We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove tha...
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We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove that the scattering operator carries a band in Hs into Hs.
Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. It is mainly considered as a powerful tool with high flexibility to approximate functions. This paper pro...
Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. It is mainly considered as a powerful tool with high flexibility to approximate functions. This paper proposes a generalized NURBS based approach to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains by using physics-informed neural networks (PINNs). Our approach is based on a posteriori error estimation in which the adjoint problem is solved for the error localization to formulate an error estimator within the framework of neural network. An efficient and easy to implement algorithm is developed to obtain a posteriori error estimate for multiple goal functionals by employing the dual-weighted residual approach, which is followed by the computation of both primal and adjoint solutions using the neural network. The present study shows that such a data-driven model based learning has superior approximation of quantities of interest even with relatively less training data. Moreover, we illustrate the versatility of activation functions in achieving better learning capabilities and improving convergence rates, especially at the early training stage, and also in increasing solutions accuracies. The novel algorithmic developments are substantiated with several numerical test examples. It has been demonstrated that deep neural networks have distinct advantages over shallow neural networks, and the techniques for enhancing convergence have also been reviewed.
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell avera...
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example.
Using the single electron model, the acceleration of electrons in combined circularly polarized intense laser fields and the spontaneous quasistatic fields （including axial and azimuthal magnetic fields, the axial an...
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Using the single electron model, the acceleration of electrons in combined circularly polarized intense laser fields and the spontaneous quasistatic fields （including axial and azimuthal magnetic fields, the axial and transverse electric fields） produced in intense laser plasma interaction is investigated analytically and numerically by fitting the proper parameters of the quasistatic fields based on the data from the experiment and numerical calculation. A new resonant condition is given. It is found that the resonance acceleration of electron depends not only on laser field, but also on the bounce frequency oscillating in the quasistatic magnetic field and electric field. The net energy gained by electron does not increase monotonously with axial electric field, but there are some optimal axial electric fields.
Based on the Dirac-Fork-Slater method combined with the multichannel quantum defect theory, the recombination processes of electrons into bare uranium ions （U92＋） are investigated in the relative energy range close...
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Based on the Dirac-Fork-Slater method combined with the multichannel quantum defect theory, the recombination processes of electrons into bare uranium ions （U92＋） are investigated in the relative energy range close to zero, and the x-ray spectrum emitted in the direct radiative recombination and cascades processes are simulated. Compared with the recent measurement, it is found that the rate enhancement comes from the additional populations on high Rydberg states. These additional populations may be produced by other recombination mechanisms, such as the external electric-magnetic effects and the many-body correlation effects, which still remains an open problem.
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized ...
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The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set Λ on which the dynamics is topologically conjugate to a shift on four symbols.
We present total cross sections in the laboratory energy range 17.5-500 keV amu(-1) for electron capture by protons in collision with He+(1s). We describe this process theoretically by performing a close-coupling (CC)...
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We present total cross sections in the laboratory energy range 17.5-500 keV amu(-1) for electron capture by protons in collision with He+(1s). We describe this process theoretically by performing a close-coupling (CC) calculation using the symmetrized variational (SV) continuum distorted-wave (CDW) collision ansatz. We discuss the SVCDW results in conjunction with another CC variational CDW calculation, with CDW perturbation theory, and also with close-coupling calculations which involve a representation of the continuum by a set of pseudo-states which may include pseudo-states of the united atom. Moreover, we compare the SVCDW results with the available experimental data. The SVCDW results are found to be in very good agreement with the experiments of Peart et al, Rinn et al and Watts et al at all energies, and consequently to be at variance with the experimental results of Angel et al. The SVCDW results are also found to be in good accord with a CC calculation involving Sturmian-type pseudo-states. We investigate this agreement further by comparing impact-parameter profiles at 50 and 17.5 keV amu(-1).
The opacities of the lithium hydride molecule are calculated for temperatures of 300 K,1000 K,1500 K,and 2000 K,at a pressure of 10 atm,in which the contributions from the five low-lying electronic states are *** ab i...
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The opacities of the lithium hydride molecule are calculated for temperatures of 300 K,1000 K,1500 K,and 2000 K,at a pressure of 10 atm,in which the contributions from the five low-lying electronic states are *** ab initio multi-reference single and double excitation configuration interaction(MRDCI)method is applied to compute the potential energy curves(PECs)of the 7 LiH,including four 1∑+states and one 1Πstate,as well as the corresponding transition dipole moments between these *** ro-vibrational energy levels are calculated based on the PECs obtained,together with the spectroscopic *** addition,the partition functions are also computed,and are provided at temperatures ranging from 10 K to 2000 K for 7 LiH,7 LiD,6 LiH,and 6 LiD.
In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress c...
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In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress chaos to unstable focuses and unstable periodic orbits. To overcome the topological limitation that the saddle-type steady state cannot be stabilized, an adaptive control based on LaSalle＇s invariance principle is used to control chaos to unstable equilibrium （i.e. saddle point, focus, node, etc.）. The control technique does not require any computer analysis of the system dynamics, and it operates without needing to know any explicit knowledge of the desired steady-state position.
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.
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