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An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations 下载免费PDF全文
Ying Yang & Benzhuo Lu 《advances in applied mathematics and mechanics.》2013,5(1):113-130
Poisson-Nernst-Planck
equations are a coupled system of nonlinear partial differential
equations consisting of the Nernst-Planck equation and
the electrostatic Poisson equation with delta distribution sources,
which describe the electrodiffusion of ions in a solvated
biomolecular system. In this paper, some error bounds for a piecewise
finite element approximation to this problem are derived. Several numerical
examples including biomolecular problems are shown to support our analysis. 相似文献
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用微乳化技术结合复合团聚法制备了纳米及亚微米茄红素胶囊,基于动态光散射测量分析了环境p H值对胶囊的粒径大小及其分布的影响.结果表明,对纳米茄红素胶囊,当p H值为3.5、6.0及6.8时能稳定的分散,而p H值为7.4时则会出现明显的聚集现象;对亚微米茄红素胶囊,当p H值为3.5、6.0、6.8及7.4时其粒径分布均为双峰状态,其中粒径较大的为亚微米茄红素胶囊,粒径较小的为包覆不良的颗粒,且p H=7.4时的粒径明显小于其它三种p H值时的粒径.虽然亚微米胶囊在p H=7.4时粒径明显变小的结果与纳米胶囊相同,但亚微米胶囊并不像纳米胶囊那样出现聚集现象. 相似文献
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Numerical Algorithms - We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The... 相似文献
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The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM. 相似文献
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Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions 总被引:1,自引:0,他引:1
In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. 相似文献
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用"相对熵"作为优化函数,提出了一个有效快速的折叠预测优化算法.使用了非格点模型,预测只关心蛋白质主链的走向.其中只用到了蛋白质主链上的两两连续的Cα原子间的距离信息以及20种氨基酸的接触势的一个扩展形式.对几个真实蛋白质做了算法测试,预测的初始结构都为比较大的去折叠态,预测构象相对于它们天然结构的均方根偏差(RMSD)为5~7 A.从原理上讲,该方法是对能量优化的改进. 相似文献