We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of un...
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We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.
This paper theoretically investigates the orbital magnetization of electron-doped （n-type） semiconductor het-erostructures and of hole-doped （p-type） bulk semiconductors, which are respectively described by a two-...
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This paper theoretically investigates the orbital magnetization of electron-doped （n-type） semiconductor het-erostructures and of hole-doped （p-type） bulk semiconductors, which are respectively described by a two-dimensional electron/hole Hamiltonian with both the included Rashba spin-orbit coupling and Zeeman splitting terms. It is the Zeeman splitting, rather than the Rashba spin-orbit coupling, that destroys the time-reversal symmetry of the semiconductor systems and results in nontrivial orbital magnetization. The results show that the magnitude of the orbital magnetization per hole and the Hall conductance in the p-type bulk semiconductors are about 10^-2-10^-1 effective Bohr magneton and 10^-1-1 e^2/h, respectively. However, the orbital magnetization per electron and the Hall conductance in the n-type semiconductor heterostructures are too small to be easily observed in experiment.
The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical ...
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The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.
The dissipative quantum Zakharov equations are mainly studied. The ex- istence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on...
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The dissipative quantum Zakharov equations are mainly studied. The ex- istence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori esti- mate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated.
The reconstruction with minimized dispersion and controllable dissipation(MDCD) optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation.A low dispersion finite...
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The reconstruction with minimized dispersion and controllable dissipation(MDCD) optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation.A low dispersion finite volume scheme based on MDCD reconstruction is proposed which is capable of handling flow discontinuities and resolving a broad range of length *** the proposed scheme is formally second order accurate,the optimized dispersion and dissipation make it very accurate and robust so that the rich flow features encountered in practical engineering applications can be handled properly.A number of test cases are computed to verify the performances of the proposed scheme.
The early stages of unsteady viscous flow past a circular cylinder at Reynolds numbers R = 3000 and R = 9500 are solved numerically. The vorticity transport equation is solved by a second-order finite-difference metho...
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The early stages of unsteady viscous flow past a circular cylinder at Reynolds numbers R = 3000 and R = 9500 are solved numerically. The vorticity transport equation is solved by a second-order finite-difference method in both directions of the flow domain. The Poisson equation for the stream-function is solved by a Fourier Galerkin method in the one direction of the flow which we assume to remain symmetrical and second-order finite-difference. The advances in time are second-order Adams-Bashforth for R = 3000 and fourth-order Runge-Kutta for R = 9500. The computed results are compared qualitatively with experimental results. The comparison is found to be satisfactory.
Based on the relativistic multichannel theory, a non-isolated resonance approach has been developed to calculate the cross sections of dielectronic recombination on He+ for △n=1 and 2 transitions. A first order appro...
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Based on the relativistic multichannel theory, a non-isolated resonance approach has been developed to calculate the cross sections of dielectronic recombination on He+ for △n=1 and 2 transitions. A first order approximation is adopted for the radiative process. The convolved cross sections for the n≤3 states in both transitions are in good agreement with those of the observations. It is shown that the l-dependence of the field ionization and the radiative decay during the time-of-flight affect significantly the measurement of the cross sections near the initial state of the field ionization.
This paper generalizes the single-shell Kidder＇s self-similar solution to the double-shell one with a discontinuity in density across the interface. An isentropic implosion model is constructed to study the Rayleigh-...
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This paper generalizes the single-shell Kidder＇s self-similar solution to the double-shell one with a discontinuity in density across the interface. An isentropic implosion model is constructed to study the Rayleigh-Taylor instability for the implosion compression. A Godunov-type method in the Lagrangian coordinates is used to compute the one-dimensional Euler equation with the initial and boundary conditions for the double-shell Kidder＇s self-similar solution in spherical geometry. Numerical results are obtained to validate the double-shell implosion model. By programming and using the linear perturbation codes, a linear stability analysis on the Rayleigh-Taylor instability for the double-shell isentropic implosion model is performed. It is found that, when the initial perturbation is concentrated much closer to the interface of the two shells, or when the spherical wave number becomes much smaller, the modal radius of the interface grows much faster, i.e., more unstable. In addition, from the spatial point of view for the compressibility effect on the perturbation evolution, the compressibility of the outer shell has a destabilization effect on the Rayleigh-Taylor instability, while the compressibility of the inner shell has a stabilization effect.
Starting from a two-variable system of reaction-diffusion equations, an algorithm is devised for efficient simulation of waves in excitable media. The spatio-temporal resolution of the simulation can be varied continu...
Starting from a two-variable system of reaction-diffusion equations, an algorithm is devised for efficient simulation of waves in excitable media. The spatio-temporal resolution of the simulation can be varied continuously. For fine resolutions the algorithm provides accurate solution of the underlying reaction-diffusion equations. For coarse resolutions, the algorithm provides qualitative simulations at small computational cost.
A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a for...
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A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.
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