In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized...This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized coordinate which represents rotation around transversal main central axis of inertia of undercarriage.The excavator is described by a system of six nonlinear,nonhomogenous differential equations of the second kind.Numerical analysis of the differential equations has been done for BTH-600 hydraulic excavator with moving mechanism with pneumatic wheels.展开更多
In this paper, we obtain some global existence results for the higher-dimensionai nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semigroup approach.
In this paper,we consider the admissibility for nonhomogeneous linear estimates on regression coefficients and parameters in multivariate random effect linear model and give eight definitions of different forms for ad...In this paper,we consider the admissibility for nonhomogeneous linear estimates on regression coefficients and parameters in multivariate random effect linear model and give eight definitions of different forms for admissibility. We not only prove that they can be divided into three identical subclasses,but also gain three kinds of necessary and sufficient conditions.展开更多
We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We c...We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo- Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.展开更多
Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-lik...Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable.展开更多
An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.
In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smo...In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smooth solutions for its Cauchy problem.展开更多
We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger (NLS) equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried...We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger (NLS) equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.展开更多
A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbala...A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.展开更多
The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schr6dinger equa...The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schr6dinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.展开更多
The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonl...The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.展开更多
In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial con...In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial convergence conclusion of the general heterogeneous HK dynamics.That is,there must be some agents who will reach static states in finite time,while the other opinions have to evolve between them with a minimum distance if all the opinions does not reach consensus.And this result leads to the convergence of several special cases of heterogeneous HK dynamics,including when the minimum confidence bound is large enough,the initial opinion difference is small enough,and so on.展开更多
The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field i...The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.展开更多
The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous dom- ination approach, a homogene...The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous dom- ination approach, a homogeneous observer and an output feedback controller with a scaling gain are designed. Then the sealing gain is adjusted such that the closed-loop system is semi-global asymptoti- cally stable. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.展开更多
The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solu...The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch.Rational Mech.Anal.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.展开更多
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
文摘This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized coordinate which represents rotation around transversal main central axis of inertia of undercarriage.The excavator is described by a system of six nonlinear,nonhomogenous differential equations of the second kind.Numerical analysis of the differential equations has been done for BTH-600 hydraulic excavator with moving mechanism with pneumatic wheels.
基金Supported by the NNSF of China(10571024, 10871040)
文摘In this paper, we obtain some global existence results for the higher-dimensionai nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semigroup approach.
文摘In this paper,we consider the admissibility for nonhomogeneous linear estimates on regression coefficients and parameters in multivariate random effect linear model and give eight definitions of different forms for admissibility. We not only prove that they can be divided into three identical subclasses,but also gain three kinds of necessary and sufficient conditions.
基金Foundation item: Supported by the National Natural Science Foundation of China(10771198)
文摘We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo- Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.
基金Supported by the Xianning University Foundation of Hubei Province under Grant No.2010CDB05103Xianning University Foundation under Grant No.BK001
文摘Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable.
基金Supported by Natural Science Foundation of Zhejiang Province of China under Grant Nos.Y604106 and Y606182the Special Foundation of "University Talent Indraught Engineering" of Guangdong Province of China under Grant No.GDU2009109the Key Academic Discipline Foundation of Guangdong Shaoguan University under Gant No.KZ2009001
文摘An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.
文摘In this paper,we discuss a class of the quasillinear hyperbolic equations with the inhomogeneous terms: u_■+σ(v)+2α(t)u=0.v_■-u-0 Under the certain of hypothesis.we prove the globally existence theorems of the smooth solutions for its Cauchy problem.
基金supported by the Kyung Hee University on sabbatical leave in 2010
文摘We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger (NLS) equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.
基金Supported by the National Natural Science Foundation of China under Grant No. 11071209the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province under Grant No. 10KJBll0011
文摘A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.
基金Supported by National Science Foundation of China under Grant No. 2006CB921605
文摘The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schr6dinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.
基金supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
文摘The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.
基金supported by the National Natural Science Foundation of China(Grant No.11371049)Fundamental Research Funds for the Central Universities(Grant No.2016JBM070)
文摘In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial convergence conclusion of the general heterogeneous HK dynamics.That is,there must be some agents who will reach static states in finite time,while the other opinions have to evolve between them with a minimum distance if all the opinions does not reach consensus.And this result leads to the convergence of several special cases of heterogeneous HK dynamics,including when the minimum confidence bound is large enough,the initial opinion difference is small enough,and so on.
基金supported by the Natural Science Foundation of Shanxi Province (Grant No. 2011011021-3)
文摘The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.
基金supported by the National Natural Science Foundation of China under Grant Nos.61374038,61473079,and 61374060
文摘The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous dom- ination approach, a homogeneous observer and an output feedback controller with a scaling gain are designed. Then the sealing gain is adjusted such that the closed-loop system is semi-global asymptoti- cally stable. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.
基金Project supported by the National Natural Science Foundation of China (No. 10728101)the Basic Research Program of China (No. 2007CB814800)+1 种基金the Doctoral Program Foundation of the Ministry of Education of Chinathe "111" Project (No. B08018) and SGST (No. 09DZ2272900)
文摘The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch.Rational Mech.Anal.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.