求解Burgers方程的一种交替分段隐式算法

首先提出一个新的求解Burgers方程的差分格式,然后在此差分格式的基础上构造了便于并行计算的交替分段隐格式,并作了线性化稳定性分析.数值结果表明,本方法具有较高的精度,尤适于扩散项系数较小时的计算,且有效避免了数值结果的非物理振荡.     

A fluctuating lattice Boltzmann scheme for the one-dimensional KPZ equation

Based on the well-known mapping between the Burgers equation with noise and the Kardar–Parisi–Zhang (KPZ) equation for fluctuating interfaces, we develop a fluctuating lattice Boltzmann (LB) scheme for growth phenomena, as described by the KPZ formalism. A very simple LB-KPZ scheme is demonstrated in 1+1 spacetime dimensions, and is shown to reproduce the scaling exponents characterizing the growth of one-dimensional fluctuating interfaces.     

Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg–de Vries Equation with Random Initial Conditions

We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.     

二氧化钛纳米晶/石墨烯复合物的制备及其光催化性能 (cited: 1)

以氧化石墨和TiO₂溶胶为前驱物,结合絮凝与水热技术制备了TiO₂纳米晶/石墨烯复合物,表征了产物的结构、形貌、孔隙率、光谱吸收性质. 结果表明：TiO₂纳米晶的存在一定程度上阻止了石墨烯片层的重组,TiO₂纳米晶/石墨烯复合物较单纯TiO₂材料具有更强的吸光性能、对亚甲基蓝分子更强的吸附性能以及更高的电荷分离效率. 在紫外光和太阳光下,TiO₂纳米晶/石墨烯复合物对亚甲基蓝的光催化降解效率均高于P25和纯TiO₂.     

Numerical simulation of the soliton solutions for a complex modified Korteweg—de Vries equation by a finite difference method

In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

Tracking elementary particles near their primary vertex: A combinatorial approach

Colliding beams experiments in High Energy Physics rely on solid state detectors to track the flight paths of charged elementary particles near their primary point of interaction. Reconstructing tracks in this region requires, per collision, a partitioning of up to 10³ highly correlated observations into an unknown number of tracks. We report on the successful implementation of a combinatorial track finding algorithm to solve this pattern recognition problem in the context of the ALEPH experiment at CERN. Central to the implementation is a 5-dimensional axial assignment model (AP5) encompassing noise and inefficiencies of the detector, whose weights of assignments are obtained by means of an extended Kalman filter. A preprocessing step, involving the clustering and geometric partitioning of the observations, ensures reasonable bounds on the size of the problems, which are solved using a branch & bound algorithm with LP relaxation. Convergence is reached within one second of CPU time on a RISC workstation in average.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

复杂背景下扩展目标极形态分形分割算法

 用极形态算子优化分形模型,提出了一种复杂背景下的扩展目标分割新算法。首先分析极坐标系中可变尺度形态结构算子的旋转缩放特性,并以此为基础进行极形态运算,再利用最小二乘法提取分形尺度误差进行二值化,然后进行边界跟踪,依据先验知识抑制背景团块,最后保留并填充面积最大的目标团块。仿真实验证明能够有效分割复杂背景下的扩展目标,并较好地保留了目标形状特征。     

Extended structures and new infinite-dimensional hidden symmetries for the Einstein–Maxwell-dilaton-axion theory with multiple vector fields

A so-called extended elliptical-complex (EEC) function method is proposed and used to further study the Einstein–Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for . An Ernst-like matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA-p theory are written as a so-called Hauser–Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA-2 theory, two Hauser–Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac–Moody algebra and Virasoro algebra (without centre charges). These results show that the studied EMDA-p theories possess very rich symmetry structures and the EEC function method is necessary and effective.