共查询到19条相似文献,搜索用时 43 毫秒
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为探讨含关联噪声的空间分数阶随机生长方程的动力学标度行为,本文利用Riesz分数阶导数和Grümwald-Letnikov分数阶导数定义方法研究了关联噪声驱动下的空间分数阶Edwards-Wilkinson (SFEW)方程在1+1维情况下的数值解,得到了不同噪声关联因子和分数阶数时的生长指数、粗糙度指数、动力学指数等,所求出的临界指数均与标度分析方法的结果相符合.研究表明噪声关联因子和分数阶数均影响到SFEW方程的动力学标度行为,且表现为连续变化的普适类. 相似文献
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提出两差分格式求解时间分数阶亚扩散方程.两个格式都是绝对稳定的,收敛阶均为O(τq+h2),其中q(q=2-β或2)与方程解的光滑性有关,β(0 < β < 1)是分数阶导数的阶、τ和h分别是时间和空间方向步长.数值实验验证了理论结果的正确性,并与其他方法进行比较,显示了本文方法的有效性和精确性. 相似文献
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研究了Caputo导数定义下带有分数阶热流条件的一维时间分数阶热波方程及其参数估计问题.首先,对正问题给出了解析解;其次,基于参数敏感性分析,利用最小二乘算法同时对分数阶阶数α和热松弛时间τ进行参数估计;最后对不同的热流分布函数所构成的两个初边值问题,分别进行参数估计仿真实验,分析温度真实值和估计值的拟合程度.实验结果表明,最小二乘算法在求解时间分数阶热波方程的两参数估计问题中是有效的.本文为分数阶热波模型的参数估计提供了一种有效的方法. 相似文献
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通过将广义Langevin方程中的系统内噪声建模为分数阶高斯噪声,推导出分数阶Langevin方程, 其分数阶导数项阶数由系统内噪声的Hurst指数所确定.讨论了处于强噪声环境下的线性过阻尼分数阶 Langevin方程在周期信号激励下的共振行为,利用Shapiro-Loginov公式和Laplace变换, 推导了系统响应的一、二阶稳态矩和稳态响应振幅、方差的解析表达式.分析表明,适当参数下, 系统稳态响应振幅和方差随噪声的某些特征参数、周期激励信号的频率及系统部分参数的变化出现了 广义的随机共振现象. 相似文献
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Carlson分形格电路是分抗的理想逼近情形,但仅具有负半阶运算性能,逼近效益随着电路节次数的增加逐渐降低.虽然可嵌套得到-1/2~n阶(n为大于或等于2的整数)分抗逼近电路,但结构复杂,无法实现任意分数阶运算.通过类比拓展Carlson分形格电路,获得具有高逼近效益的任意实数阶微积算子的分抗逼近电路——标度分形格分抗,并用非正则格型标度方程进行数学描述.分别探讨非正则格型标度方程的近似求解和真实解.通过调节电阻递进比α与电容递进比β的取值,可构造出具有任意运算阶的标度分形格分抗逼近电路.标度拓展极大地提高了标度分形格分抗电路的逼近效益.随着标度因子的增加,负半阶标度分形格分抗的逼近效益逐渐增大并明显高于Carlson分形格分抗.设计了基于五节Carlson分形格分抗与负半阶标度分形格分抗的半阶微分运算电路,并对周期三角波和周期方波信号进行半阶微分运算,实验测试结果与理论分析一致. 相似文献
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Exact Solutions of a Generalized Multi-Fractional Nonlinear Diffusion Equation in Radical Symmetry 总被引:1,自引:0,他引:1
This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalous diffusion equation in radical symmetry. The presence of external force and absorption is also considered. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solutions, and the solutions found here can have a compact behavior or a long tailed behavior. 相似文献
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Scaling Equation for Invariant Measure 总被引:1,自引:0,他引:1
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle. 相似文献
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Limiting distributions of the parabolically rescaled solutions of the heat equation with singular non-Gaussian initial data with long-range dependence are described in terms of their multiple stochastic integral representations. 相似文献
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The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen.
31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.
AMS Subject Classifications: 60G60, 60G15, 62M15, 60H15 相似文献
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A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation 下载免费PDF全文
Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail. 相似文献
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M. A. Zahran 《Journal of statistical physics》2002,109(5-6):1005-1016
From the generalized scheme of random walks on the comblike structure, it is shown how a 1/2-order fractional Fokker–Planck equation can be derived. The operator method for the moments associated with the distribution function p(x,t) is used to solve the resulting equation. Also the anomalous diffusion along the backbone of the structure has been considered. 相似文献
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Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L.Wearne, Phys. Rev. Lett. 100(2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law;and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented. 相似文献
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Based upon the Adomian decomposition method, a scheme is developed to obtain numerical solutions of a fractional Boussinesq equation with initial condition, which is introduced by replacing some order time and space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the traditional Adomian decomposition method for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional differential equations. The solutions of our model equation are calculated in the form of convergent series with easily computable components. 相似文献
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In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform,and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too.And the solitary wave exists in generalized dynamical systems and functional systems. 相似文献