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.

Convergent evolution: floral guides, stingless bee nest entrances, and insectivorous pitchers

Several recent hypotheses, including sensory drive and sensory exploitation, suggest that receiver biases may drive selection of biological signals in the context of sexual selection. Here we suggest that a similar mechanism may have led to convergence of patterns in flowers, stingless bee nest entrances, and pitchers of insectivorous plants. A survey of these non-related visual stimuli shows that they share features such as stripes, dark centre, and peripheral dots. Next, we experimentally show that in stingless bees the close-up approach to a flower is guided by dark centre preference. Moreover, in the approach towards their nest entrance, they have a spontaneous preference for entrance patterns containing a dark centre and disrupted ornamentation. Together with existing empirical evidence on the honeybee's and other insects' orientation to flowers, this suggests that the signal receivers of the natural patterns we examined, mainly Hymenoptera, have spontaneous preferences for radiating stripes, dark centres, and peripheral dots. These receiver biases may have evolved in other behavioural contexts in the ancestors of Hymenoptera, but our findings suggest that they have triggered the convergent evolution of visual stimuli in floral guides, stingless bee nest entrances, and insectivorous pitchers.

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.

Colloidal stable silica encapsulated nano-magnetic composite as a novel bio-catalyst carrier

A colloidal stable silica-encapsulated magnetic nano-composite of a controlled dimension is, for the first time, employed to carry beta-lactamase via chemical linkage on the silica overlayer: activity study reflects that this new type of immobilisation allows site (enzyme) isolation, accessibility as good as free enzyme and recovery & reusability upon application of magnetic separation.

Thermoselective phase property of silica tethered with fluorinated chains for controlled 'release' and 'capture' of catalytic fluorous tin species

The temperature dependent mixing of organic and fluorous phases is one of the key principals of fluorous biphasic systems (FBS). Given the high cost of the perfluorous solvents and their impacts to the environment, it is apparent that elimination of these solvents in bulk quantity in the FBS is advantageous. We report for the first time, the surface coverage of silica with a fluorous solvent like material that traps (at ambient temperatures) and releases (at elevated temperatures) a fluorous tin bromide in organic solvent. Here, we demonstrate the catalytic utilisation of this species for the hydrocyclisation of 6-bromo-1-hexene with NaBH4. (C) 2002 Elsevier Science B.V. All rights reserved.

Silica coated noble metal nanoparticle hydrosols as supported catalyst precursors

Synthesis of well-defined nanoparticles has been intensively pursued not only for their fundamental scientific interest, but also for many technological applications. One important development of the nanomaterial is in the area of chemical catalysis. We have now developed a new aqueous-based method for the synthesis of silica encapsulated noble metal nanoparticles in controlled dimensions. Thus, colloid stable silica encapsulated similar to 5 nm platinum nanoparticle is synthesized by a multi-step method. The thickness of the silica coating could be controlled using a different amount of silica precursor. These particles supported on a high surface area alumina are also demonstrated to display a superior hydrogenation activity and stability against metal sintering after thermal activation.