We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion ...We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.展开更多
Runoff series of the Yangtze River presents an intricate variation tendency under the reinforced influence of human activities.The Morlet Wavelet Transform method has been applied to analyze the annual runoff data fro...Runoff series of the Yangtze River presents an intricate variation tendency under the reinforced influence of human activities.The Morlet Wavelet Transform method has been applied to analyze the annual runoff data from 1950 to 2011 at the Yangtze River Estuary.It can clearly reveal the multi-time scales structure,break point,change and distribution of periodic variation in the different time scales of the runoff series.The main conclusions are that:1) Repeated periodic oscillations accompanied by an extremely large fluctuation are presented in the runoff series with an obvious difference between wet and dry years,and the major periods of the time series are about 3,8,16 and 23 years respectively.Among them,the presented maximum periodic oscillation is 23 years scale.2) In the 23-year time scale,the wet periods are 1950-1958,1969-1980 and 1992-2003,and the dry periods are 1959-1968,1981-1991 and 2004-2011.3) It can be predicted from the view of long time scales that the low annual runoff will likely occur in the near future.展开更多
A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate...A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate cyclically with the magnitudes of the principal stresses keeping constant. The anisotropy of the reconstituted clay is analyzed from the monotonic shearing tests. Obvious pore pressure is induced by the principal stress rotation alone even with shear stress q0=5 k Pa. Strain components also accumulate with increasing the number of cycles and increases suddenly at the onset of failure. The deviatoric shear strain of 7.5% can be taken as the failure criterion for clay subjected to the pure cyclic principal stress rotation. The intermediate principal stress parameter b plays a significant role in the development of pore pressure and strain. Specimens are weakened by cyclic rotational shearing as the shear modulus decreases with increasing the number of cycles, and the shear modulus reduces more quickly with larger b. Clear deviation between the directions of the principal plastic strain increment and the principal stress is observed during pure principal stress rotation. Both the coaxial and non-coaxial plastic mechanisms should be taken into consideration to simulate the deformation behavior of clay under pure principal stress rotation. The mechanism of the soil response to the pure principal stress rotation is discussed based on the experimental observations.展开更多
From March 2004 to February 2005,seasonal variations in lipid content and fatty acid composition of gonad of the cockle Fulvia mutica(Reeve) were studied on the eastern coast of China in relation to the reproductive c...From March 2004 to February 2005,seasonal variations in lipid content and fatty acid composition of gonad of the cockle Fulvia mutica(Reeve) were studied on the eastern coast of China in relation to the reproductive cycle and environment conditions(e.g.,temperature and food availability).Histological analysis as well as lipid and fatty acid analyses were performed on neutral and polar lipids of the gonad.Results showed that gametogenesis occurred in winter and spring at the expense of lipids previously accumulated in summer and autumn,whereas spawning occurred in summer(20.4-24.6℃).The seasonal variation in lipid content was similar to that of the mean oocyte diameter.In both neutral and polar lipids,the 20:5n-3 and 22:6n-3 levels were relatively higher than saturated fatty acids,and polyunsaturated fatty acids were abundant,with series n-3 as the predominant component.Seasonal variations in the 20:5n-3 and 22:6n-3 levels and the principal n-3 fatty acids were clearly related to the reproductive cycle.The ∑(n-3) and ∑(n-6) values were relatively high during January-May,and the associated unsaturation index was significantly higher than that in other months.The results suggest that fatty acids play an important role in the gametogenesis of F.mutica.展开更多
New exact quasi-periodic and non-periodic solutions for the (2+ 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions wit...New exact quasi-periodic and non-periodic solutions for the (2+ 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.展开更多
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+ 1)-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd ...Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+ 1)-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.展开更多
In a recent paper [Commun. Theor. Phys. (Beijing, China) 49 (2008) 268], Huang et al. gave a general variable separation solution to the (2+1)-dimensional breaking soliton equation via a special Biicldund trans...In a recent paper [Commun. Theor. Phys. (Beijing, China) 49 (2008) 268], Huang et al. gave a general variable separation solution to the (2+1)-dimensional breaking soliton equation via a special Biicldund transformation and the variable separation approach. In terms of the derived variable separation solution and by introducing Jacobi elliptic functions, they claimed that nonelastic types of interaction between Jacobi elliptic function waves are investigated both analytically and graphically. We show that some inappropriateness or errors exist in their paper, and say nothing of the conclusion that some nonelastic types of interaction between Jacobi elliptic function waves in the (2+1)-dimensional breaking soliton equation have been found.展开更多
Almost all works in the field of boundary layer flow under the breaking wave consider the flow similar as the flow in an oscillating pressure tube. Although the two flows are similar, there are many differences. The r...Almost all works in the field of boundary layer flow under the breaking wave consider the flow similar as the flow in an oscillating pressure tube. Although the two flows are similar, there are many differences. The results achieved in such manner are therefore also only similar to the results that can be achieved during measurements in the surf zone. Present article deals with boundary layer measurements on an inclined bottom under breaking waves. The measurements over the whole wave cycle were carried out, and the shear velocity under the breaking wave was calculated based on the measurements. It was found that there is a considerable space and time variation of the term in the surf zone. The turbulence generated during the wave breaking changes the shape of the shear velocity profile in comparison to the profile measured before breaking. As the values of shear velocity are directly correlated with the description of the whole velocity field in the wave, it can be assumed that the enhanced description of the shear velocity results in better understanding of the whole velocity field under breaking waves. Therefore, the article brings a new insight into the field and aims to make a discussion about the need to rethink the way of describing the boundary layer flow in the surf zone.展开更多
基金河南省自然科学基金,河南省教育厅自然科学基金,the Science Foundation of Henan University of Science and Technology
文摘We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.
基金supported by the National Key Basic Research Program of China (Grant No. 2012CB957704) Marine Public Welfare Program of China (Grant No. 201305003)
文摘Runoff series of the Yangtze River presents an intricate variation tendency under the reinforced influence of human activities.The Morlet Wavelet Transform method has been applied to analyze the annual runoff data from 1950 to 2011 at the Yangtze River Estuary.It can clearly reveal the multi-time scales structure,break point,change and distribution of periodic variation in the different time scales of the runoff series.The main conclusions are that:1) Repeated periodic oscillations accompanied by an extremely large fluctuation are presented in the runoff series with an obvious difference between wet and dry years,and the major periods of the time series are about 3,8,16 and 23 years respectively.Among them,the presented maximum periodic oscillation is 23 years scale.2) In the 23-year time scale,the wet periods are 1950-1958,1969-1980 and 1992-2003,and the dry periods are 1959-1968,1981-1991 and 2004-2011.3) It can be predicted from the view of long time scales that the low annual runoff will likely occur in the near future.
基金Projects(51338009,51178422)supported by the National Natural Science Foundation of China
文摘A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate cyclically with the magnitudes of the principal stresses keeping constant. The anisotropy of the reconstituted clay is analyzed from the monotonic shearing tests. Obvious pore pressure is induced by the principal stress rotation alone even with shear stress q0=5 k Pa. Strain components also accumulate with increasing the number of cycles and increases suddenly at the onset of failure. The deviatoric shear strain of 7.5% can be taken as the failure criterion for clay subjected to the pure cyclic principal stress rotation. The intermediate principal stress parameter b plays a significant role in the development of pore pressure and strain. Specimens are weakened by cyclic rotational shearing as the shear modulus decreases with increasing the number of cycles, and the shear modulus reduces more quickly with larger b. Clear deviation between the directions of the principal plastic strain increment and the principal stress is observed during pure principal stress rotation. Both the coaxial and non-coaxial plastic mechanisms should be taken into consideration to simulate the deformation behavior of clay under pure principal stress rotation. The mechanism of the soil response to the pure principal stress rotation is discussed based on the experimental observations.
基金the National Marine Public Welfare Research Program(201205023)the Scientific and Technical Supporting Program(2011BAD13B03)
文摘From March 2004 to February 2005,seasonal variations in lipid content and fatty acid composition of gonad of the cockle Fulvia mutica(Reeve) were studied on the eastern coast of China in relation to the reproductive cycle and environment conditions(e.g.,temperature and food availability).Histological analysis as well as lipid and fatty acid analyses were performed on neutral and polar lipids of the gonad.Results showed that gametogenesis occurred in winter and spring at the expense of lipids previously accumulated in summer and autumn,whereas spawning occurred in summer(20.4-24.6℃).The seasonal variation in lipid content was similar to that of the mean oocyte diameter.In both neutral and polar lipids,the 20:5n-3 and 22:6n-3 levels were relatively higher than saturated fatty acids,and polyunsaturated fatty acids were abundant,with series n-3 as the predominant component.Seasonal variations in the 20:5n-3 and 22:6n-3 levels and the principal n-3 fatty acids were clearly related to the reproductive cycle.The ∑(n-3) and ∑(n-6) values were relatively high during January-May,and the associated unsaturation index was significantly higher than that in other months.The results suggest that fatty acids play an important role in the gametogenesis of F.mutica.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 90203001 and 10475055 Acknowledgment The authors are indebt to the discussions with Dr H.C. Hu
文摘New exact quasi-periodic and non-periodic solutions for the (2+ 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.
基金The project supported by the National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province of China under Grant No. Y504111, and the Science Research Foundation of Huzhou University
文摘Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+ 1)-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.
基金supported by National Natural Science Foundation of China under Grant No. 10272071the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106
文摘In a recent paper [Commun. Theor. Phys. (Beijing, China) 49 (2008) 268], Huang et al. gave a general variable separation solution to the (2+1)-dimensional breaking soliton equation via a special Biicldund transformation and the variable separation approach. In terms of the derived variable separation solution and by introducing Jacobi elliptic functions, they claimed that nonelastic types of interaction between Jacobi elliptic function waves are investigated both analytically and graphically. We show that some inappropriateness or errors exist in their paper, and say nothing of the conclusion that some nonelastic types of interaction between Jacobi elliptic function waves in the (2+1)-dimensional breaking soliton equation have been found.
文摘Almost all works in the field of boundary layer flow under the breaking wave consider the flow similar as the flow in an oscillating pressure tube. Although the two flows are similar, there are many differences. The results achieved in such manner are therefore also only similar to the results that can be achieved during measurements in the surf zone. Present article deals with boundary layer measurements on an inclined bottom under breaking waves. The measurements over the whole wave cycle were carried out, and the shear velocity under the breaking wave was calculated based on the measurements. It was found that there is a considerable space and time variation of the term in the surf zone. The turbulence generated during the wave breaking changes the shape of the shear velocity profile in comparison to the profile measured before breaking. As the values of shear velocity are directly correlated with the description of the whole velocity field in the wave, it can be assumed that the enhanced description of the shear velocity results in better understanding of the whole velocity field under breaking waves. Therefore, the article brings a new insight into the field and aims to make a discussion about the need to rethink the way of describing the boundary layer flow in the surf zone.