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1.
Variational regularization method of solving the Cauchy problem for Laplace's equation: Innovation of the Grad-Shafranov (GS) reconstruction
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The simplified linear model of Grad-Shafranov (GS) reconstruction can be reformulated into an inverse boundary value problem of Laplace's equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace's equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace's equation. Then, the 'L-Curve' principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3. 相似文献
2.
New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer- Kaup- Kupershmidt system
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Some new exact solutions of an auxiliary ordinary differential
equation are obtained, which were neglected by Sirendaoreji {\it et
al in their auxiliary equation method. By using this method and
these new solutions the combined Korteweg--de Vries (KdV) and
modified KdV (mKdV) equation and (2+1)-dimensional
Broer--Kaup--Kupershmidt system are investigated and abundant exact
travelling wave solutions are obtained that include new solitary wave
solutions and triangular periodic wave solutions. 相似文献
3.
HUANG Wen-Hua 《理论物理通讯》2008,50(10):827-831
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-order Broer-Kaup equation by means of WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are found to be completely elastic. 相似文献
4.
Theoretical Investigation on Excitation,Ionization and Capture in H(1s, 2s) + H(1s, 2s) Collisions
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Cross sections of electron-loss in H(1s)+ H(1s) collisions and total collisional destruction of H(2s) in H(1s) 4- H(2s) collisions are calculatted by four-body classical-trajectory Monte Caylo (CTMC) method and compared with previous theoretical and experimental data over the energy range of 4-100 keV. For the former a good agreement is obtained within different four-body CTMC calculations, and for the incident energy Ep 〉 10 keV, comparison with the experimental data shows a better agreement than the results calculated by the impact parameter approx- imation. For the latter, our theory predicts the correct experimental behaviour, and the discrepancies between our results and experimental ones are less than 30%. Based on the successive comparison with experiments, the cross sections for excitation to H(2p), single- and double-ionization and H- formation in H(2s)+H(2s) collisions are calculated in the energy range of 4-100 keV for the first time, and compared with those in H(1s)+H(1s) and H(1s)+U(2s) collisions. 相似文献
5.
New periodic wave solutions,localized excitations and their interaction for (2+l)-dimensional Burgers equation
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Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+l)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution). 相似文献
6.
7.
Lie group analysis,numerical and non-traveling wave solutions for the (2+l)-dimensional diffusion-advection equation with variable coefficients
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In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (Gl/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions. 相似文献
8.
LIU Cheng-Shi 《理论物理通讯》2008,49(2):291-296
Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u" +p(u)(u')^2 + q(u) = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u"+p(u)(u')^2+q(u) = 0 includes the equation (u')^2 = f(u) as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method. 相似文献
9.
The multicomponent (2+1)-dimensional Glachette-Johnson (GJ) equation hierarchy and its super-integrable coupling system
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This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette-Johnson (G J) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem. 相似文献
10.
Effects of a reagent's rotational and vibrational excitations on reactionO(3p)+ H2(v=0, 3, j = 0, 3, 5, 7, 9, 12, 15) → OH + H
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To investigate the effect of a reagent’s rotational and vibrational excitations on the stereo-dynamics of the reaction product, the title reaction is theoretically simulated using the quasi-classical trajectory (QCT) method on the 3 A and 3 A potential energy surfaces (PESs). The reaction cross section is considered as the only scalar property in this work at four different collision energies. Furthermore the vector properties including two polarization-dependent differential cross sections (PDDCSs), the angular distributions of product’ rotational momentum are discussed at one fixed collision energy. Effects of reagents’ rotational excitation on the reaction do exist regularly. 相似文献
11.
Electric-dipole allowed (El) and forbidden (E2, M1 and M2) transition probabilities of 4f for N+
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By applying systematically enlarged multi-configuration Dirac-Fock wavefunction, the transitions for electricdipole allowed (E1) and forbidden (E2, M1 and M2) lines are studied among 4f pair coupling and low-lying configurations for singly ionized nitrogen. Most important effects of relativity, electron correlation, the rearrangement of electron density, Breit interaction, and quantum electrodynamic effects are included in the computation. Then, allowed (E1) and forbidden (E2, M1 and M2) transition probabilities of 4f for N+ are obtained and compared with experimental results. Good agreement with available experimental results is found and most of the data of 4f are presented for the first time. 相似文献
12.
Analytical potential energy function for the electronic states 2^∏1/2 and 2^∏3/2 of O^x2 (x=+1, -1)
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The splitting of potential energy levels for ground state X^2∏g of O^x2 (x = +1,-1) under spin-orbit coupling (SOC) has been calculated by using the spin-orbit (SO) multi-configuration quasi-degenerate perturbation theory (SO-MCQDPT). Their Murrell-Sorbie (M S) potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 (x = +1,-1) are v[O2+1^(2∏3/2→X^2∏1/2)] =195.652cm^-1, and v[O2^-1(2^∏1/2 →X^2∏3/2)] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time. 相似文献
13.
The interactions of dihydrogen with lithium containing organic complexes C4H4-m Lim and C5H5-m Lim (m = 1, 2) were studied by means of density functional theory (DFT) calculation. For all the complexes considered, each bonded lithium atom can adsorb up to five H2 molecules with the mean binding energy of 0.59 eV/H2 molecule. The interactions can be attributed to the charge transfer from the H2 bonding orbitals to the Li 2s orbitals. The kinetic stability of these hydrogen-covered organolithium molecules is discussed in terms of the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). The results indicate that these organiclithium structures can perhaps be used as building units for potential hydrogen storage materials. 相似文献
14.
Structures and luminescence properties of Yb3+ in the double perovskites Ba2YB'O6 (B'=Ta5+, Nb5+) phosphors
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The Yb3+ doped Ba2YB'O6 (B'=Ta5+, Nb5+) were prepared by high temperature solid-state reaction method, their structures were determined by x-ray diffraction and refined by Rietveld method. The diffuse reflection absorption, excitation and emission spectra of Yb3+:Ba2YB'O6 (B'=,Ta5+, Nb5+) were measured at room temperature. Under the excitation of ultraviolet light, these phosphors exhibit broad charge transfer band emissions of TaO6 or NbO6 centre with large Stokes shift. The Yb3+ doped into these hosts are situated at Y3+ sites of cubic symmetry (Oh). The experimental energy levels of Yb3+ in Ba2YTaO6 and Ba2YNbO6 were determined by photoluminescence and diffuse reflection absorption spectra. Their wavefunctions and theoretical energy levels were obtained by diagonalising the Hamiltonian matrix. The experimental energy levels were fitted by Levenberg--Marquardt iteration algorithm to determine crystal field parameters. Then, the magnetic-pole transition line strengths of Yb3+:Ba2YB'O6(B'=Ta5+, Nb5+) from (2F5/2)Γ8- to the low-energy states were calculated. 相似文献
15.
Theoretical investigations of the local distortion and electron paramagnetic resonance parameter for CdCl2:V2+ and CsMgX3:V<sup>2+(X=Cl,Br) systems
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This paper systematically investigates the local distortion and electron paramagnetic resonance (EPR) parameter for CdCl 2 :V 2+ and CsMgX 3 :V 2+ (X=Cl, Br) systems on the basis of the complete energy matrix, in which not only the contributions due to the spin–orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin–orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin–orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl 2 :V 2+ and elongation distortions for CsMgX 3 :V 2+ (X=Cl, Br), respectively. It notes that the empirical formula R ≈ R H + (r i-r h )/2 is not suitable for CdCl 2 :V 2+ and CsMgX 3 :V 2+ (X=Cl, Br) systems. The contributions of ligand to spin–orbit coupling interaction cannot be neglected for strong covalent systems, especially for V 2+ doped in CsMgBr 3 :V 2+ . 相似文献