共查询到17条相似文献,搜索用时 140 毫秒
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一类非线性发展方程的特征中心差分法 总被引:1,自引:0,他引:1
给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度ut及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,ut对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性. 相似文献
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本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)ut=(g(x)D(u)ux)x+h(x)P(u)ux+q(x)Q(u)进行研究. 当扩散项D(u)取um (m≠-1,0,1)和eu两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解.
关键词:
广义条件对称
精确解
非线性反应扩散方程 相似文献
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考虑一类演化方程ut=au∂2k+1(其中a是常数,u∂2k+1=∂2k+1u/∂x2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。 相似文献
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采用简立方格点上的Monte Carlo模拟,研究一端被无限大不可穿透平面壁吸附的高分子链的均方末端距<R2>,以及高分子链的质量中心到平面吸附壁的平均距离<Z>,与链长N、参数u(u=e-ε/kT,ε是链骨架原子间的相互作用能量,k是玻耳兹曼常数,T是热力学温度)的关系。结果表明:<R2>和<Z>都服从标度律,<R2>=αNγ,<Z>=βNη,其中,γ、η、α、β都是u的函数;u从1减小到0.5,则γ从1.01增大到1.19,η从0.51增大到0.60. 相似文献
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色散方程的一类具任意稳定性的显格式 总被引:4,自引:0,他引:4
本文对色散方程ur=auxxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。 相似文献
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给出了等价电子正则杨盘T[λ]ig的基本对称算子、完全对称算子概念,同时给出了这些对称算子作用于任一Slater函数i所产生的根态、生成态概念.由正交归一化杨盘T[λ]ie的纵置换算子A[λ]ie的构造规则,给出了A[λ]ie中存在的对称算子和确定T[λ]ie的等概率比对方法,从而基本避免了牵涉到许多算子的极其复杂的代数,给出了求解N值较大的电子系统杨盘基问题的新方法.
关键词:
正则杨盘
对称算子
根态
等概率比对方法 相似文献
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本文提出了予测稠苯芳杂环及其烷基链上质子化学位移的计算方法。
将稠苯芳杂环化合物用凯库勒式表示,计算式为为需考虑的苯环内的乙烯基效应。σmi,ci为各苯环的环流效应。σ1,Hc为各芳杂环的屏蔽效应,对杂环上质子它就是该单独芳杂环上相应质子的δ值,对苯环上质子要将它分解为各结构因素的效应,即:σ1,He=(1/2)d-1δx=y(或σz)+σc-c·σm,H.
σx-y与σz为杂原子或其基团的屏蔽效应,σc=c为存在于芳杂环中的乙烯基的效应,σm,Hc为芳杂环的环流效应,d为对不同质子所考虑的键数。有取代基时需考虑取代基的效应。计算环上烷基质子的公式为:δ=σp,CH3+ασc,CH3+βσt,CH3+σl,G
σl,G为稠苯芳杂环基的某级效应。 相似文献
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绕弹体的超声速气流与发动机喷流相互作用,在尾部形成复杂的干扰流场。本文用有限差分法求解全N-S方程,对这一复杂流场进行了数值模拟,得到了实验观察到的各种流场结构及其随喷口压力比的变化规律。外流M∞=1.94,Re∞=2.2×105,喷流Mj=3.0,喷口压力比pj/p∞分别为1.03,0.527,0.15三种。差分算法为一种改进的Beam-Warming格式。计算底部压力和激波在喷流中心的反射位置与实验数据进行了比较,吻合较好。 相似文献
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The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u, ux)uxx +B(u, ux) is studied by using the conditional Lie–Ba¨cklund symmetry method. The variant forms of the considered equations,which admit the corresponding conditional Lie–Ba¨cklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. 相似文献
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It is shown that each one-parameter subgroup of SL(2,R) gives rise to a local correspondence theorem between suitably generic solutions of arbitrary scalar equations describing pseudo-spherical surfaces. Thus, if appropriate genericity conditions are satisfied, there exist local transformations between any two solutions of scalar equations arising as integrability conditions of sl(2,R)-valued linear problems.
A complete characterization of evolution equations ut=K(x,t,u,ux,…,uxk) which are of strictly pseudo-spherical type is also provided. 相似文献
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Helga Baum 《Journal of Geometry and Physics》1987,4(4):503-522
Let
(P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let DA be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote Tω:=
(DA(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (Tω · e-t(DA−f)2) near t=0 define 1-forms a(k)f, K=0, 1, 2, … on
(P). In this paper we calculate aa(0)f, a(1)f, a(2)f and study some of their properties. For instance using the 1-form a(2)f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S4. 相似文献
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Juan-Fang Han Dong-Ning Gao Heng Zhang Xiao-Yun Wang Wen-Shan Duan 《Frontiers of Physics》2015,10(5):105201
The effects of the dust size distribution in ultracold quantum dusty plasmas are investigated. The amplitude φm and width ω of quantum dust acoustic waves are studied with different dust size distributions in the system. The φm and ω of the quantum dust acoustic waves are found to increase as the total number density increases. The φm and ω are greater for unusual dusty plasmas than for typical dusty plasmas. Moreover, as the Fermi temperature of the dust grains increases, the φm of the wave decreases. The ω of quantum dust acoustic waves increases as the speed u0 of the wave increases. 相似文献
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Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, uBB=uAB=−1, and for non-repulsive energy between AA nearest-neighbour sites, uAA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when uAA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of uAA. 相似文献
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H. Akbar-Zadeh 《Journal of Geometry and Physics》1995,17(4):342-380
A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F0(M, gt) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g0 F0(gt) of the integral I(gt) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (gt) for G = g0, then for a CID we show that for certain Finslerian manifolds, I″(g0) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs. 相似文献
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Partha Guha 《Journal of Geometry and Physics》2003,46(3-4):231-242
It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L2 metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S1. The space of differential operators Δ(n)=∂n+u2∂n−2++un form the space of extended or generalized projective connections. If a projective connection is factorizable Δ(n)=(∂−((n+1)/2−1)p1)(∂+(n−1)/2pn) with respect to quasi primary fields pi’s, then these fields satisfy ∑i=1n((n+1)/2−i)pi=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections. 相似文献