The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the(1+2)-dimensional Minkowski space to an arbitrary compact smooth Riemannian mani...The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the(1+2)-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. The author can also treat non-compact manifold under some additional assumptions which generalize the existing ones.展开更多
When a target manifold is complete with a bounded curvature, we prove that there exists a unique global solution which satisfies the Euler-lagrange equation of for the given Cauchy data.
A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original gener...A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original generalized complex Burgers equation is obtained. This method can find the approximation of arbitrary order of precision simply and reliably.展开更多
A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can a...A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can analyse operations sequentially.展开更多
In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses...In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.展开更多
The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been s...The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.展开更多
Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an a...Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an algorithm for detecting TWA using Poincare mapping method which is a technique for nonlinear dynamic systems to display periodic behavior. Sample series of beat to beat cycles were selected to prepare Poincare mapping method. Vector Angle Index (VAI), which is the mean of the difference between θi (the angle between the line connecting the i point to the origin and the X axis) and 45 degrees was used to present the presence or absence of TWA. The value of 0.9 rad ≤ VAI ≤ 1.03 rad is accepted as a level determinative for presence of TWA. VAI via Poincare mapping method (PM) is used for correlation analysis with T-wave alternans voltage (Vtwa) by way of the spectral method (SM). The cross-correlation coefficient between Vtwa and VAI is γ = 0.8601. The algorithm can identify the absence and presence of TWA accurately and provide idea for further study of TWA-PM.展开更多
The effect of fragrances on drivers has been examined, in order to optimize driver’s condition during driving. A map that can clearly show the positioning of various fragrances is created as an initial step of this r...The effect of fragrances on drivers has been examined, in order to optimize driver’s condition during driving. A map that can clearly show the positioning of various fragrances is created as an initial step of this research and development. Sensory evaluation data of 12 kinds of fragrance samples, which are tested on 64 subjects, are used for the creation of this map. The “Aromatic Image Map” can be used to confirm the distribution of the characteristics and the subjects’ preferences for each fragrance. Furthermore, the validity of the “Aromatic Image Map” is inspected experimentally, based on the difference in recovery from stress among the fragrances. Six subjects participate in the experiment, and the four kinds of fragrances that stand at the specific positions on the “Aromatic Image Map” are used. As a result, this enables us to inspect the validity of the position of each fragrance on “Aromatic Image Map”.展开更多
On the basis of maps of sea level anomalies data set from October 1992 to January 2004, pronounced low frequency variations with periods of about 500 d are detected in the area near 20°N from 160°W to 130...On the basis of maps of sea level anomalies data set from October 1992 to January 2004, pronounced low frequency variations with periods of about 500 d are detected in the area near 20°N from 160°W to 130°E. A linear two-layer model is employed to explain the mechanism. It is found that the first-mode long baroclinic Rossby waves at 20°N in the northwest Pacific propagate westward in the form of free waves at a speed of about 10.3 cm/s. This confirms that the observed low frequency variabilities appear as baroclinic Rossby waves. It further shows that these low frequency variabilities around 20°N in the northwest Pacific can potentially be predicted with a lead up to 900 d.展开更多
The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the com...The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Furthermore appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacements of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method (FEM).展开更多
Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with...Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV展开更多
Guwahati, the major city in the North Eastern region of India is growing rapidly in every aspect with major infrastructures like sports complex, educational institutions, hospitals, flyovers, multiplex halls, etc. Kno...Guwahati, the major city in the North Eastern region of India is growing rapidly in every aspect with major infrastructures like sports complex, educational institutions, hospitals, flyovers, multiplex halls, etc. Knowledge of the subsurface soil condition is necessary to ensure the structural safety and serviceability of the above mentioned structures before any construction. Therefore, contour maps of Standard penetration test N value, ground water table and shear wave velocity map using Geographical Information System (GIS) platform will be of great help to the foundation designers at the initial stage for site selection and preliminary foundation design under static and seismic condition. Contour maps of Standard penetration test N value at different depth and average contour map of N value of Guwahati city have been prepared. Standard penetration Test N values and depth of water table were taken from a data base of 200 boreholes up to 30 meter depth to prepare N value contour map of Guwahati city. A regression equation between shear wave velocity V<sub>s</sub> and Standard penetration test N value based on twenty seven previous similar correlations was also developed. This regression equation was used to determine shear wave velocity of Guwahati city. The average shear wave velocities for 30 m depth for all locations had been determined and used to generate map on (GIS) platform. Other subsurface geotechnical information of Guwahati city like soil classification and depth to water level from ground surface is also presented in the form of GIS based maps in order to form a data base.展开更多
By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is de...By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.展开更多
Because zero-offset VSP (Vertical Seismic Profile) data can only provide the information of rock properties and structure in the area around the Fresnel zone within the well, the scheme of VSP with offset was develope...Because zero-offset VSP (Vertical Seismic Profile) data can only provide the information of rock properties and structure in the area around the Fresnel zone within the well, the scheme of VSP with offset was developed to acquire the reflection information away from the borehole in order to widen the range of VSP survey and to improve the precision of imaging. In this paper, we present a new CDP (Common Depth Point) mapping approach to image the reflecting structure by using offset VSP data. For the processing of offSet VSP data, we firstly separated the up-going and down-going wave-fields from VSP data by means of F-K filtering technique, and we can calculate the mapping conditions (position and reflecting traveltime for CDP point) in homogeneous media, and then reconstruct the inner structure of the earth. This method is tested by using the offset VSP data which are used to simulate the case of super-deep borehole by means of finite-difference method. The imaged structure matches the real model very well. The results show that the method present here could accurately image the inner structure of the earth if the deviation of initial velocity model from the true model is less than 10%. Finally, we presented the imaged results for the real offset data by using this method.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem...By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.展开更多
In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional diss...In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.展开更多
基金supported by the National Natural Science Foundation of China(No.12171097)the Key Laboratory of Mathematics for Nonlinear Sciences(Fudan University),Ministry of Education of China,Shanghai Key Laboratory for Contemporary Applied Mathematics,School of Mathematical Sciences,Fudan UniversityShanghai Science and Technology Program(No.21JC1400600)。
文摘The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the(1+2)-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. The author can also treat non-compact manifold under some additional assumptions which generalize the existing ones.
文摘When a target manifold is complete with a bounded curvature, we prove that there exists a unique global solution which satisfies the Euler-lagrange equation of for the given Cauchy data.
基金Project supported by the National Natural Science Foundation of China （Grant No. 40876010）, the Main Direction Program of the Knowledge Innovation Project of the Chinese Academy of Sciences （Grant No. KZCX2-YW-Q03-08）, the R ＆ D Special Fund for Public Welfare Industry （Meteorology） （Grant No. GYHY200806010）, the LASG State Key Laboratory Special Fund, the Foundation of E-Institutes of Shanghai Municipal Education Commission （Crant No. E03004） and the Natural Science Foundation of Zhejiang Province of China （Grant No. Y6090164）.
文摘A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original generalized complex Burgers equation is obtained. This method can find the approximation of arbitrary order of precision simply and reliably.
基金Project supported by the National Natural Science Foundation of China (Grant No. 40876010)the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KZCX2-YW-Q03-08)+1 种基金LASG State Key Laboratory Special Fund,E-Institutes of Shanghai Municipal Education Commission (Grant No. E03004)the Natural Science Foundation of Zhejiang Province,China(Grant No. Y6090L4)
文摘A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can analyse operations sequentially.
基金supported by the National Natural Science Foundation of China(51178037,10632020)the 973 State Key Development Program for Basic Research of China(2010CB732104)
文摘In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.
基金supported by the National Natural Science Foundation of China (90916007 and 91116008)
文摘The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.
文摘Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an algorithm for detecting TWA using Poincare mapping method which is a technique for nonlinear dynamic systems to display periodic behavior. Sample series of beat to beat cycles were selected to prepare Poincare mapping method. Vector Angle Index (VAI), which is the mean of the difference between θi (the angle between the line connecting the i point to the origin and the X axis) and 45 degrees was used to present the presence or absence of TWA. The value of 0.9 rad ≤ VAI ≤ 1.03 rad is accepted as a level determinative for presence of TWA. VAI via Poincare mapping method (PM) is used for correlation analysis with T-wave alternans voltage (Vtwa) by way of the spectral method (SM). The cross-correlation coefficient between Vtwa and VAI is γ = 0.8601. The algorithm can identify the absence and presence of TWA accurately and provide idea for further study of TWA-PM.
文摘The effect of fragrances on drivers has been examined, in order to optimize driver’s condition during driving. A map that can clearly show the positioning of various fragrances is created as an initial step of this research and development. Sensory evaluation data of 12 kinds of fragrance samples, which are tested on 64 subjects, are used for the creation of this map. The “Aromatic Image Map” can be used to confirm the distribution of the characteristics and the subjects’ preferences for each fragrance. Furthermore, the validity of the “Aromatic Image Map” is inspected experimentally, based on the difference in recovery from stress among the fragrances. Six subjects participate in the experiment, and the four kinds of fragrances that stand at the specific positions on the “Aromatic Image Map” are used. As a result, this enables us to inspect the validity of the position of each fragrance on “Aromatic Image Map”.
基金This study was supported by the National Natural Science Foundation of China under contract Nos 40136010 and 40520140074.
文摘On the basis of maps of sea level anomalies data set from October 1992 to January 2004, pronounced low frequency variations with periods of about 500 d are detected in the area near 20°N from 160°W to 130°E. A linear two-layer model is employed to explain the mechanism. It is found that the first-mode long baroclinic Rossby waves at 20°N in the northwest Pacific propagate westward in the form of free waves at a speed of about 10.3 cm/s. This confirms that the observed low frequency variabilities appear as baroclinic Rossby waves. It further shows that these low frequency variabilities around 20°N in the northwest Pacific can potentially be predicted with a lead up to 900 d.
文摘The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Furthermore appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacements of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method (FEM).
基金Project supported by the National Natural Science Foundation of China （Grant No 10172056）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y604106）, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Zhejiang Provincial Education Department of China （Grant No 20070568） and the Natural Science Foundation of Zhejiang Lishui University （Grant No KZ04008）.
文摘Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV
文摘Guwahati, the major city in the North Eastern region of India is growing rapidly in every aspect with major infrastructures like sports complex, educational institutions, hospitals, flyovers, multiplex halls, etc. Knowledge of the subsurface soil condition is necessary to ensure the structural safety and serviceability of the above mentioned structures before any construction. Therefore, contour maps of Standard penetration test N value, ground water table and shear wave velocity map using Geographical Information System (GIS) platform will be of great help to the foundation designers at the initial stage for site selection and preliminary foundation design under static and seismic condition. Contour maps of Standard penetration test N value at different depth and average contour map of N value of Guwahati city have been prepared. Standard penetration Test N values and depth of water table were taken from a data base of 200 boreholes up to 30 meter depth to prepare N value contour map of Guwahati city. A regression equation between shear wave velocity V<sub>s</sub> and Standard penetration test N value based on twenty seven previous similar correlations was also developed. This regression equation was used to determine shear wave velocity of Guwahati city. The average shear wave velocities for 30 m depth for all locations had been determined and used to generate map on (GIS) platform. Other subsurface geotechnical information of Guwahati city like soil classification and depth to water level from ground surface is also presented in the form of GIS based maps in order to form a data base.
基金Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6100257 and Y6110140)
文摘By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.
文摘Because zero-offset VSP (Vertical Seismic Profile) data can only provide the information of rock properties and structure in the area around the Fresnel zone within the well, the scheme of VSP with offset was developed to acquire the reflection information away from the borehole in order to widen the range of VSP survey and to improve the precision of imaging. In this paper, we present a new CDP (Common Depth Point) mapping approach to image the reflecting structure by using offset VSP data. For the processing of offSet VSP data, we firstly separated the up-going and down-going wave-fields from VSP data by means of F-K filtering technique, and we can calculate the mapping conditions (position and reflecting traveltime for CDP point) in homogeneous media, and then reconstruct the inner structure of the earth. This method is tested by using the offset VSP data which are used to simulate the case of super-deep borehole by means of finite-difference method. The imaged structure matches the real model very well. The results show that the method present here could accurately image the inner structure of the earth if the deviation of initial velocity model from the true model is less than 10%. Finally, we presented the imaged results for the real offset data by using this method.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
文摘By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.
文摘In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.
