Dynamics of quantum entanglement of two qubits in two identical quantum Rabi models is studied analytically in the framework of corrections to the rotating-wave approximations. A closed-form expression for the entangl...Dynamics of quantum entanglement of two qubits in two identical quantum Rabi models is studied analytically in the framework of corrections to the rotating-wave approximations. A closed-form expression for the entanglement dynamics initiated from the well-known Bell states is derived, which is very close to the numerical exact results up to the ultrastrong coupling regime. It is found that the vanishing entanglement can be purely induced by the counter-rotating terms, and can be enhanced with the atom-cavity coupling.展开更多
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. A frequency-weighted network of Kuramoto oscilla...The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. A frequency-weighted network of Kuramoto oscillators is proposed, where the oscillators are asymmetrically coupled with the weights depending on their own native frequencies. Moreover, the characteristics of the whole network can be described by a single weighting exponent β. To obtain some analytical results, we focus on three special values of the weighting exponent β. Obviously, the network of oscillators in connection with the heterogeneous coupling scheme turns out to exhibit richer dy- namics. Our findings indicate that the weighting exponents should be of importance to affect the network＇s synchronization ability.展开更多
Based on the product rule of the Fourier series and some relevant results inreferences[1, 2]. a method on solving the large deflection equations of plates and shells by means of the Fourier series is proposed in the p...Based on the product rule of the Fourier series and some relevant results inreferences[1, 2]. a method on solving the large deflection equations of plates and shells by means of the Fourier series is proposed in the present paper,Applying this method .we derive a type solution to the Navier’s solution of the nonlinear differential equations of the rectangular hyperboloidal shallow shells of the orthotropic compositessimply supported .This solution is suitable for plates and shells with large deflection orsmall deflection whether it is isotropic or orthotropic.Their data processing results are correlative with those found in the classical examples and from the experiments.展开更多
In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitut...In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitute an interval, with a method called the sign-variation analysis. The results are compared with the parametrization technique offered by Elishakoff and Miglis, and with the solution yielded by minimization and maximization commands of the Maple software. Solutions for some interval word problems are also provided to edulcorate the methodology. This article only focuses on the real roots of those quadratic equations, complex solutions being beyond this investigation.展开更多
In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear e...In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11174254 and 11474256
文摘Dynamics of quantum entanglement of two qubits in two identical quantum Rabi models is studied analytically in the framework of corrections to the rotating-wave approximations. A closed-form expression for the entanglement dynamics initiated from the well-known Bell states is derived, which is very close to the numerical exact results up to the ultrastrong coupling regime. It is found that the vanishing entanglement can be purely induced by the counter-rotating terms, and can be enhanced with the atom-cavity coupling.
基金Supported by the National Natural Science Foundation of China under Grant Grant Nos 11162019 and 11047003
文摘The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. A frequency-weighted network of Kuramoto oscillators is proposed, where the oscillators are asymmetrically coupled with the weights depending on their own native frequencies. Moreover, the characteristics of the whole network can be described by a single weighting exponent β. To obtain some analytical results, we focus on three special values of the weighting exponent β. Obviously, the network of oscillators in connection with the heterogeneous coupling scheme turns out to exhibit richer dy- namics. Our findings indicate that the weighting exponents should be of importance to affect the network＇s synchronization ability.
文摘Based on the product rule of the Fourier series and some relevant results inreferences[1, 2]. a method on solving the large deflection equations of plates and shells by means of the Fourier series is proposed in the present paper,Applying this method .we derive a type solution to the Navier’s solution of the nonlinear differential equations of the rectangular hyperboloidal shallow shells of the orthotropic compositessimply supported .This solution is suitable for plates and shells with large deflection orsmall deflection whether it is isotropic or orthotropic.Their data processing results are correlative with those found in the classical examples and from the experiments.
文摘In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitute an interval, with a method called the sign-variation analysis. The results are compared with the parametrization technique offered by Elishakoff and Miglis, and with the solution yielded by minimization and maximization commands of the Maple software. Solutions for some interval word problems are also provided to edulcorate the methodology. This article only focuses on the real roots of those quadratic equations, complex solutions being beyond this investigation.
文摘In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.
