A semiclassical molecular nonsequential double ionization theory is developed based on the rescattering model. We show that, in the nonsequential double ionization of D2, the kinetic energy of the returning electron c...
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A semiclassical molecular nonsequential double ionization theory is developed based on the rescattering model. We show that, in the nonsequential double ionization of D2, the kinetic energy of the returning electron changes from below to above the ionization threshold of the parent ion as the laser varies from short to long wavelength, resulting in the dominance of collisional ionization at shorter laser wavelength and field ionization at longer laser wavelength. We also calculate the double ionization time distribution of D2 and the kinetic energy distribution of D+. The theoretical results are qualitatively consistent with experimental measurements. The nonsequential double to single ionization ratio of N22+∕N2+ is also calculated and compared with available experimental results.
Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by exp...
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Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
In this paper, we provide a new mixed finite element approximation of the variational inequality resulting from the unilateral contact problem in elasticity. We use the continuous piecewise P2-P1 finite element to app...
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In this paper, we provide a new mixed finite element approximation of the variational inequality resulting from the unilateral contact problem in elasticity. We use the continuous piecewise P2-P1 finite element to approximate the displacement field and the normal stress component on the contact region. Optimal convergence rates are obtained under the reasonable regularity hypotheses. Numerical example verifies our results.
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the uni...
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Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Gal...
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Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.
The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, ...
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The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.
We develop a semiclassical model to describe the non-sequential double ionization of diatomic molecules in an intense linearly polarized field, achieving insight into the two-electron correlation effect in the ionizat...
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We develop a semiclassical model to describe the non-sequential double ionization of diatomic molecules in an intense linearly polarized field, achieving insight into the two-electron correlation effect in the ionization dynamics. Compared to the experimental data of nitrogen molecules, our model shows a good agreement in the tunnelling regime and a qualitative agreement in the over-barrier regime. We find that the classical collisional trajectories are the main source of the double ionization in the tunnelling regime. As a prediction of our theory, we also calculate the double ionization ratios of H2^2＋/H2^＋ for hydrogen molecules and predict a ratio less than that of nitrogen molecules.
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress func...
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After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.
A stationary convection-diffusion problem with a small parameter multiplying the highest derivative is considered. The problem is discretized on a uniform rectangular grid by the central-difference scheme. A new class...
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In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = ...
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In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.
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