastic waves in disordered periodic multi span rib stiffened plates is investigated. The transfer matrix method is employed to obtain the transfer matrix of the system, and the metho...The 1 dimensional localization of elastic waves in disordered periodic multi span rib stiffened plates is investigated. The transfer matrix method is employed to obtain the transfer matrix of the system, and the method for calculating the Lyapunov exponents in continuous dynamic systems presented by Wolf is used to determine the localization factor. As examples, the numerical results of the localization factors are given for a disordered rib stiffened plate. The effects of the degree of disorder of span...展开更多
A series of physical model tests are conducted for local scour around a circular cylinder of a relatively large diameter (0 15< D/L <0.5) under the action of irregular waves. The laws of change of the topogra...A series of physical model tests are conducted for local scour around a circular cylinder of a relatively large diameter (0 15< D/L <0.5) under the action of irregular waves. The laws of change of the topography around the cylinder are systematically studied. The effects of wave height, wave period, water depth, sediment grain size and cylinder diameter are taken into account. The mechanism of formation of the topography around the cylinder is analyzed. A detailed analysis is given to bed sediment grain size, and it is considered that the depth of scour around the cylinder under wave action is not inversely proportional to the sediment grain diameter. On such a basis, an equation is proposed for calculation of the maximum depth of scour around a cylinder as well as its position under the action of irregular waves.展开更多
In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the mater...In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.展开更多
We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,...We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.展开更多
We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of ...We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of the rolls perpendic- ular to their axes. For a negative enough separation ratio, two types of quite different confined states were documented by applying different control processes. One branch of localized travelling waves survives only in a very narrow band within subcritical regime, while another branch straddles the onset of convection existing both in subcritical and super- critical regions. We elucidated that concentration field and its current are key to understand how confined convection is sustained when conductive state is absolutely unstable, The weak structures in the conducting region are demonstrated too.展开更多
We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector sol...We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed：（i） the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; （ii） hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; （iii） hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.展开更多
A horizontal two-dimensional numerical model is developed for estimation of sediment transport and sea bed change around it large circular cylinder tinder wave action, The wave model is based on an elliptic mild slope...A horizontal two-dimensional numerical model is developed for estimation of sediment transport and sea bed change around it large circular cylinder tinder wave action, The wave model is based on an elliptic mild slope equation. The wave-induced current by the gradient of radiation stress is considered and a depth integrated shallow water equation is applied to the calculation of the current. The mass transport velocity and the bed shear stress due to streaming are considered, which are important factors affecting the sediment transport around a structure due to waves, especially in reflective areas. Wave-current interaction is taken into account in the model for computing the bed shear stress. The model is implemented by it finite element method, The results of this model are compared with those from other methods and agree well with experimental data.展开更多
The model tests are performed with regular waves, and the effect of wave height, wave period, water depth, sediment size and pile diameter is evaluated. The shape and size of local scour around piles are studied. Ther...The model tests are performed with regular waves, and the effect of wave height, wave period, water depth, sediment size and pile diameter is evaluated. The shape and size of local scour around piles are studied. There are three typical scour patterns due to wave action. It is found that a relationship exists between the erosion depth and the wave number. An empirical formula of the maximum local scour is thus derived.展开更多
In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set ...In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set of triple integral equations is solved using anew method, namely Schimidt's method. This method is more exact andmore reasonable than Erigen's for solving this Kind of problem. Theresult of the stress near the crack tip was obtained. Contrary to theclassical elas- Ticity solution, it is found that no stresssingularity is present at the crack tip, which can explain theProblem of macroscopic and microscopic mechanics.展开更多
Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjuga...Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjugation conditions to the related solitons,some novel localized wave solutions are obtained,which contain higher-order breathers and lumps as well as their interactions.In particular,by choosing appropriate parameters involved in the N-solitons,two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution.Five solutions including two breathers,two lumps,and interaction solutions between one breather and two bell-shaped solitons,one breather and one lump,or one lump and two bell-shaped solitons are constructed from the4-soliton solution.Five interaction solutions mixed by one breather/lump and three bell-shaped solitons,two breathers/lumps and a bell-shaped soliton,as well as mixing with one lump,one breather and a bell-shaped soliton are constructed from the 5-soliton solution.To study the behaviors that the obtained interaction solutions may have,we present some illustrative numerical simulations,which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties.The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations.The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 61075118,Grant No. 61005056,Grant No. 60975016)National Key Technology Support Program of China (Grant No. 2007BAH11B02)+1 种基金Zhejiang Provincial Natural Science Foundation of China (Grant No. Y1100880)Open Project Program of State Key Laboratory of CAD&CG of China (Grant No. A0906)
文摘As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.
基金supported by National Natural Science Foundation of China under Grant No. 50805014
文摘Aiming at the mode mixture in local wave decomposition（LWD） caused by a noise signal, the original data is preprocessed using the lifting wavelet transformation to suppress abnormal interference of noise and improve the quality of decomposition. It is employed to analyze the vibration signal of rotor rub-impact for extracting the weak impulsive feature. The signal is decomposed into intrinsic mode functions by LWD, then the high-frequency components are analyzed by Hilbert envelop demodulation. The period of the impulse response can be achieved, and the modulate fault feature of the vibration signal of a rotor system with rub-impact fault can be extracted exactly. Analysis results show that the proposed method is accurate and efficient, and is expected to be applied in engineering practice effectively.
文摘The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.
文摘A new method of fault analysis and detection by signal classification inrotating machines is presented. The Local Wave time-frequency spectrum which is a new method forprocessing a non-stationary signal is used to produce the representation of the signal. This methodallows the decomposition of one-dimensional signals into intrinsic mode functions (IMFs) usingempirical mode decomposition and the calculation of a meaningful multi-component instantaneousfrequency. Applied to fault signals , it provides new time-frequency attributes. Then the momentsand margins of the time-frequency spectrum are calculated as the feature vectors. The probabilisticneural network is used to classify different fault modes. The accuracy and robustness of theproposed methods is investigated on signals obtained during the different fault modes (early rub,loose, misalignment of the rotor).
文摘To diagnosethe reciprocating mechanical fault.We utilizedlocal waveti me-frequency approach.Firstly,we gave the principle.Secondly,the application of local wave ti me-frequency was given.Finally,we discusseditsvirtue in reciprocating mechanical fault diagnosis.
基金Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
基金supported by the National Natural Science Foundation of China(Grant No.12071432)Zhejiang Provincial Natural Science Foundation(Grant No.LZ24A010007)。
文摘The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method.From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation,we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation.These solutions,including soliton solutions,Jordan-block solutions and interaction solutions,exhibit localized structure,whose dynamics are analyzed with graphical illustration.The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.
基金supported by the National Natural Science Foundation of China(Nos.11875040 and 11571225)。
文摘In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of media.The nonisospectral Korteweg–de Vries,modified Korteweg–de Vries and the Hirota equations are employed to demonstrate the idea.Their solutions are presented in terms of Wronskians and double Wronskians and space-time localized dynamics are illustrated.
基金National Natural Science F oundation of China (19972 0 18) and Projectsupported by the National Key Basic Research Foun-dation of China (G19980 2 0 3 17)
文摘The 1 dimensional localization of elastic waves in disordered periodic multi span rib stiffened plates is investigated. The transfer matrix method is employed to obtain the transfer matrix of the system, and the method for calculating the Lyapunov exponents in continuous dynamic systems presented by Wolf is used to determine the localization factor. As examples, the numerical results of the localization factors are given for a disordered rib stiffened plate. The effects of the degree of disorder of span...
基金Project supported by the National Science Fund of Distinguished Young Scholars (No.10025211) the NJTU Paper Foundation (No.PD250) and the China Postdoctoral Science Foundation.
文摘A series of physical model tests are conducted for local scour around a circular cylinder of a relatively large diameter (0 15< D/L <0.5) under the action of irregular waves. The laws of change of the topography around the cylinder are systematically studied. The effects of wave height, wave period, water depth, sediment grain size and cylinder diameter are taken into account. The mechanism of formation of the topography around the cylinder is analyzed. A detailed analysis is given to bed sediment grain size, and it is considered that the depth of scour around the cylinder under wave action is not inversely proportional to the sediment grain diameter. On such a basis, an equation is proposed for calculation of the maximum depth of scour around a cylinder as well as its position under the action of irregular waves.
基金The project supported by the National Natural Science Foundation of China(90405016,10572044)the Specialized Research Fund for the Doctoral Program of Higher Education(20040213034)
文摘In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11275072 and 11435005)+2 种基金the Doctoral Program of Higher Education of China(Grant No.20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China(Grant No.61321064)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things,China(Grant No.ZF1213)
文摘We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.
文摘We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of the rolls perpendic- ular to their axes. For a negative enough separation ratio, two types of quite different confined states were documented by applying different control processes. One branch of localized travelling waves survives only in a very narrow band within subcritical regime, while another branch straddles the onset of convection existing both in subcritical and super- critical regions. We elucidated that concentration field and its current are key to understand how confined convection is sustained when conductive state is absolutely unstable, The weak structures in the conducting region are demonstrated too.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11675054 and 11435005)+1 种基金the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)the Natural Science Foundation of Hebei Province,China(Grant No.A2014210140)
文摘We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed：（i） the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; （ii） hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; （iii） hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.
基金The present work is financially supported by the National Natural Science Foundation of China (Grant No. 19732040 and No.50025924)
文摘A horizontal two-dimensional numerical model is developed for estimation of sediment transport and sea bed change around it large circular cylinder tinder wave action, The wave model is based on an elliptic mild slope equation. The wave-induced current by the gradient of radiation stress is considered and a depth integrated shallow water equation is applied to the calculation of the current. The mass transport velocity and the bed shear stress due to streaming are considered, which are important factors affecting the sediment transport around a structure due to waves, especially in reflective areas. Wave-current interaction is taken into account in the model for computing the bed shear stress. The model is implemented by it finite element method, The results of this model are compared with those from other methods and agree well with experimental data.
文摘The model tests are performed with regular waves, and the effect of wave height, wave period, water depth, sediment size and pile diameter is evaluated. The shape and size of local scour around piles are studied. There are three typical scour patterns due to wave action. It is found that a relationship exists between the erosion depth and the wave number. An empirical formula of the maximum local scour is thus derived.
文摘In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set of triple integral equations is solved using anew method, namely Schimidt's method. This method is more exact andmore reasonable than Erigen's for solving this Kind of problem. Theresult of the stress near the crack tip was obtained. Contrary to theclassical elas- Ticity solution, it is found that no stresssingularity is present at the crack tip, which can explain theProblem of macroscopic and microscopic mechanics.
基金supported by the National Natural Science Foundation of China under grant No.11775116Jiangsu Qinglan highlevel talent Project。
文摘Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjugation conditions to the related solitons,some novel localized wave solutions are obtained,which contain higher-order breathers and lumps as well as their interactions.In particular,by choosing appropriate parameters involved in the N-solitons,two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution.Five solutions including two breathers,two lumps,and interaction solutions between one breather and two bell-shaped solitons,one breather and one lump,or one lump and two bell-shaped solitons are constructed from the4-soliton solution.Five interaction solutions mixed by one breather/lump and three bell-shaped solitons,two breathers/lumps and a bell-shaped soliton,as well as mixing with one lump,one breather and a bell-shaped soliton are constructed from the 5-soliton solution.To study the behaviors that the obtained interaction solutions may have,we present some illustrative numerical simulations,which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties.The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations.The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.
