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111.
《Optimization》2012,61(1):161-174
This paper is concerned with a study of local controllability to discrete inclusions with delay. The sufficient conditions for relative and complete local controllability are obtained on the base of using Mordukhovich's nonsmooth constructions. 相似文献
112.
J. Cuevas Q.E. Hoq H. Susanto P.G. Kevrekidis 《Physica D: Nonlinear Phenomena》2009,238(22):2216-2226
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites. 相似文献
113.
Mixed‐order interpolation for the Galerkin coarse‐grid approximations in algebraic multigrid solvers
R. Webster 《国际流体数值方法杂志》2011,67(2):175-188
An empirical investigation is made of AMG solver performance for the fully coupled set of Navier–Stokes equations. The investigation focuses on two different FV discretizations for the standard driven cavity test problem. One is a collocated vertex‐based discretization; the other is a cell‐centred staggered‐grid discretization. Both employ otherwise identical orthogonal Cartesian meshes. It is found that if mixed‐order interpolation is used in the construction of the Galerkin coarse‐grid approximation (CGA), a close‐to‐optimum mesh‐independent scaling of the AMG convergence is observed with similar convergence rates for both discretizations. If, on the other hand, an equal‐order interpolation is used, convergence rates are mesh‐dependent but the scaling differs in each case. For the collocated‐grid case, it depends both on the mesh size, h (or bandwidth Q~h?1) and on the total number of grids, G, whereas for the staggered‐grid case it depends only on Q. Comparing the two characteristics reveals that the Q‐dependent parts are very similar; it is only in the G‐dependent convergence for the collocated‐grid case that they differ. This takes the form of stepped reductions in the AMG convergence rate (implying step reductions in the quality of the Galerkin CGA that correlate exactly with step increases in G). These findings reinforce previous evidence that, for optimum mesh‐independent performance, mixed‐order interpolations should be used in forming Galerkin CGAs for coupled Navier–Stokes problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
114.
任颜波 《数学年刊A辑(中文版)》2015,36(2):119-128
对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理. 相似文献
115.
We investigate the stability and phase transition of localized modes in Bose–Einstein Condensates (BECs) in an optical lattice with the discrete nonlinear Schrödinger model by considering both two- and three-body interactions. We find that there are three types of localized modes, bright discrete breather (DB), discrete kink (DK), and multi-breather (MUB). Moreover, both two- and three-body on-site repulsive interactions can stabilize DB, while on-site attractive three-body interactions destabilize it. There is a critical value for the three-body interaction with which both DK and MUB become the most stable ones. We give analytically the energy thresholds for the destabilization of localized states and find that they are unstable (stable) when the total energy of the system is higher (lower) than the thresholds. The stability and dynamics characters of DB and MUB are general for extended lattice systems. Our result is useful for the blocking, filtering, and transfer of the norm in nonlinear lattices for BECs with both two- and three-body interactions. 相似文献
116.
Khawla Qamhieh Mirfit Amleh Mai Khaleel 《Journal of Dispersion Science and Technology》2013,34(11):1517-1525
The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ?0 and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ?0 and ξ potentials are increased. 相似文献
117.
We consider an algebraic method for reconstruction of a function satisfying the Poisson equation with a polynomial right-hand side in the unit disk. The given data, besides the right-hand side, is assumed to be in the form of a finite number of values of Radon projections of the unknown function. We first homogenize the problem by finding a polynomial which satisfies the given Poisson equation. This leads to an interpolation problem for a harmonic function, which we solve in the space of harmonic polynomials using a previously established method. For the special case where the Radon projections are taken along chords that form a regular convex polygon, we extend the error estimates from the harmonic case to this Poisson problem. Finally we give some numerical examples. 相似文献
118.
The mixed moments for the Askey–Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey–Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied. 相似文献
119.
Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics. 相似文献
120.
Matti Schneider 《Mathematical Methods in the Applied Sciences》2015,38(13):2761-2778
The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because of its wide range of applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the homogenization method of Moulinec–Suquet, which can be interpreted as a spectral collocation method. Such methods are well‐known to converge for sufficiently smooth coefficients. We extend this result to rough coefficients. More precisely, we prove convergence of the fields involved for Riemann‐integrable coercive coefficients without the need for an a priori regularization. We show that our L2 estimates are optimal and extend to mildly nonlinear situations and Lp estimates for p in the vicinity of 2. The results carry over to the case of scalar elliptic and curl ? curl‐type equations, encountered, for instance, in stationary electromagnetism. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献