Moving boundary value problems for the wave equation

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.

Boundary value problems for the N-wave interaction equations

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.

Wave functions for the methane molecule

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

Wave-driven wind jets in the marine atmospheric boundary layer

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.

A Nyström method for a boundary value problem arising in unsteady water wave problems

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.

Proposed design for an ultrasonic optical force-feedback microphone

We discuss a novel approach that would lead to the development of an ultrasonic optical force-feedback measurement microphone.

Follicle-stimulating hormone isoforms and plasma concentrations of estradiol and inhibin A in dairy cows with ovulatory and non-ovulatory follicles during the first postpartum follicle wave

Following parturition, all cows display a wave of ovarian follicular growth, but a large proportion fail to generate a preovulatory rise in estradiol, and hence fail to ovulate. Follicle-stimulating hormone (FSH) exists as multiple isoforms in the circulation depending on the type and extent of glycosylation, and this has pronounced effects on its biological properties. This study examined differences in plasma FSH, estradiol, and inhibin A concentrations, and the distribution of FSH isoforms in cows with ovulatory or atretic dominant follicles during the first postpartum follicle wave. Plasma FSH isoform distribution was examined in both groups during the period of final development of the dominant follicle by liquid phase isoelectric focusing. Cows with an ovulatory follicle had higher circulating estradiol and inhibin A concentrations, and lower plasma FSH concentrations. The distribution of FSH isoforms displayed a marked shift toward the less acidic isoforms in cows with ovulatory follicles. A higher proportion of the FSH isoforms had a pl>5.0 in cows with ovulatory follicles compared to those with atretic follicles. In addition, cows with ovulatory follicles had greater dry matter intake, superior energy balance, elevated circulating concentrations of insulin and insulin-like growth factor-I, and lower plasma nonesterified fatty acids. The shift in FSH isoforms toward a greater abundance of the less acidic isoforms appears to be a key component in determining the capability for producing a preovulatory rise in estradiol, and this shift in FSH isoforms was associated with more favorable bioenergetic and metabolic status. (C) 2008 Elsevier Inc. All rights reserved.

Ultrasonic chemical oxidative degradations of 1,3-dialkylimidazolium ionic liquids and their mechanistic elucidations

A highly efficient process for oxidative degradation of 1,3-dialkylimidazolium ionic liquids in hydrogen peroxide/acetic acid aqueous medium assisted by ultrasonic chemical irradiation is, for the first time, described. It is shown that more than 93% of the 1,3-dialkylimidazolium cation with the corresponding Cl-, Br-, BF4- and PF6- counter-anions at a concentration of 2.5 mM can be degraded at 50 degrees C within 12 h while at 72 h the conversions approach 99%. A tentative mechanism for the degradation of these ILs is for the first time proposed through a detailed kinetic analysis of several characteristic transients and/or immediate products, which are identified during the ILs degradation using GC-MS. The results clearly indicate that three hydrogen atoms in the imidazolium ring are the first sites preferably oxidized, followed by cleavage of the alkyl groups attached to the N atoms from the ring. The nature of the alkyl chain length on the imidazolium ring and the type of counter anion do not seem to affect the degradation process. Further, selective fragmentations of C-N bonds of the imidazolium or derived ring lead to ring opening, forming degraded intermediates. It is also shown that acetoxyacetic acid and biurea are the final kinetically stable degraded products from the ILs under the degradation conditions.