In this paper, a linearly implicit conservative difference scheme for the coupled nonlinear Schrödinger equations with space fractional derivative is proposed. This scheme conserves the mass and energy in the dis...
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Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and exper...
Whole genome sequences are generally accepted as excellent tools for studying evolutionary relationships. Due to the problems caused by the uncertainty in alignment, existing tools for phylogenetic analysis based on m...
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An iterative discontinuous Galerkin(DG)method is proposed to solve the nonlinear Poisson Boltzmann(PB)*** first identify a function space inwhich the solution of the nonlinear PB equation is iteratively approximated t...
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An iterative discontinuous Galerkin(DG)method is proposed to solve the nonlinear Poisson Boltzmann(PB)*** first identify a function space inwhich the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations,while an appropriate initial guess and a suitable iterative parameter are selected so that the solutions of linear PB equations are monotone within the identified solution *** the spatial discretization we apply the direct discontinuous Galerkin method to those linear PB *** precisely,we use one initial guess when the Debye parameter l=O(1),and a special initial guess for l≪1 to ensure *** iterative parameter is carefully chosen to guarantee the existence,uniqueness,and convergence of the *** particular,iteration steps can be reduced for a variable iterative *** one and two-dimensional numerical results are carried out to demonstrate both accuracy and capacity of the iterative DG method for both cases of l=O(1)and l≪***(m+1)th order of accuracy for L2 and mth order of accuracy for H1 for Pm elements are numerically obtained.
In this paper, we aim at predicting protein structural classes for low-homology data sets based on predicted secondary structures. We propose a new and simple kernel method, named as SSEAKSVM, to predict protein struc...
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In this paper,a numerical method is presented for simulating the 3D interfacial flows with insoluble *** numerical scheme consists of a 3D immersed interface method(IIM)for solving Stokes equations with jumps across t...
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In this paper,a numerical method is presented for simulating the 3D interfacial flows with insoluble *** numerical scheme consists of a 3D immersed interface method(IIM)for solving Stokes equations with jumps across the interface and a 3D level-set method for solving the surfactant convection-diffusion equation along a moving and deforming *** 3D IIM Poisson solver modifies the one in the literature by assuming that the jump conditions of the solution and the flux are implicitly given at the grid points in a small neighborhood of the *** assumption is convenient in conjunction with the level-set *** allows standard Lagrangian interpolation for quantities at the projection points on the *** interface jump relations are re-derived accordingly.A novel rotational procedure is given to generate smooth local coordinate systems and make effective *** examples demonstrate that the IIM Poisson solver and the Stokes solver achieve second-order accuracy.A 3D drop with insoluble surfactant under shear flow is investigated numerically by studying the influences of different physical parameters on the drop deformation.
We investigate the well-posedness of a perfectly matched layer model developed by Cohen and Monk [Comput Methods Appl Mech Eng 169 (1999), 197-217]. A new time-domain finite element method is proposed to solve the mod...
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The initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications. In order to reduce the computation cost, implicit–explicit (IMEX) met...
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The initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications. In order to reduce the computation cost, implicit–explicit (IMEX) methods are often applied to these problems, i.e. the stiff and non-stiff terms are discretized by using implicit and explicit methods, respectively. In this paper, we mainly consider the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems, and present two classes of the IMEX multistep methods by combining implicit one-leg methods with explicit linear multistep methods and explicit one-leg methods, respectively. The order conditions and the convergence results of these methods are obtained. Some efficient methods are constructed. Some numerical examples are given to verify the validity of the obtained theoretical results.
The Gross–Pitaevskii equation is the model equation of the single-particle wave function in a Bose–Einstein condensation. A computation difficulty of the Gross–Pitaevskii equation comes from the semiclassical probl...
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The Gross–Pitaevskii equation is the model equation of the single-particle wave function in a Bose–Einstein condensation. A computation difficulty of the Gross–Pitaevskii equation comes from the semiclassical problem in supercritical case. In this paper, we apply a diffeomorphism to transform the original one-dimensional Gross–Pitaevskii equation into a modified equation. The adaptive grids are constructed through the interpolating wavelet method. Then, we use the time-splitting finite difference method with the wavelet-adaptive grids to solve the modified Gross–Pitaevskii equation, where the approximation to the second-order derivative is given by the Lagrange interpolation method. At last, the numerical results are given. It is shown that the obtained time-splitting finite difference method with the wavelet-adaptive grids is very efficient for solving the one-dimensional semiclassical Gross–Pitaevskii equation in supercritical case and it is suitable to deal with the local high oscillation of the solution.
This paper identifies some scaling relationships between solar activity and geomagnetic activity. We examine the scaling properties of hourly data for two geomagnetic indices (ap and AE), two solar indices (solar X-ra...
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