906 resultados para Wave Diffraction


Relevância:

20.00% 20.00%

Publicador:

Resumo:

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

We consider boundary value problems for the N-wave interaction equations in one and two space dimensions, posed for x [greater-or-equal, slanted] 0 and x,y [greater-or-equal, slanted] 0, respectively. Following the recent work of Fokas, we develop an inverse scattering formalism to solve these problems by considering the simultaneous spectral analysis of the two ordinary differential equations in the associated Lax pair. The solution of the boundary value problems is obtained through the solution of a local Riemann–Hilbert problem in the one-dimensional case, and a nonlocal Riemann–Hilbert problem in the two-dimensional case.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Gallaborane (GaBH6, 1), synthesized by the metathesis of LiBH4 with [H2GaCl]n at ca. 250 K, has been characterized by chemical analysis and by its IR and 1H and 11B NMR spectra. The IR spectrum of the vapor at low pressure implies the presence of only one species, viz. H2Ga(μ-H)2BH2, with a diborane-like structure conforming to C2v symmetry. The structure of this molecule has been determined by gas-phase electron diffraction (GED) measurements afforced by the results of ab initio molecular orbital calculations. Hence the principal distances (rα in Å) and angles ( α in deg) are as follows: r(Ga•••B), 2.197(3); r(Ga−Ht), 1.555(6); r(Ga−Hb), 1.800(6); r(B−Ht), 1.189(7); r(B−Hb), 1.286(7); Hb−Ga−Hb, 71.6(4); and Hb−B−Hb, 110.0(5) (t = terminal, b = bridging). Aggregation of the molecules occurs in the condensed phases. X-ray crystallographic studies of a single crystal at 110 K reveal a polymeric network with helical chains made up of alternating pseudotetrahedral GaH4 and BH4 units linked through single hydrogen bridges; the average Ga•••B distance is now 2.473(7) Å. The compound decomposes in the condensed phases at temperatures exceeding ca. 240 K with the formation of elemental Ga and H2 and B2H6. The reactions with NH3, Me3N, and Me3P are also described.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The interaction between ocean surface waves and the overlying wind leads to a transfer of momentum across the air–sea interface. Atmospheric and oceanic models typically allow for momentum transfer to be directed only downward, from the atmosphere to the ocean. Recent observations have suggested that momentum can also be transferred upward when long wavelength waves, characteristic of remotely generated swell, propagate faster than the wind speed. The effect of upward momentum transfer on the marine atmospheric boundary layer is investigated here using idealized models that solve the momentum budget above the ocean surface. A variant of the classical Ekman model that accounts for the wave-induced stress demonstrates that, although the momentum flux due to the waves penetrates only a small fraction of the depth of the boundary layer, the wind profile is profoundly changed through its whole depth. When the upward momentum transfer from surface waves sufficiently exceeds the downward turbulent momentum flux, then the near-surface wind accelerates, resulting in a low-level wave-driven wind jet. This increases the Coriolis force in the boundary layer, and so the wind turns in the opposite direction to the classical Ekman layer. Calculations of the wave-induced stress due to a wave spectrum representative of fast-moving swell demonstrate upward momentum transfer that is dominated by contributions from waves in the vicinity of the peak in the swell spectrum. This is in contrast to wind-driven waves whose wave-induced stress is dominated by very short wavelength waves. Hence the role of swell can be characterized by the inverse wave age based on the wave phase speed corresponding to the peak in the spectrum. For a spectrum of waves, the total momentum flux is found to reverse sign and become upward, from waves to wind, when the inverse wave age drops below the range 0.15–0.2, which agrees reasonably well with previously published oceanic observations.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.