共查询到20条相似文献,搜索用时 15 毫秒
1.
A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate. 相似文献
2.
A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate. 相似文献
3.
We present a general strategy for proving ergodicity for stochastically forced nonlinear dissipative PDEs. It consists of two main steps. The first step is the reduction to a finite dimensional Gibbsian dynamics of the low modes. The second step is to prove the equivalence between measures induced by different past histories using Girsanov theorem. As applications, we prove ergodicity for Ginzburg–Landau, Kuramoto–Sivashinsky and Cahn–Hilliard equations with stochastic forcing. 相似文献
4.
Tao Zhou 《advances in applied mathematics and mechanics.》2014,6(4):403-418
In this work, we concern with the numerical approach for delay differential equations
with random coefficients. We first show that the exact solution of the problem considered admits good regularity in the random space, provided that the given data satisfy some reasonable assumptions. A stochastic collocation method is proposed to approximate the solution in the random space, and we use the Legendre spectral collocation method to solve the resulting deterministic delay differential equations. Convergence property of the proposed method is analyzed. It is shown that the numerical method yields the familiar exponential order of convergence in both the random space and the time space. Numerical examples are given to illustrate the theoretical results. 相似文献
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6.
A general and easy-to-code numerical method based on radial basis functions
(RBFs) collocation is proposed for the solution of delay differential equations
(DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which allow
for a large accuracy over a scattered and relatively small discretization support.
Hardy's multiquadric is chosen as RBF and combined with the Residual Subsampling
Algorithm of Driscoll and Heryudono for support adaptivity. The performance
of the method is very satisfactory, as demonstrated over a cross-section of
benchmark DDEs, and by comparison with existing general-purpose and specialized
numerical schemes for DDEs. 相似文献
7.
This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique. 相似文献
8.
We construct a second order elliptic equation in divergence form in3, with a nonzero solution which vanishes in a half-space.The coefficients are -Hölder continuous of any order < 1. This improves a previous counterexample of Miller (1972, 1974).Moreover, we obtain coefficients which belong to a finer class ofsmoothness, expressed in terms of the modulus of continuity. 相似文献
9.
二维核磁共振测井观测模式是以获取特定地层信息为目标的数据采集方式,它直接决定着核磁共振谱仪对不同类型储层的适应性以及获取原始数据的可信度.本文从观测模式的组成元素以及工作机理出发,采用C#语言开发了一套具有可视化功能的二维核磁共振测井观测模式设计软件.该软件支持二维核磁共振测井以及核磁共振岩心分析仪的观测模式设计,同时提供了三种采集参数编辑方式、观测模式优化机制以及图形化显示等功能,实现了观测模式的灵活调整,解决了当前主流二维核磁共振测井观测模式中存在的采集参数固定、不宜灵活调整从而导致所采集的原始数据信噪比低下、储层中流体弛豫特性加载不完全等问题.此外,软件还提供了观测模式的采集参数信息以及采集时序信息的输出功能等. 相似文献
10.
Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential
evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution
equations were lifted to the corresponding functional partial differential equations in functional space by introducing the
time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The
algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact
analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution
equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer
numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic
dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution
equations both analytically and numerically.
Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program
Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China 相似文献
11.
Meiqing Wang Chensi Huang Chao Zeng & Choi-Hong Lai 《advances in applied mathematics and mechanics.》2012,4(6):769-779
The digital image inpainting technology based on partial differential
equations (PDEs) has become an intensive research topic over the last
few years due to the mature theory and prolific numerical algorithms of
PDEs. However, PDE based models are not effective when used to inpaint
large missing areas of images, such as that produced by object removal.
To overcome this problem, in this paper, a two-phase image inpainting
method is proposed. First, some edges which cross the damaged regions
are located and the missing parts of these edges are fitted by using the
cubic spline interpolation. These fitted edges partition the damaged regions
into some smaller damaged regions. Then these smaller regions may be inpainted
by using classical PDE models. Experiment results show that the inpainting
results by using the proposed method are better than those of BSCB model and TV model. 相似文献
12.
Huajun Zhu Songhe Song & Yaming Chen 《advances in applied mathematics and mechanics.》2011,3(6):663-688
In this paper, we develop a multi-symplectic wavelet collocation method for
three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation
of the equations, wavelet collocation method based on autocorrelation functions
is applied for spatial discretization and appropriate symplectic scheme is employed
for time integration. Theoretical analysis shows that the proposed method is
multi-symplectic, unconditionally stable and energy-preserving under periodic
boundary conditions. The numerical dispersion relation is investigated. Combined
with splitting scheme, an explicit splitting symplectic wavelet collocation method
is also constructed. Numerical experiments illustrate that the proposed methods are
efficient, have high spatial accuracy and can preserve energy conservation laws exactly. 相似文献
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14.
This paper deals with the solvability and the convergence of a class of
unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial
basis function (RBF) kernels generated trial spaces. Local weak-form
testings are done with step-functions. It is proved that
subject to sufficiently many appropriate testings, solvability of the
unsymmetric RBF-MLPG resultant systems can be guaranteed.
Moreover, an error analysis shows that this numerical approximation
converges at the same rate as found in RBF interpolation.
Numerical results (in double precision) give good agreement with
the provided theory. 相似文献
15.
Tristan Rivière 《Letters in Mathematical Physics》1998,45(3):229-238
We introduce a formulation of the Skyrme problem using differential forms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S3
r R4, and S3
1 is the unique minimizer, modulo isometries, of the Skyrme energy in its homotopy class, for any R less than some critical value R0 (3/2, 2]. We then establish a stability result for this Skyrme-form problem from which we can recover the result of M. Loss and N. S. Manton which states that this homothetic map is stable only up to R = 2. 相似文献
16.
《Journal of Nonlinear Mathematical Physics》2013,20(4):517-519
It is shown that the deformed Nonlinear Schrödinger (NLS), Hirota and AKNS equations with (1 + 1) dimension admit infinitely many generalized (nonpoint) symmetries and polynomial conserved quantities, master symmetries and recursion operator ensuring their complete integrability. Also shown that each of them admits infinitely many nonlocal symmetries. The nature of the deformed equation whether bi-Hamiltonian or not is briefly analyzed. 相似文献
17.
Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method. 相似文献
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19.
《Journal of Nonlinear Mathematical Physics》2013,20(3):379-396
A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point of complete integrability, is presented. Following the procedure of Ablowitz, Kaup, Newell and Segur (AKNS) we find that the deformed version of Nonlinear Schrodinger equation, Hirota equation and AKNS equation admit Lax pairs. We report that each of the identified deformed equations possesses the Painlevé property for partial differential equations and admits trilinear representation obtained by truncating the associated Painlevé expansions. Hence the above mentioned deformed equations are completely integrable. 相似文献
20.
On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow 下载免费PDF全文
D. Lesnic 《advances in applied mathematics and mechanics.》2009,1(1):140-150
In this paper, the two-dimensional slowly rotating highly viscous
fluid flow in small cavities is modelled by the triharmonic equation
for the streamfunction. The Dirichlet problem for this triharmonic
equation is recast as a set of three boundary integral equations
which however, do not have a unique solution for three exceptional
geometries of the boundary curve surrounding the planar solution
domain. This defect can be removed either by using modified
fundamental solutions or by adding two supplementary boundary
integral conditions which the solution of the boundary integral
equations must satisfy. The analysis is further generalized to
polyharmonic equations. 相似文献