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961.
A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes
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We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
962.
963.
964.
Paolo Amore 《Annals of Physics》2010,325(12):2679-427
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very accurate approximations which are compared both with the results of WKB method and with the numerical results obtained with a collocation approach. Finally, we show that the asymptotic behaviour of the energies of the string obtained with perturbation theory, worked to second order in the inhomogeneities, agrees with that obtained with the WKB method and implies a different functional dependence on the density that in two and higher dimensions. 相似文献
965.
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
966.
Antonio M. Scarfone Hiroki Suyari Tatsuaki Wada 《Central European Journal of Physics》2009,7(3):414-420
We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product
arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product
and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an
asymptotic power-law behavior.
相似文献
967.
In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P10 breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer coefficients times trivial exponential factor. This formula drastically simplifies for the “initial values” namely for t=0 or x=0. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x=0,t=0), the PN breather is distinguished by the fact that PN(0,0)=2N+1 and, in the aforementioned class of quasi-rational solutions, it is an absolute maximum. At the end we also make a few remarks concerning the rational deformations of P10 breather involving 2N−2 free real parameters chosen in a way that PN breather itself corresponds to the zero values of these parameters although we have no intention to discuss the properties of these deformations here. 相似文献
968.
969.
We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D. 相似文献
970.
The Allen-Cahn equation ? Δu = u ? u 3 in ?2 has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u 3. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?3. 相似文献