A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With itera...
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A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.
A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of...
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A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.
This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be re...
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This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.
This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-sca...
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This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chem- ical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.
This paper considers the steady Swift-Hohenberg equation u＇＇＇＋β2u＇＇＋u^3-u=*** the dynamic approach, the authors prove that it has a homoclinic solution for each β∈ （4√8-ε0,4 √8）, where ε0 is a small po...
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This paper considers the steady Swift-Hohenberg equation u＇＇＇＋β2u＇＇＋u^3-u=*** the dynamic approach, the authors prove that it has a homoclinic solution for each β∈ （4√8-ε0,4 √8）, where ε0 is a small positive constant. This slightly complements Santra and Wei＇s result [Santra, S. and Wei, J., Homoclinic solutions for fourth order traveling wave equations, SIAM J. Math. Anal., 41, 2009, 2038-2056], which stated that it admits a homoclinic solution for each β∈C （0,β0） where β0 = 0.9342 ....
Zakharov equations have a fairly abundant physical background. In this paper, the existence of the weak global solution for quantum Zakharov equations for the plasmas model is obtained by means of the Arzela-Ascoli th...
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Zakharov equations have a fairly abundant physical background. In this paper, the existence of the weak global solution for quantum Zakharov equations for the plasmas model is obtained by means of the Arzela-Ascoli theorem, Faedo-Galerkin methods, and compactness property.
We calculated the vibrational free energies of the selected ordered compounds in the Ag-Cu system by using two kinds of methods: (1) calculating the phonon dispersion and density of states and the consequently vibrati...
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We calculated the vibrational free energies of the selected ordered compounds in the Ag-Cu system by using two kinds of methods: (1) calculating the phonon dispersion and density of states and the consequently vibrational free energies by using the method of ab initio inverted interatomic potentials and dynamic matrix;(2) the vibrational free energies determined by a Debye-Griineisen approximation. The Ag-Cu phase diagram is calculated by the cluster variation method. The results show that the solubility at Ag-rich end of the calculated phase diagram considering vibrational modes by using the first method is in better agreement with the experimental.
This paper studies the nonsequential double ionization （NSDI） process of diatomic molecules aligned parallel and perpendicular to an intense linearly polarized laser field by using a three-dimensional semiclassical ...
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This paper studies the nonsequential double ionization （NSDI） process of diatomic molecules aligned parallel and perpendicular to an intense linearly polarized laser field by using a three-dimensional semiclassical model. With this model, it achieves insight into the ion momentum distribution under the combined influence of a two-centre Coulomb potential and an intense laser field, and this result shows the significant influence of molecular alignment on the ratio between double and single ionization rate. Careful investigations show that the NSDI process for different alignment molecules has a close relation to the laser intensity and the different bounding electron distribution has a significant influence on the final ion momentum distribution.
We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in...
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We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.
The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate...
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The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two- point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.
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