In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial *** show the squeezing property and the existence of fimte dimen- sional exponential attractors for this e...
详细信息
In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial *** show the squeezing property and the existence of fimte dimen- sional exponential attractors for this equation
In this paper, we apply arbitrary Riemann solvers, which may not satisfy the Maire＇s requirement, to the Maire＇s node-based Lagrangian scheme developed in [P. H. Maire et al., SIAM J. Sci. Comput, 29 （2007）, 1781-...
详细信息
In this paper, we apply arbitrary Riemann solvers, which may not satisfy the Maire＇s requirement, to the Maire＇s node-based Lagrangian scheme developed in [P. H. Maire et al., SIAM J. Sci. Comput, 29 （2007）, 1781-1824]. In particular, we apply the so-called Multi-Fluid Channel on Averaged Volume （MFCAV） Riemann solver and a Riemann solver that adaptively combines the MFCAV solver with other more dissipative Riemann solvers to the Maire＇s scheme. It is noted that neither of the two solvers satisfies the Maire＇s requirement. Numerical experiments are presented to demonstrate that the application of the two Riemann solvers is successful.
This study advances hydraulic fracturing simulations in shale reservoirs using two computational paradigms, Physics-Informed Neural Networks (PINNs) and the Variational Quantum Eigensolver (VQE). PINNs are employed to...
详细信息
A modified weak Galerkin（MWG） finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In t...
详细信息
A modified weak Galerkin（MWG） finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In the MWG finite element method, discontinuous piecewise polynomials of degree k and k-1 are used to approximate the velocity u and the pressure p, respectively. The main idea of the MWG finite element method is to replace the boundary functions by the average of the interior functions. Therefore, the MWG finite element method has fewer degrees of freedom than the WG finite element method without loss of accuracy. The MWG finite element method satisfies the stability conditions for any polynomial with degree no more than k-1. The MWG finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape *** order error estimates are established for the velocity and pressure approximations in H1and L2norms. Some numerical examples are presented to demonstrate the accuracy, convergence and stability of the method.
Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schrodinger equation of a hydrogen- like atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectru...
详细信息
Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schrodinger equation of a hydrogen- like atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectrum in abovethreshold ionization is obtained and further analyzed. We find that with the increase of the laser intensity, the abovethreshold ionization emission spectrum exhibits periodic resonance structure. By analyzing the population of atomic bound states, we find that it is the multi-photon excitation of bound state that leads to the occurrence of this phenomenon, which is in fairly good agreement with the experimental results.
Ebola virus disease （EVD） has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynam...
详细信息
Ebola virus disease （EVD） has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, R0 is less than unity. It is also shown that there exists a unique endemic equilibrium when R0 〉 1. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.
Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this *** problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling b...
详细信息
Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this *** problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling between fine particles and fluid *** model is first validated in laminar cases,after which the transient growth of coherent perturbations in turbulent channel flow is investigated,where the mean particle concentration distribution is obtained by direct numerical *** is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks,as was previously found in numerical simulations of particle-laden channel *** indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall *** current study also considers the transient growth of small-and large-scale perturbations at relatively high Reynolds numbers,which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.
In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() ...
详细信息
In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() and prove that the Davey-Stewartson system possesses a compact global attractor Ap in Lp(). Furthermore, one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.
The suppression of linear transient growth in turbulent channel flows via linear optimal controls is investigated. The control algorithms are the LQR control based on full information of flow fields and the LQG contro...
详细信息
The suppression of linear transient growth in turbulent channel flows via linear optimal controls is investigated. The control algorithms are the LQR control based on full information of flow fields and the LQG control based on the information measured at walls. The influence of these controls on the development of small-scale and large-scale perturbations are considered respectively. It is found that the energy amplification of large-scale perturbations is suppressed significantly by both LQR and LQG control, while small-scale perturbations can be only affect by LQR control. Effects of the weighting parameters and control price on the control performance of both controls are analysed. It turns out that the different weighting parameters in cost function do not qualitatively change the evalution of control performance. As control price raises, the effectiveness of both controls decreases distinctly. For small-scale perturbations, the upper limit of the effective range of control price is lower than that for large-scale perturbations. As Reynolds number increases, it indicates that both LQR and LQG control get more effective on suppressing the energy amplification of large-scale perturbations.
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...
详细信息
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
暂无评论