The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in ...The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in H 0 1 .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.
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
Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions.We show the squeezing property and the existence of fimte dimen- sional exponential attractors ...In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions.We show the squeezing property and the existence of fimte dimen- sional exponential attractors for this equation展开更多
The generalized derivative Ginzburg-Landau equation in two spatial dimensions is discussed. The existence and uniqueness of global solution are obtained by Galerkin method and by a priori estimates on the solution in ...The generalized derivative Ginzburg-Landau equation in two spatial dimensions is discussed. The existence and uniqueness of global solution are obtained by Galerkin method and by a priori estimates on the solution in H+1 -norm and H +2-norm.展开更多
In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obta...In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obtained by uniform a priori estimates of the solution. Furthermore, the existence of a global attractor and an exponential attractor with finite dimensions are proved.展开更多
The mixed state of two-band II-superconductor is analyzed by the multi-symplectic method. As to the Ginzburg-Landau equation depending on time that describes the mixed state of two-band II-superconductor, the multi-sy...The mixed state of two-band II-superconductor is analyzed by the multi-symplectic method. As to the Ginzburg-Landau equation depending on time that describes the mixed state of two-band II-superconductor, the multi-symplectic formulations with several conservation laws: a multi-symplectic conservation law, an energy con- servation law, as well as a momentum conservation law, are presented firstly; then an eighteen points scheme is constructed to simulate the multi-symplectic partial differential equations (PDEs) that are derived from the Ginzburg-Landau equation; finally, based on the simulation results, the volt-ampere characteristic curves are obtained, as well as the relationships between the temperature and resistivity of a suppositional two-band II-superconductor model under different magnetic intensi- ties. From the results of the numerical experiments, it is concluded that the notable property of the mixed state of the two-band II-superconductor is that: The trans- formation temperature decreases and the resistivity ρ increases rapidly with the increase of the magnetic intensity B. In addition, the simulation results show that the multi-symplectic method has two remarkable advantages: high accuracy and excellent long-time numerical behavior.展开更多
In this paper, we consider the dynamics of modulated waves in an unmagnetized, non-isothermal self-gravitating dusty plasma model. The varying charge on the moving dust, as it moves in and out of regions of differing ...In this paper, we consider the dynamics of modulated waves in an unmagnetized, non-isothermal self-gravitating dusty plasma model. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the electrostatic potential), will be out of phase with the equilibrium charge. The effect of the dust is to increase the phase velocity of the ion-acoustic (IA) waves i.e. decrease the Landau damping. In the low-amplitude limit and weak damping, we apply the reductive perturbation method on the model that resulted to the complex cubic Ginzburg-Landau (CCGL) equation. From these results, it is observed that, the plasma parameters strongly influence the properties of the solitary wave solution namely, the amplitude and the width. The effects of non-isothermal electrons, gravity, dust charge fluctuations and drifting motion on the ion-acoustic solitary waves are discussed with application in astrophysical contexts. It is also observed that the number of charges residing on the dust grains increases the modulational stability of the plane waves in the plasma, thus, enhancing the generation of modulated waves.展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
In this paper,we find the solutions for fractional potential Korteweg-de Vries(p-KdV)and Benjamin equations using q-homotopy analysis transform method(q-HATM).The considered method is the mixture of q-homotopy analysi...In this paper,we find the solutions for fractional potential Korteweg-de Vries(p-KdV)and Benjamin equations using q-homotopy analysis transform method(q-HATM).The considered method is the mixture of q-homotopy analysis method and Laplace transform,and the Caputo fractional operator is considered in the present investigation.The projected solution procedure manipulates and controls the obtained results in a large admissible domain.Further,it offers a simple algorithm to adjust the convergence province of the obtained solution.To validate the q-HATM is accurate and reliable,the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables.Comparison between the obtained solutions with the exact solutions exhibits that,the considered method is efficient and effective in solving nonlinear problems associated with science and technology.展开更多
The macroscopic electromagnetic properties of type-II superconductors are mainly influenced by the behavior of micro-scopic superconducting flux quantum units.Time-dependent Ginzburg-Landau(TDGL)theory is a well-known...The macroscopic electromagnetic properties of type-II superconductors are mainly influenced by the behavior of micro-scopic superconducting flux quantum units.Time-dependent Ginzburg-Landau(TDGL)theory is a well-known tool for describing and examining both the statics and dynamics of these superconducting entities.It have been instrumental in replicating and elucidat-ing numerous experimental results over the past decades.This paper provides a comprehensive overview of the progress in TDGL simulations,focusing on three key aspects of superconductor applications.We delve first into vortex rectification in supercon-ductors described within the TDGL framework,specifically highlighting the achievement of superconducting diode effect through asymmetric pinning landscapes and the reversible manipulation of vortex ratchets with dynamic pinning landscapes.In terms of the achievements of TDGL simulations concerning the critical current density of superconductors,we emphasize particularly on the optimization of pinning sites,including vortex pinning and dynamics in polycrystalline Nb3Sn with grain boundaries.In the third aspect,we concentrate on numerical modeling of vortex penetration and dynamics in superconducting radio-frequency cavities,including a discussion on superconductor-insulator-superconductor multilayer structures.Finally,we present key findings,insights,and perspectives derived from the discussed simulations.展开更多
We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the ...We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.展开更多
We study the partial regularity of weak solutions to the 2-dimensional Landau- Lifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration se...We study the partial regularity of weak solutions to the 2-dimensional Landau- Lifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic Hausdorff measure, we prove the uniform local C∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points.展开更多
The upper critical field of clean MgB2 is investigated using the two-band layered Ginzburg-Landau （GL） theory. The calculated results are fitted to the experimental data of clean MgB2 crystal very well in a broad te...The upper critical field of clean MgB2 is investigated using the two-band layered Ginzburg-Landau （GL） theory. The calculated results are fitted to the experimental data of clean MgB2 crystal very well in a broad temperature range. Based on the GL theory for clean superconductors, a phenomenological theory for dirty superconductor is proposed. Selecting appropriate parameters, two-band layered GL theory is successfully applied to the crystal of Mg（B1-xCx）2 and the neutron irradiation samples of MgB2.展开更多
The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit fo...The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.展开更多
The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velo...The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velocity. After studying the linear conditions, a generalized nonlinear kine- matic model is then derived to present the physical system. Applying the boundary conditions, analytical solutions are obtained using the long-wave perturbation method. In the first step, the normal mode method is used to characterize the linear behaviors. In the second step, the nonlinear film flow model is solved by using the method of multiple scales, to obtain Ginzburg-Landau equation. The influence of some physical parameters is discussed in both linear and nonlinear steps of the problem, and the results are displayed in many plots showing the stability criteria in various param- eter planes.展开更多
In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor .Ai in Hi（Ω） is actually equal...In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor .Ai in Hi（Ω） is actually equal to a global attractor Aj in HJ （Ω） （i ≠j, i, j = 1, 2, .. m）.展开更多
文摘The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in H 0 1 .
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.
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Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
基金The author is supported by the Postdoctoral Foundation of China
文摘In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions.We show the squeezing property and the existence of fimte dimen- sional exponential attractors for this equation
基金supported by National Key R&D Program of China(Grant No.2022YFA1403201)National Natural Science Foundation of China(Grant No.12274205 and No.11874205).
文摘The generalized derivative Ginzburg-Landau equation in two spatial dimensions is discussed. The existence and uniqueness of global solution are obtained by Galerkin method and by a priori estimates on the solution in H+1 -norm and H +2-norm.
基金the National Natural Science Foundation of China (Nos.10432010 and 10571010)
文摘In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obtained by uniform a priori estimates of the solution. Furthermore, the existence of a global attractor and an exponential attractor with finite dimensions are proved.
基金the National Natural Science Foundation of China (Grant Nos. 10572119, 10772147 and 10632030)the Doctoral Program Founda-tion of Education Ministry of China (Grant No. 20070699028)+1 种基金the Natural Science Foundation of Shaanxi Province of China (Grant No. 2006A07)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment
文摘The mixed state of two-band II-superconductor is analyzed by the multi-symplectic method. As to the Ginzburg-Landau equation depending on time that describes the mixed state of two-band II-superconductor, the multi-symplectic formulations with several conservation laws: a multi-symplectic conservation law, an energy con- servation law, as well as a momentum conservation law, are presented firstly; then an eighteen points scheme is constructed to simulate the multi-symplectic partial differential equations (PDEs) that are derived from the Ginzburg-Landau equation; finally, based on the simulation results, the volt-ampere characteristic curves are obtained, as well as the relationships between the temperature and resistivity of a suppositional two-band II-superconductor model under different magnetic intensi- ties. From the results of the numerical experiments, it is concluded that the notable property of the mixed state of the two-band II-superconductor is that: The trans- formation temperature decreases and the resistivity ρ increases rapidly with the increase of the magnetic intensity B. In addition, the simulation results show that the multi-symplectic method has two remarkable advantages: high accuracy and excellent long-time numerical behavior.
文摘In this paper, we consider the dynamics of modulated waves in an unmagnetized, non-isothermal self-gravitating dusty plasma model. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the electrostatic potential), will be out of phase with the equilibrium charge. The effect of the dust is to increase the phase velocity of the ion-acoustic (IA) waves i.e. decrease the Landau damping. In the low-amplitude limit and weak damping, we apply the reductive perturbation method on the model that resulted to the complex cubic Ginzburg-Landau (CCGL) equation. From these results, it is observed that, the plasma parameters strongly influence the properties of the solitary wave solution namely, the amplitude and the width. The effects of non-isothermal electrons, gravity, dust charge fluctuations and drifting motion on the ion-acoustic solitary waves are discussed with application in astrophysical contexts. It is also observed that the number of charges residing on the dust grains increases the modulational stability of the plane waves in the plasma, thus, enhancing the generation of modulated waves.
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
文摘In this paper,we find the solutions for fractional potential Korteweg-de Vries(p-KdV)and Benjamin equations using q-homotopy analysis transform method(q-HATM).The considered method is the mixture of q-homotopy analysis method and Laplace transform,and the Caputo fractional operator is considered in the present investigation.The projected solution procedure manipulates and controls the obtained results in a large admissible domain.Further,it offers a simple algorithm to adjust the convergence province of the obtained solution.To validate the q-HATM is accurate and reliable,the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables.Comparison between the obtained solutions with the exact solutions exhibits that,the considered method is efficient and effective in solving nonlinear problems associated with science and technology.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.12372210 and 11972298).
文摘The macroscopic electromagnetic properties of type-II superconductors are mainly influenced by the behavior of micro-scopic superconducting flux quantum units.Time-dependent Ginzburg-Landau(TDGL)theory is a well-known tool for describing and examining both the statics and dynamics of these superconducting entities.It have been instrumental in replicating and elucidat-ing numerous experimental results over the past decades.This paper provides a comprehensive overview of the progress in TDGL simulations,focusing on three key aspects of superconductor applications.We delve first into vortex rectification in supercon-ductors described within the TDGL framework,specifically highlighting the achievement of superconducting diode effect through asymmetric pinning landscapes and the reversible manipulation of vortex ratchets with dynamic pinning landscapes.In terms of the achievements of TDGL simulations concerning the critical current density of superconductors,we emphasize particularly on the optimization of pinning sites,including vortex pinning and dynamics in polycrystalline Nb3Sn with grain boundaries.In the third aspect,we concentrate on numerical modeling of vortex penetration and dynamics in superconducting radio-frequency cavities,including a discussion on superconductor-insulator-superconductor multilayer structures.Finally,we present key findings,insights,and perspectives derived from the discussed simulations.
基金partially supported by National Natural Science Foundation of China (Grant No.11001058)Specialized Research Fund for the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central Universities
文摘We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.
基金supported by the National Natural Science Foundation of China (10471050)Guangdong Provincial Natural Science Foundation (031495)National 973 Project (2006CB805902)
文摘We study the partial regularity of weak solutions to the 2-dimensional Landau- Lifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic Hausdorff measure, we prove the uniform local C∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points.
文摘The upper critical field of clean MgB2 is investigated using the two-band layered Ginzburg-Landau （GL） theory. The calculated results are fitted to the experimental data of clean MgB2 crystal very well in a broad temperature range. Based on the GL theory for clean superconductors, a phenomenological theory for dirty superconductor is proposed. Selecting appropriate parameters, two-band layered GL theory is successfully applied to the crystal of Mg（B1-xCx）2 and the neutron irradiation samples of MgB2.
基金Supported by the National Natural Science Foundation of China (10271091)
文摘The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.
文摘The present work discusses both the linear and nonlinear stability conditions of a viscous falling film down the outer surface of a solid vertical cylinder which moves in the direction of its axis with a constant velocity. After studying the linear conditions, a generalized nonlinear kine- matic model is then derived to present the physical system. Applying the boundary conditions, analytical solutions are obtained using the long-wave perturbation method. In the first step, the normal mode method is used to characterize the linear behaviors. In the second step, the nonlinear film flow model is solved by using the method of multiple scales, to obtain Ginzburg-Landau equation. The influence of some physical parameters is discussed in both linear and nonlinear steps of the problem, and the results are displayed in many plots showing the stability criteria in various param- eter planes.
基金Supported by the NationalNatural Science Foundation of China(No.11061003)Guangxi Natural Science Foundation Grant(No.0832065)Guangxi excellent talents funded project(No.0825)
文摘In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor .Ai in Hi（Ω） is actually equal to a global attractor Aj in HJ （Ω） （i ≠j, i, j = 1, 2, .. m）.
