In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Sc...In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.展开更多
The stability and dynamical behavior of flexible and articulated rigid pipes conveying fluid have attracted the attention of many researchers in the field of fluid-structure interactions.The system of an articulated p...The stability and dynamical behavior of flexible and articulated rigid pipes conveying fluid have attracted the attention of many researchers in the field of fluid-structure interactions.The system of an articulated pipe composed of a flexible pipe and a rigid pipe is a class of hybrid flexible-rigid dynamical problems involving flow-induced vibrations.This paper establishes the governing equations of motion of a hybrid flexible-rigid pipe system based on Hamilton's principle,with the rigid pipe being hinged to the lower end of a flexible cantilevered pipe via a rotational spring.The coupling equations of motion are discretized via a Galerkin's approach.The mathematical model is validated by comparing the eigenvalue branches of a degenerated system by choosing extreme values of the parameters of the hybrid pipe with previous results.In the theoretical analysis,the critical flow velocities are calculated as a function of the stiffness of the rotational spring,mass ratio and length ratio of the rigid and flexible pipes.The unstable modes are detected from the eigenvalue branches and compared with those of a flexible cantilevered pipe.Numerical results show that the critical flow velocity is greatly influenced by several structural parameters.It is found that a small stiffness of the rotational spring tends to predict higher-mode instability,whereas a large rotational spring stiffness would generate a second-mode instability in most cases.In several system parameter spaces,the hybrid pipe may experience a transference of unstable modes with the increase of flow velocity.It is also shown that the hybrid pipe system may lose stability first in the fourth mode in some cases.Some of the fresh results obtained for the hybrid pipe system are expected to be helpful in understanding and controlling the dynamical responses of hybrid flexible-rigid fluid-conveying pipes.展开更多
This paper describes the calculation method for unsteady state conditions in the secondary air systems in gas turbines. The 1D-3D-Structure coupled method was applied. A 1D code was used to model the standard componen...This paper describes the calculation method for unsteady state conditions in the secondary air systems in gas turbines. The 1D-3D-Structure coupled method was applied. A 1D code was used to model the standard components that have typical geometric characteristics. Their flow and heat transfer were described by empirical correlations based on experimental data or CFD calculations. A 3D code was used to model the non-standard components that cannot be described by typical geometric languages, while a finite element analysis was carried out to compute the structural deformation and heat conduction at certain important positions. These codes were coupled through their interfaces. Thus, the changes in heat transfer and structure and their interactions caused by exterior disturbances can be reflected. The results of the coupling method in an unsteady state showed an apparent deviation from the existing data, while the results in the steady state were highly consistent with the existing data. The difference in the results in the unsteady state was caused primarily by structural deformation that cannot be predicted by the 1D method. Thus, in order to obtain the unsteady state performance of a secondary air system more accurately and efficiently, the 1D-3D-Structure coupled method should be used.展开更多
In this paper, the equilibrium properties of spin-1 Blume–Emery–Griffiths model are studied by using constant-coupling approximation. The dipolar and quadrupolar order parameters, the stable, metastable and unstable...In this paper, the equilibrium properties of spin-1 Blume–Emery–Griffiths model are studied by using constant-coupling approximation. The dipolar and quadrupolar order parameters, the stable, metastable and unstable states and free energy of the model are investigated. The states are defined in terms of local minima of the free energy of system. The numerical calculations are presented for several values of exchange interactions on the simple cubic lattice with q = 6.展开更多
Stationary entanglement in a four-mode optomechanical system,especially under room-temperature,is discussed.In this scheme,when the coupling strengths between the two target modes and the mechanical resonator are equa...Stationary entanglement in a four-mode optomechanical system,especially under room-temperature,is discussed.In this scheme,when the coupling strengths between the two target modes and the mechanical resonator are equal,the results cannot be explained by the Bogoliubov-mode-based scheme.This is related to the idea of quantummechanics-free subspace,which plays an important role when the thermal noise of the mechanical modes is considered.Significantly prominent steady-state entanglement can be available under room-temperature.展开更多
We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway ...We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidate pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to a one-step process with a single pathway.Interestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibits an unexpected maximum as a function ofμ. The results are in an excellent agreement with our numerical simulations by forward flux sampling.展开更多
A phenomenon about optical bistability is successfully investigated in a layered structure consisting of a silver film with Kerr medium and a silver grating sandwiched between semi-infinite linear dielectrics.This typ...A phenomenon about optical bistability is successfully investigated in a layered structure consisting of a silver film with Kerr medium and a silver grating sandwiched between semi-infinite linear dielectrics.This type of structure can lead to the optical bistability phenomena occurring in reflection and transmission.There exists an optimal thickness of the metal grating that can cut off the effect of the near-field enhancement and may have the lowest effect on conversion from surface plasmon to light.This structure can realize the functions of the beam splitter and the polarization splitter and will be essential for future classical and quantum information processing.展开更多
The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient,via state-feedback or output-feedback.The system is more general than that of the related literatu...The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient,via state-feedback or output-feedback.The system is more general than that of the related literature due to the presence of the spatially varying coefficient which makes the problem more difficult to solve.By infinite-dimensional backstepping method,both state-feedback and output-feedback stabilizing controllers are explicitly constructed,which guarantee that the closed-loop system is exponentially stable in the sense of certain norm.It is worthwhile pointing out that,in the case of output-feedback,by appropriately choosing the state observer gains,the severe restriction on the ODE sub-system in the existing results is completely removed.A simulation example is presented to illustrate the effectiveness of the proposed method.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（40537034）
文摘In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.
基金supported by the National Natural Science Foundation of China(Grant Nos.11902112,11972167,and 12072119)Hubei Superior and Distinctive Discipline Group of"Mechatronics and Automobiles"(Grant No.XKQ2021042).
文摘The stability and dynamical behavior of flexible and articulated rigid pipes conveying fluid have attracted the attention of many researchers in the field of fluid-structure interactions.The system of an articulated pipe composed of a flexible pipe and a rigid pipe is a class of hybrid flexible-rigid dynamical problems involving flow-induced vibrations.This paper establishes the governing equations of motion of a hybrid flexible-rigid pipe system based on Hamilton's principle,with the rigid pipe being hinged to the lower end of a flexible cantilevered pipe via a rotational spring.The coupling equations of motion are discretized via a Galerkin's approach.The mathematical model is validated by comparing the eigenvalue branches of a degenerated system by choosing extreme values of the parameters of the hybrid pipe with previous results.In the theoretical analysis,the critical flow velocities are calculated as a function of the stiffness of the rotational spring,mass ratio and length ratio of the rigid and flexible pipes.The unstable modes are detected from the eigenvalue branches and compared with those of a flexible cantilevered pipe.Numerical results show that the critical flow velocity is greatly influenced by several structural parameters.It is found that a small stiffness of the rotational spring tends to predict higher-mode instability,whereas a large rotational spring stiffness would generate a second-mode instability in most cases.In several system parameter spaces,the hybrid pipe may experience a transference of unstable modes with the increase of flow velocity.It is also shown that the hybrid pipe system may lose stability first in the fourth mode in some cases.Some of the fresh results obtained for the hybrid pipe system are expected to be helpful in understanding and controlling the dynamical responses of hybrid flexible-rigid fluid-conveying pipes.
基金supported by funds from National natural science foundation of China(Grant No.51176004)
文摘This paper describes the calculation method for unsteady state conditions in the secondary air systems in gas turbines. The 1D-3D-Structure coupled method was applied. A 1D code was used to model the standard components that have typical geometric characteristics. Their flow and heat transfer were described by empirical correlations based on experimental data or CFD calculations. A 3D code was used to model the non-standard components that cannot be described by typical geometric languages, while a finite element analysis was carried out to compute the structural deformation and heat conduction at certain important positions. These codes were coupled through their interfaces. Thus, the changes in heat transfer and structure and their interactions caused by exterior disturbances can be reflected. The results of the coupling method in an unsteady state showed an apparent deviation from the existing data, while the results in the steady state were highly consistent with the existing data. The difference in the results in the unsteady state was caused primarily by structural deformation that cannot be predicted by the 1D method. Thus, in order to obtain the unsteady state performance of a secondary air system more accurately and efficiently, the 1D-3D-Structure coupled method should be used.
文摘In this paper, the equilibrium properties of spin-1 Blume–Emery–Griffiths model are studied by using constant-coupling approximation. The dipolar and quadrupolar order parameters, the stable, metastable and unstable states and free energy of the model are investigated. The states are defined in terms of local minima of the free energy of system. The numerical calculations are presented for several values of exchange interactions on the simple cubic lattice with q = 6.
基金Supported by National Natural Science Foundation of China under Grant No.11174109
文摘Stationary entanglement in a four-mode optomechanical system,especially under room-temperature,is discussed.In this scheme,when the coupling strengths between the two target modes and the mechanical resonator are equal,the results cannot be explained by the Bogoliubov-mode-based scheme.This is related to the idea of quantummechanics-free subspace,which plays an important role when the thermal noise of the mechanical modes is considered.Significantly prominent steady-state entanglement can be available under room-temperature.
基金Supported by Natural Science Foundation of China under Grant Nos.11205002,11475003,21125313"211 project"of Anhui University under Grant No.02303319-33190133
文摘We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidate pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to a one-step process with a single pathway.Interestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibits an unexpected maximum as a function ofμ. The results are in an excellent agreement with our numerical simulations by forward flux sampling.
基金supported by National Basic Research Program of China(Grant No.2010CB923202)
文摘A phenomenon about optical bistability is successfully investigated in a layered structure consisting of a silver film with Kerr medium and a silver grating sandwiched between semi-infinite linear dielectrics.This type of structure can lead to the optical bistability phenomena occurring in reflection and transmission.There exists an optimal thickness of the metal grating that can cut off the effect of the near-field enhancement and may have the lowest effect on conversion from surface plasmon to light.This structure can realize the functions of the beam splitter and the polarization splitter and will be essential for future classical and quantum information processing.
基金supported by the National Natural Science Foundations of China under Grant Nos.60974003,61143011,61273084,and 61233014the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China under Grant No.JQ200919the Independent Innovation Foundation of Shandong University under Grant No.2012JC014
文摘The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient,via state-feedback or output-feedback.The system is more general than that of the related literature due to the presence of the spatially varying coefficient which makes the problem more difficult to solve.By infinite-dimensional backstepping method,both state-feedback and output-feedback stabilizing controllers are explicitly constructed,which guarantee that the closed-loop system is exponentially stable in the sense of certain norm.It is worthwhile pointing out that,in the case of output-feedback,by appropriately choosing the state observer gains,the severe restriction on the ODE sub-system in the existing results is completely removed.A simulation example is presented to illustrate the effectiveness of the proposed method.
