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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.
We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets. 相似文献
3.
B. Dubrulle F. Hersant 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(3):379-386
We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy
in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds
numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν2
L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η3/2(1 - η)-7/4
R
3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no
exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50
. These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity
fluctuations are also provided.
Received 7 June 2001 and Received in final form 7 December 2001 相似文献
4.
本文应用上、下解方法和 Leray-Schauder不动点定理 ,证明了一类拟线性椭圆方程边值问题弱解的存在性 ,并且给出了一个应用实例 相似文献
5.
Dalila B. M. M. Fontes Eleni Hadjiconstantinou Nicos Christofides 《Journal of Global Optimization》2006,34(1):97-125
In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations
of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on
the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving
transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation
of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial
solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as
a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively
improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications.
Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to
improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can
be obtained for concave cost network flow problems, particularly for fixed-charge problems. 相似文献
6.
7.
A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland. 相似文献
8.
本文考察了包括平面上的各种广义 Cantor集 ,Sierpinski集和包括某些连续不可微曲线在内的广义 Sierpinski集 .由相似变换 ,导出了它们的级数表达式 ,并利用它和字符串空间的对应关系 ,计算出它们的Hausdorff维数 相似文献
9.
10.
In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献