The demand for large antennas in future space missions has increasingly stimulated the development of deployable membrane antenna structures owing to their light weight and small stowage volume. However, there is litt...The demand for large antennas in future space missions has increasingly stimulated the development of deployable membrane antenna structures owing to their light weight and small stowage volume. However, there is little literature providing a comprehensive review and comparison of different membrane antenna structures. Space-borne membrane antenna structures are mainly classified as either parabolic or planar membrane antenna structures. For parabolic membrane antenna structures, there are five deploying and forming methods, including inflation, inflation-rigidization, elastic ribs driven, Shape Memory Polymer （SMP）-inflation, and electrostatic form- ing. The development and detailed comparison of these five methods are presented. Then, properties of membrane materials （including polyester film and polyimide film） for parabolic membrane antennas are compared. Additionally, for planar membrane antenna structures, frame shapes have changed from circular to rectangular, and different ten- sioning systems have emerged successively, including single Miura-Natori, double, and multi-layer tensioning systems. Recent advances in structural configurations, tensioning system design, and dynamic analysis for planar membrane antenna structures are investigated. Finally, future trends for large space membrane antenna structures are pointed out and technical problems are proposed, including design and analysis of membrane structures,materials and processes, membrane packing, surface accuracy stability, and test and verification technology. Through a review of large deployable membrane antenna structures, guidance for space membrane-antenna research and applications is provided.展开更多
In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation ar...In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.展开更多
H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximat...H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.展开更多
In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained.
In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computa...In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computational requirements are greatly reduced without assuming more regularities on the solution u.展开更多
A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accura...A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.展开更多
The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in whic...The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the mathematical model discussed in this paper belongs to the second order parabolic equations with non-negative characteristic form, namely, there exists a degeneracy on the lateral boundaries of the domain. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions which must be satisfied by the minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor modification of the cost functional and some a priori regularity conditions imposed on the forward operator, the convergence of the minimizer for the noisy input data is obtained in this paper. The results can be extended to more general degenerate parabolic equations.展开更多
This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditi...This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.展开更多
The non-uniform concentrated solar flux distribution on the outer surface of the absorber tube can lead to large circumferential temperature difference and high local temperature of the absorber tube wall,which is one...The non-uniform concentrated solar flux distribution on the outer surface of the absorber tube can lead to large circumferential temperature difference and high local temperature of the absorber tube wall,which is one of the primary causes of parabolic trough solar receiver(PTR)failures.In this paper,a secondary reflector used as a homogenizing reflector(HR)in a conventional parabolic trough solar collector(PTSC)was recommended to homogenize the solar flux distribution and thus increase the reliability of the PTR.The design method of this new type PTSC with a HR was also proposed.Meanwhile,the concentrated solar flux distribution was calculated by adopting the Monte Carlo ray-trace(MCRT)method.Then,the coupled heat transfer process within the PTR was simulated by treating the solar flux calculated by the MCRT method as the heat flux boundary condition for the finite volume method model.The solar flux distribution on the outer surface of the absorber tube,the temperature field of the absorber tube wall,and the collector efficiency were analyzed in detail.It was revealed that the absorber tube could almost be heated uniformly in the PTSC with a HR.As a result,the circumferential temperature difference and the maximum temperature could be reduced significantly,while the efficiency tended to decrease slightly due to the inevitably increased optical loss.Under the conditions studied in this paper,although the collector efficiency decreased by about 4%,the circumferential temperature difference was reduced from about 25 to 3 K and the maximum temperature was reduced from667 to 661 K.展开更多
Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.
The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u wi...The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u with r>0.展开更多
An optimization theoretic approach of coefficients in semilinear parabolic equation is presented. It is based on convex analysis techniques. General theorems on existence are proved in L1 setting. A necessary conditio...An optimization theoretic approach of coefficients in semilinear parabolic equation is presented. It is based on convex analysis techniques. General theorems on existence are proved in L1 setting. A necessary condition is given for the solutions of the parameter estimatioll problem.展开更多
It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution ...It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.展开更多
In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the ex...In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.展开更多
In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is...In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.展开更多
This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solu...This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.展开更多
This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconduct...This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.展开更多
It is proved that the vortices of a Ginzburg-Landau system are attracted by impurities or inhomogeneities in the super-conducting materials. The strong H1-convergence for the system is also studied.
基金Supported by Research Fund of Institute of Spacecraft System Engineering,China Academy of Space Technology,China(Grant No.ZTBYY-7)
文摘The demand for large antennas in future space missions has increasingly stimulated the development of deployable membrane antenna structures owing to their light weight and small stowage volume. However, there is little literature providing a comprehensive review and comparison of different membrane antenna structures. Space-borne membrane antenna structures are mainly classified as either parabolic or planar membrane antenna structures. For parabolic membrane antenna structures, there are five deploying and forming methods, including inflation, inflation-rigidization, elastic ribs driven, Shape Memory Polymer （SMP）-inflation, and electrostatic form- ing. The development and detailed comparison of these five methods are presented. Then, properties of membrane materials （including polyester film and polyimide film） for parabolic membrane antennas are compared. Additionally, for planar membrane antenna structures, frame shapes have changed from circular to rectangular, and different ten- sioning systems have emerged successively, including single Miura-Natori, double, and multi-layer tensioning systems. Recent advances in structural configurations, tensioning system design, and dynamic analysis for planar membrane antenna structures are investigated. Finally, future trends for large space membrane antenna structures are pointed out and technical problems are proposed, including design and analysis of membrane structures,materials and processes, membrane packing, surface accuracy stability, and test and verification technology. Through a review of large deployable membrane antenna structures, guidance for space membrane-antenna research and applications is provided.
基金This work is supported by National Natural Science Foundation of China (40373003 and 40372121).
文摘In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.
基金Foundation item： the National Natural Science Foundation of China （Nos. 10671184 10371113）.
文摘H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.
基金Subeidized by the Special Funds for Major State Basic Research Projects.
文摘In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained.
文摘In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computational requirements are greatly reduced without assuming more regularities on the solution u.
基金supported by National Natural Science Foundation of China (Grant Nos. 10871022, 10771065,and 60573158)Natural Science Foundation of Hebei Province (Grant No. A2007001027)
文摘A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.
基金supported by the National Natural Science Foundation of China(Nos.11061018,11261029)the Youth Foundation of Lanzhou Jiaotong University(No.2011028)+1 种基金the Long Yuan Young Creative Talents Support Program(No.252003)the Joint Funds of the Gansu Provincial Natural Science Foundation of China(No.1212RJZA043)
文摘The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the mathematical model discussed in this paper belongs to the second order parabolic equations with non-negative characteristic form, namely, there exists a degeneracy on the lateral boundaries of the domain. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions which must be satisfied by the minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor modification of the cost functional and some a priori regularity conditions imposed on the forward operator, the convergence of the minimizer for the noisy input data is obtained in this paper. The results can be extended to more general degenerate parabolic equations.
文摘This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.
基金supported by the National Natural Science Foundation of China(Grant Nos.51176155 and 51306149)the Research Project of Chinese Ministry of Education(Grant No.113055A)
文摘The non-uniform concentrated solar flux distribution on the outer surface of the absorber tube can lead to large circumferential temperature difference and high local temperature of the absorber tube wall,which is one of the primary causes of parabolic trough solar receiver(PTR)failures.In this paper,a secondary reflector used as a homogenizing reflector(HR)in a conventional parabolic trough solar collector(PTSC)was recommended to homogenize the solar flux distribution and thus increase the reliability of the PTR.The design method of this new type PTSC with a HR was also proposed.Meanwhile,the concentrated solar flux distribution was calculated by adopting the Monte Carlo ray-trace(MCRT)method.Then,the coupled heat transfer process within the PTR was simulated by treating the solar flux calculated by the MCRT method as the heat flux boundary condition for the finite volume method model.The solar flux distribution on the outer surface of the absorber tube,the temperature field of the absorber tube wall,and the collector efficiency were analyzed in detail.It was revealed that the absorber tube could almost be heated uniformly in the PTSC with a HR.As a result,the circumferential temperature difference and the maximum temperature could be reduced significantly,while the efficiency tended to decrease slightly due to the inevitably increased optical loss.Under the conditions studied in this paper,although the collector efficiency decreased by about 4%,the circumferential temperature difference was reduced from about 25 to 3 K and the maximum temperature was reduced from667 to 661 K.
文摘Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.
基金supported by the National Natural Sciences Foundation of China (No.19701018).
文摘The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u with r>0.
基金the post-doctoral funds of China and funds of State Educational Commission of China for returned scholars from abroad
文摘An optimization theoretic approach of coefficients in semilinear parabolic equation is presented. It is based on convex analysis techniques. General theorems on existence are proved in L1 setting. A necessary condition is given for the solutions of the parameter estimatioll problem.
文摘It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.
文摘In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10631020)Basic Research Grant of Tsinghua University (Grant No. JCJC2005071).
文摘In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.10471013,10471022)the Ministry of Education of China Science and Technology Major Projects (Grant No.104090)
文摘This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.
基金Supported by National 973-Project and Basic Research Grant of Tsinghua University
文摘This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.
文摘It is proved that the vortices of a Ginzburg-Landau system are attracted by impurities or inhomogeneities in the super-conducting materials. The strong H1-convergence for the system is also studied.
