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Application of self-consistent field theory to self-assembled bilayer membranes

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Chinese Physics B 2015年第12期24卷 45-52页

作者：张平文史安昌 lmam CAPT & School of Mathematical Sciences Peking University Department of Physics & Astronomy Mc Master University

Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.

关键词： amphiphilic molecules bilayer membranes elastic moduli self-consistent field theory

A SIMPLE ITERATIVE ALGORITHM FOR MAXCUT

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Journal of Computational Mathematics 2024年第5期42卷 1277-1304页

作者： Sihong Shao Dong Zhang Weixi Zhang capt LMAM and School of Mathematical SciencesPeking UniversityBeijing 100871China lmam and School of Mathematical Sciences Peking UniversityBeijing 100871China

We propose a simple iterative(SI)algorithm for the maxcut problem through fully using an equivalent continuous *** does not need rounding at all and has advantages that all subproblems have explicit analytic solutions,the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient *** experiments on G-set demonstrate the *** particular,the ratios between the best cut values achieved by SI and those by some advanced combinatorial algorithms in[***.,248(2017),365-403]are at least 0.986 and can be further improved to at least 0.997 by a preliminary attempt to break out of local optima.

关键词： Maxcut Iterative algorithm Exact solution Subgradient selection Fractional programming

AnAdaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

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Communications in Computational Physics 2012年第1期11卷 114-146页

作者： Peng He Huazhong Tang HEDPS CAPT&LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871China

This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)*** algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration *** the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing *** second part is an iterative *** each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative *** numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

关键词： Adaptive moving mesh method finite volume method conservative interpolation relativistic hydrodynamics

Numerical comparison of three stochastic methods for nonlinear PN junction problems

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Frontiers of Mathematics in China 2014年第3期9卷 659-698页

作者： Wenqi YAO Tiao LU School of Mathematical Sciences Peking University Beijing 100871 China HEDPS CAPT and LMAM Peking University Beijing 100871 China

We apply the Monte Carlo, stochastic Galerkin, and stochastic collocation methods to solving the drift-diffusion equations coupled with the Poisson equation arising in semiconductor devices with random rough surfaces. Instead of dividing the rough surface into slices, we use stochastic mapping to transform the original deterministic equations in a random domain into stochastic equations in the corresponding deterministic domain. A finite element discretization with the help of AFEPack is applied to the physical space, and the equations obtained are solved by the approximate Newton iterative method. Comparison of the three stochastic methods through numerical experiment on different PN junctions are given. The numerical results show that, for such a complicated nonlinear problem, the stochastic Galerkin method has no obvious advantages on efficiency except accuracy over the other two methods, and the stochastic collocation method combines the accuracy of the stochastic Galerkin method and the easy implementation of the Monte Carlo method.

关键词： Stochastic partial differential equation stochastic Galerkin method stochastic collocation method Monte Carlo method

RECONSTRUCTED DISCONTINUOUS APPROXIMATION TO STOKES EQUATION IN A SEQUENTIAL LEAST SQUARES FORMULATION

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Journal of Computational Mathematics 2023年第1期41卷 39-71页

作者： Ruo Li Fanyi Yang capt LMAM and School of Mathematical SciencesPeking UniversityBeijing 100871China School of Mathematics Sichuan UniversityChengdu 610064China

We propose a new least squares finite element method to solve the Stokes problem with two sequential *** approximation spaces are constructed by the patch reconstruction with one unknown per *** the first step,we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero *** this space,we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the *** the second step,we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free *** derive error estimates for all unknowns under both L 2 norms and energy *** results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.

关键词： Stokes problem Least squares finite element method Reconstructed discontinuous approximation Solenoid and irrotational polynomial bases

A High-Order Accurate Gas-Kinetic Scheme for One-and Two-Dimensional Flow Simulation

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Communications in Computational Physics 2014年第4期15卷 911-943页

作者： Na Liu Huazhong Tang HEDPS CAPT&LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871P.R.China

This paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one-and two-dimensional flow simulations,which is an extension of the third-order accurate gas-kinetic scheme[***,***,and ***,***.,229(2010),6715-6731]and the second-order accurate gas-kinetic scheme[***,***.,171(2001),289-335].It is formed by two parts:quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux *** first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the“initial”cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell *** is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic *** generalized moment limiter is employed there to suppress the possible numerical *** the second part,the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level,*** transport and the Bhatnagar-Gross-Krook(BGK)*** other words,the fourth-order flux evolution is based on the solution(*** particle velocity distribution function)of the BGK model for the Boltzmann *** 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic *** comparing with the exact solutions or the numerical solutions obtained the secondorder or third-order accurate gas-kinetic scheme,the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows,and the accuracy of the high-order GKS depends on the choice of the(numerical)collision time.

关键词： Gas-kinetic scheme initial reconstruction BGK model Boltzmann equation velocity distribution function

A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs

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Communications in Computational Physics 2011年第7期10卷 305-338页

作者： Tiao Lu Gang Du Xiaoyan Liu Pingwen Zhang School of Mathematical Sciences LMAM and CAPTPeking UniversityBeijing 100871China Institute of Microelectronics Peking UniversityBeijing 100871China

We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation(MSBTE)for the two dimensional(2D)electron gas in double gate metal oxide semiconductor field effect transistors(MOSFETs)with flared out source/drain contacts.A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is *** propose a second order finite volume method based on the positive and flux conservative(PFC)method to discretize the Boltzmann transport equations(BTEs).The transport part of the BTEs is split into two *** is a 1D transport problem in the position space,and the other is a 2D transport problem in the wavevector *** order to reduce the splitting error,the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D *** solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is *** of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.

关键词： Double gate MOSFET multi subband Boltzmann transport equation 2D electron gas deterministic solver PFC method

Green Function Method for Quantum Transport Based on the Generalized Fourier Transform

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Numerical Mathematics(Theory,Methods and Applications) 2023年第3期16卷 701-719页

作者： Haiyan Jiang Xingming Gao Yueguang Hu Tiao Lu School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China HEDPS CAPTLMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871China

The rigorous relations between the propagators of transient Schr¨odinger equations and stationary Green functions are *** on the generalized Fourier transform,non-singular transparent boundary condition for transient problem is proposed in a representation of Green *** unified framework of Green function method is presented for converting an open boundary problem into a bounded boundary *** scheme for time-dependent Schr¨odinger equation with non-singular transparent boundary condition is designed to simulate the propagations of a free Gaussian wave packet and the resonant tunnelling through double *** results validate the effectiveness of non-singular transparent boundary condition.

关键词： Schrodinger equation Green function generalized Fourier transform transparent boundary condition

An Efficient Mapped WENO Scheme Using Approximate Constant Mapping

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Numerical Mathematics(Theory,Methods and Applications) 2022年第1期15卷 1-41页

作者： Ruo Li Wei Zhong capt LMAMPeking UniversityBeijing 100871China School of Mathematical Sciences Peking UniversityBeijing 100871China Northwest Institute of Nuclear Technology Xi’an 710024China

We present a novel mapping approach for WENO schemes through the use of an approximate constant mapping function which is constructed by employing an approximation of the classic signum *** new approximate constant mapping function is designed to meet the overall criteria for a proper mapping function required in the design of the WENO-PM6 *** WENO-PM6 scheme was proposed to overcome the potential loss of accuracy of the WENO-M scheme which was developed to recover the optimal convergence order of the WENO-JS scheme at critical *** new mapped WENO scheme,denoted as WENOACM,maintains almost all advantages of the WENO-PM6 scheme,including low dissipation and high resolution,while decreases the number of mathematical operations remarkably in every mapping process leading to a significant improvement of *** convergence rates of the WENO-ACM scheme have been shown through one-dimensional linear advection equation with various initial *** results of one-dimensional Euler equations for the Riemann problems,the Mach 3 shock-density wave interaction and the Woodward-Colella interacting blastwaves are improved in comparison with the results obtained by the WENO-JS,WENO-M and WENO-PM6 *** experiments with two-dimensional problems as the 2D Riemann problem,the shock-vortex interaction,the 2D explosion problem,the double Mach reflection and the forward-facing step problem modeled via the two dimensional Euler equations have been conducted to demonstrate the high resolution and the effectiveness of the WENO-ACM *** WENOACM scheme provides significantly better resolution than the WENO-M scheme and slightly better resolution than the WENO-PM6 scheme,and compared to the WENOM and WENO-PM6 schemes,the extra computational cost is reduced by more than 83%and 93%,respectively.

关键词： WENO approximate constant mapping hyperbolic problems high resolution low computational cost