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1.
Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels 下载免费PDF全文
A spectral Jacobi-collocation approximation is proposed for Volterra delay
integro-differential equations with weakly singular kernels. In this paper, we consider
the special case that the underlying solutions of equations are sufficiently smooth. We
provide a rigorous error analysis for the proposed method, which shows that both
the errors of approximate solutions and the errors of approximate derivatives decay
exponentially in $L^∞$ norm and weighted $L^2$ norm. Finally, two numerical examples are
presented to demonstrate our error analysis. 相似文献
2.
Five different structures of the 1150.48°
{131} grain boundary in the bcc lattice, obtained by computer simulation, are analysed on the basis of their symmetry. It is demonstrated that the singular character of a grain boundary is not determined by the macroscopic geometrical degrees of freedom, but is associated with a particular grain boundary structure. This may have important consequences for the grain boundary properties. Implications for the transformations between different metastable boundary structures are discussed using a new concept of Displacement Position Map. 相似文献
3.
Yuichi Itto 《Entropy (Basel, Switzerland)》2021,23(3)
A formal analogy of fluctuating diffusivity to thermodynamics is discussed for messenger RNA molecules fluorescently fused to a protein in living cells. Regarding the average value of the fluctuating diffusivity of such RNA-protein particles as the analog of the internal energy, the analogs of the quantity of heat and work are identified. The Clausius-like inequality is shown to hold for the entropy associated with diffusivity fluctuations, which plays a role analogous to the thermodynamic entropy, and the analog of the quantity of heat. The change of the statistical fluctuation distribution is also examined from a geometric perspective. The present discussions may contribute to a deeper understanding of the fluctuating diffusivity in view of the laws of thermodynamics. 相似文献
4.
A simple algorithm to construct the generator of gauge transformation for a constrained canonical system with a singular higher-order Lagrangian in field theories is developed. Based on phase-space generating functional of Green function for such a system, the generalized canonical Ward identities under the non-local transformation have been deduced. For the gauge-invariant system, based on configuration-space generating functional, the generalized Ward identities under the non-local transformation have been also derived.The conservation laws are deduced at the quantum level. The applications of the above results to the gauge invariance massive vector field and non-Abelian Chern–Simons(CS) theories with higher-order derivatives are given, a new form of gauge-ghost proper vertices, and Ward–Takahashi identity under BRS transformation and BRS charge at the quantum level are obtained. In the canonical formulation one does not need to carry out the integration over canonical momenta in phase-space path integral as usually performed. 相似文献
5.
We consider a physical system which is coupled indirectly to a Markovian resevoir through an oscillator mode. This is the
case, for example, in the usual model of an atomic sample in a leaky optical cavity which is ubiquitous in quantum optics.
In the strong coupling limit the oscillator can be eliminated entirely from the model, leaving an effective direct coupling
between the system an the resevoir. Here we provide a mathematically rigorous treatment of this limit as a weak limit of the
time evolution and observables on a suitably chosen exponential domain in Fock space. The resulting effective model may contain
emission and absorption as well as scattering interactions.
R.v.H. is supported by the Army Research Office under Grant W911NF-06-1-0378. 相似文献
6.
Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions 下载免费PDF全文
The theory of a class of spectral methods is extended to Volterra
integro-differential equations which contain a weakly singular
kernel $(t-s)^{-\mu}$ with $0<\mu<1$. In this work, we consider the
case when the underlying solutions of weakly singular Volterra
integro-differential equations are sufficiently smooth. We provide a
rigorous error analysis for the spectral methods, which shows that
both the errors of approximate solutions and the errors of
approximate derivatives of the solutions decay exponentially in
$L^\infty$-norm and weighted $L^2$-norm. The numerical examples are
given to illustrate the theoretical results. 相似文献
7.
We apply the multiscale basis functions for the singularly perturbed
reaction-diffusion problem on adaptively graded meshes, which can provide a good
balance between the numerical accuracy and computational cost. The multiscale space
is built through standard finite element basis functions enriched with multiscale basis
functions. The multiscale basis functions have abilities to capture originally perturbed
information in the local problem, as a result, our method is capable of reducing the
boundary layer errors remarkably on graded meshes, where the layer-adapted meshes
are generated by a given parameter. Through numerical experiments we demonstrate
that the multiscale method can acquire second order convergence in the L2 norm and
first order convergence in the energy norm on graded meshes, which is independent
of ε. In contrast with the conventional methods, our method is much more accurate
and effective. 相似文献
8.
利用余项修正法建立奇异退化扩散反应方程非均匀网格上的高阶紧致差分式,其时间具有二阶精度,空间具有三阶至四阶精度. 利用等分布原理建立时间和空间的网格自适应方法.最后通过具有精确解的数值算例验证方法的可靠性和精确性,并研究一维爆破问题. 相似文献
9.
Singular value decomposition with normalized period for magnetocaridiography signal processing 下载免费PDF全文
In this paper, we have developed an algorithm based on singular value
decomposition (SVD) for matrix. And the novel SVD algorithm with normalized
period of cardiac cycles is presented. The results from real
magnetocardiography (MCG) data processing show that the new algorithm is
better than the standard one not only in suppressing noises, but also in
providing high-fidelity MCG signals. 相似文献
10.
References: 《理论物理通讯》2007,47(3):409-412
In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results. 相似文献
11.
Hryniv Rostyslav O. Mykytyuk Yaroslav V. 《Mathematical Physics, Analysis and Geometry》2004,7(2):119-149
We construct transformation operators for Sturm-Liouville operators with singular potentials from the space W
−1
2(0,1) and show that these transformation operators naturally appear during factorisation of Fredholm operators of a special
form. Some applications to the spectral analysis of Sturm-Liouville operators with singular potentials under consideration
are also given.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
This article addresses the resolution of the inverse problem for the parameter
identification in orthotropic materials with a number of measurements merely on
the boundaries. The inverse problem is formulated as an optimization problem of
a residual functional which evaluates the differences between the experimental and
predicted displacements. The singular boundary method, an integration-free, mathematically
simple and boundary-only meshless method, is employed to numerically
determine the predicted displacements. The residual functional is minimized by the
Levenberg-Marquardt method. Three numerical examples are carried out to illustrate
the robustness, efficiency, and accuracy of the proposed scheme. In addition, different
levels of noise are added into the boundary conditions to verify the stability of the
present methodology. 相似文献
13.
FAN Hong-Yi TANG Xu-Bing 《理论物理通讯》2007,47(5):865-868
We employ the invariant eigen-operator (lEO) method to find the invariant eigen-operators of N-body singular oscillators' Hamiltonians and then derive their energy gaps. The Hamiltonians of parametric amplifiers with singular potential are also discussed in this way. 相似文献
14.
In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution, which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance. 相似文献
15.
16.
Wetting of 975 grain boundaries (GB's) by liquid Cu in an iron-based alloy has been studied as a function of the five macroscopic degrees of freedom (DoF's) of grain boundary character. In addition, models of GB energy in terms of all five DoF's, and of anisotropic solid-liquid interfacial energy have been developed. The experimentally observed wetting behavior is interpreted in terms of the model, and it is shown that reasonable overall agreement is obtained between experimental results and model predictions. 相似文献
17.
ZHAO Shu-Hong LIANG Li-Fu QIAO Yong-Fen 《理论物理通讯》2007,48(5):791-794
We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result. 相似文献
18.
Microstructure evolution and grain growth in nanostructured aluminium films has been examined. The films were produced by vacuum evaporation on NaCl (100) substrate. Time dependences of mean grain area are presented. It has been revealed that the normal grain growth takes place in the films. The obtained data on the normal grain growth in 3-D films were compared with those for 2-D aluminium strips and foils. It was concluded that in the temperature range studied the grain growth kinetics is determined by triple junctions dragging force. 相似文献
19.
20.
A numerical study is given on the spectral methods and the high order
WENO finite difference scheme for the solution of linear and nonlinear hyperbolic
partial differential equations with stationary and non-stationary singular sources.
The singular source term is represented by the $δ$-function. For the approximation
of the $δ$-function, the direct projection method is used that was proposed in [6].
The $δ$-function is constructed in a consistent way to the derivative operator. Nonlinear
sine-Gordon equation with a stationary singular source was solved with the
Chebyshev collocation method. The $δ$-function with the spectral method is highly
oscillatory but yields good results with small number of collocation points. The
results are compared with those computed by the second order finite difference
method. In modeling general hyperbolic equations with a non-stationary singular
source, however, the solution of the linear scalar wave equation with the non-stationary
singular source using the direct projection method yields non-physical
oscillations for both the spectral method and the WENO scheme. The numerical
artifacts arising when the non-stationary singular source term is considered on the
discrete grids are explained. 相似文献