A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This mode...A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This model includes much more physiological factors. It couples the interaction of blood flow with mechanical factors such as the displacement, deformation, strain and stress etc. of the curved blood vessel. It is of great importance for investigating the circulation rules of the cardiovascular system and the nonlinear pulse wave propagation in curved blood vessels.展开更多
We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves ...In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motion of curves in the Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers＇ equations.展开更多
Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of ...Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.展开更多
In this study, the kinetic energy formula of the projection curve under 1-parameter closed homothetic motion is expressed and as a result, theorem is given. Also some special cases are given related with that formula.
It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping r...The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.展开更多
Investigated in this study is the flow induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system und...Investigated in this study is the flow induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.展开更多
In this paper,numerical investigations for peristaltic motion of dusty nanofluids in a curved channel are performed.Two systems of partial differential equations are presented for the nanofluid and dusty phases and th...In this paper,numerical investigations for peristaltic motion of dusty nanofluids in a curved channel are performed.Two systems of partial differential equations are presented for the nanofluid and dusty phases and then the approximations of the long wave length and low Reynolds number are applied.The physical domain is transformed to a rectangular computational model using suitable grid transformations.The resulting systems are solved numerically using shooting method and mathematical forms for the pressure distributions are introduced.The controlling parameters in this study are the thermal buoyancy parameter G_(r),the concentration buoyancy parameter Gc,the amplitude ratio,the Eckert number Ec,the thermophoresis parameter N_(t) and the Brownian motion parameter Nb and the dusty parameters D_(s);α_(s).The obtained results revealed that an increase in the Eckert number enhances the temperature of the fluid and dusty particles while the nanoparticle volume fraction is reduced.Also,both of the temperature and nanoparticles volume fraction are supported by the growing of the Brownian motion parameter.展开更多
In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the c...In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the chaotic domain and principal resonance curve is discussed. By analyzing the stability of principal resonance curve weinfer that chaotic motion would occur near the frequency at which the principalresonance curve has vertical tangent.Results of numerical simulation confirm thisinference.Thus we offer an effective way to seek the chaotic motion of the systems which are hard to he investigated by Melnikoy method.展开更多
We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kine...We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kinematic surfaces with scalar curvature K is non-zero constant. We describe the equations that govern such the surfaces.展开更多
The time-frequency analysis of the signal acquired by a single ground-based microphone shows a two-dimensional interference pattern in the time-frequency plane,which is caused by the time delay of the received signal ...The time-frequency analysis of the signal acquired by a single ground-based microphone shows a two-dimensional interference pattern in the time-frequency plane,which is caused by the time delay of the received signal emitted from a low flying aircraft via the direct path and the ground-re-flected path. A model is developed for estimating the motion parameters of an aircraft flying along a straight line at a constant height and with a constant speed. Monte Carlo simulation results and ex-perimental results are presented to validate the model,and an error analysis of the model is presented to verify the effectiveness of the estimation scheme advocated.展开更多
基金Project supported by the National Natural Science Foundation of China(No.19872009)the Foundation of University Key Teachers by the Ministry of Education(No.GG-831-10005-1497)
文摘A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This model includes much more physiological factors. It couples the interaction of blood flow with mechanical factors such as the displacement, deformation, strain and stress etc. of the curved blood vessel. It is of great importance for investigating the circulation rules of the cardiovascular system and the nonlinear pulse wave propagation in curved blood vessels.
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
文摘In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motion of curves in the Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers＇ equations.
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10371098 and the Natural Science Foundation of Shaanxi Province of ChinaIt is my pleasure to thank Prof. Qu Chang-Zheng for his helpful discussion
文摘Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.
文摘In this study, the kinetic energy formula of the projection curve under 1-parameter closed homothetic motion is expressed and as a result, theorem is given. Also some special cases are given related with that formula.
文摘It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
文摘Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
基金Project supported by the National Science and Technology Major Project(NMP)of China(No.2013ZX04011-011)
文摘The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.
文摘Investigated in this study is the flow induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.
基金the Deanship of Scientific Research atKing Khalid University for funding this work through research groups program under Grant Number(R.G.P2/72/41).
文摘In this paper,numerical investigations for peristaltic motion of dusty nanofluids in a curved channel are performed.Two systems of partial differential equations are presented for the nanofluid and dusty phases and then the approximations of the long wave length and low Reynolds number are applied.The physical domain is transformed to a rectangular computational model using suitable grid transformations.The resulting systems are solved numerically using shooting method and mathematical forms for the pressure distributions are introduced.The controlling parameters in this study are the thermal buoyancy parameter G_(r),the concentration buoyancy parameter Gc,the amplitude ratio,the Eckert number Ec,the thermophoresis parameter N_(t) and the Brownian motion parameter Nb and the dusty parameters D_(s);α_(s).The obtained results revealed that an increase in the Eckert number enhances the temperature of the fluid and dusty particles while the nanoparticle volume fraction is reduced.Also,both of the temperature and nanoparticles volume fraction are supported by the growing of the Brownian motion parameter.
文摘In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the chaotic domain and principal resonance curve is discussed. By analyzing the stability of principal resonance curve weinfer that chaotic motion would occur near the frequency at which the principalresonance curve has vertical tangent.Results of numerical simulation confirm thisinference.Thus we offer an effective way to seek the chaotic motion of the systems which are hard to he investigated by Melnikoy method.
文摘We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kinematic surfaces with scalar curvature K is non-zero constant. We describe the equations that govern such the surfaces.
文摘The time-frequency analysis of the signal acquired by a single ground-based microphone shows a two-dimensional interference pattern in the time-frequency plane,which is caused by the time delay of the received signal emitted from a low flying aircraft via the direct path and the ground-re-flected path. A model is developed for estimating the motion parameters of an aircraft flying along a straight line at a constant height and with a constant speed. Monte Carlo simulation results and ex-perimental results are presented to validate the model,and an error analysis of the model is presented to verify the effectiveness of the estimation scheme advocated.
