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1.
Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota. 相似文献
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In recent years there has emerged significant interest in low pressure radio frequency (rf) glow discharges which are used widely particulary in IC fabrication. Various parameters of the rf glow discharge have been found to be useful for its electrical characterization; however, there is no uniformity and agreement. Extensive experimental investigations on various discharge systems have shown, that the self-bias on the rf driven electrode, the complex conductivity and the breakdown characteristic are preferable parameters of rf discharges. Advantageously the self-bias and the complex conductivity should be presented in dependence on the pressure and the applied rf voltage. The discharge current cannot be measured quite accurately due to currents via leaky capacitors and the deviations from a sinusoidal form of the current due to nonlinearities. 相似文献
5.
Let X be a locally self-similar stochastic process of index 0<H<1 whose sample paths are a.s. CH?ε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2?H. To cite this article: A. Benassi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
6.
This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum
fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose
within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of
the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic
black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods
of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption
of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in
earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests
the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize
the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting
physically meaningful information.
Dedicated to Rafael Sorkin on the occasion of his 60th birthday. 相似文献
7.
Nanocrystalline FeS2 cathode material of lithium cell was synthesized from cheap materials of FeSO4, Na2S2O3, and sulfur by a hydrothermal process. The scanning electron microscopy analysis showed the obtained material was nano-sized,
about 500 nm. The X-ray powder diffraction analysis showed that the synthetic FeS2 material had two phases of the crystalline structure, pyrite and marcasite. The phase of marcasite seems to have no negative
effect on the electrochemical performance of the material. The synthetic FeS2 showed a significant improvement of electrochemical performance for Li/FeS2 cells. 相似文献
8.
Sonya V. Roberson Albert J. Fahey Amit Sehgal Alamgir Karim 《Applied Surface Science》2002,200(1-4):150-164
We present a simple method for chemical modification of chlorosilane self-assembled monolayers (SAMs) on Si surfaces by exposure to a gradient of UV-ozone radiation to create stable substrates with a range of contact angles (θH2O≈5–95°) and surface energies on a single substrate. These gradient energy substrates are developed to potentially generate libraries for combinatorial studies of thin film phenomenology, where a systematic variation of interfacial surface energy represents one of the significant parameters along one axis. The graded oxidation process presents a systematic variation of surface chemical composition. We have utilized contact angle measurements and time-of-flight secondary ion mass spectrometry (ToF-SIMS) to investigate this variation for a series of ions, among which are SiCH3+, SiOH+ and COOH−. We show that the macroscopic measurements of surface free energy/contact angle correlate with the detailed analysis of surface chemistry (as assessed by ToF-SIMS) on these test substrates. 相似文献
9.
M. Le Vassor D’yerville D. Monge D. Cassagne J. P. Albert 《Optical and Quantum Electronics》2002,34(5-6):445-454
We present here a tight-binding-like modelling of two-dimensional (2D) photonic crystals (PCs). Adopted from solid-state physics,
the concept of generalized Wannier functions is used to construct a localized state basis that allows a parameter-free ab
initio study of defects in PCs. We demonstrate here for a 2D triangular lattice of dielectric rods in air, the existence of
this localized basis and the possibility to study large scale complex dielectric structures deviating from periodicity. Specific
numerical simulations on a split waveguide embedded in this triangular lattice are performed, and they demonstrate the superiority
of this method over plane wave based techniques. 相似文献
10.
Albert Cohen Sidi Mahmoud Kaber Siegfried Mü ller Marie Postel. 《Mathematics of Computation》2003,72(241):183-225
The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.