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1.
In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself. 相似文献
2.
Volker Elling. 《Mathematics of Computation》2006,75(256):1721-1733
A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.
3.
利用分子动力学方法模拟计算了单晶铜中纳米孔洞在沿〈111〉晶向冲击加载下增长的早期过程.测量发现不同加载强度下等效孔洞半径随时间近似成线性变化.观测到单孔洞增长的两种位错生长机理:加载强度较低时,只在沿着冲击加载方向的孔洞顶点附近区域有位错的成核和运动;而随着加载强度超过一定阈值,在沿冲击加载和其垂直方向的孔洞顶点区域都观察到位错的成核和运动.在前一种机理作用下,孔洞只沿加载方向增长;在后一种机理作用下,孔洞同时沿加载和垂直于加载方向增长.分析孔洞表面原子的位移历史,发现沿加载及与其垂直方向的孔洞顶点沿径向的速度基本恒定,由此提出了一个孔洞生长模型,可以解释孔洞增长的线性生长规律.
关键词:
纳米孔洞
分子动力学
冲击加载
位错 相似文献
4.
Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means
of 1H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The
19F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the
information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by
means of correlation techniques without any preparation or marking of the pastes.
Received: 8 May 2000 Accepted: 1 May 2001 相似文献
5.
6.
R. S. Martynov Yu. M. Nechepurenko 《Computational Mathematics and Mathematical Physics》2006,46(7):1155-1167
For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented. 相似文献
7.
The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.This paper is dedicated to J. K. Percus in honor of his 65th birthday. 相似文献
8.
Teresa Regińska 《BIT Numerical Mathematics》2004,44(1):119-133
The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied
to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution
is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the
nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is
analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is
proved under the assumption of the suitable relation between the discretization level and the data error. As an example the
method of truncated singular value decomposition with regularization is considered.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Marko Nedeljkov 《Mathematical Methods in the Applied Sciences》2004,27(8):931-955
This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau‐type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd. 相似文献
10.
A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献